Scipedia: Documents published in 2020

Unstructured multigrid methods for elliptic problems

María Jesús Samper — Thu, 09 Jul 2020 16:12:42 +0200

A multigrid algorithm for implementation on unstructured meshes is proposed. The algorithm uses a sequence of unnested grids and requires the development of efficient inter-grid interpolation procedures. It is demonstrated how elliptic problems can be solved in this fashion by using Jacobi smoothers

An adaptive finite element scheme for transient problems in CFD

María Jesús Samper — Thu, 09 Jul 2020 16:05:29 +0200

An adaptive finite element scheme for transient problems is presented. The classic h-enrichment / coarsening is employed in conjunction with a triangular finite element discretization in two dimensions. A mesh change is performed every n timesteps, depending on the Courant number employed and the number of ‘protective layers’ added ahead of the refined region. In order to simplify the refinement/ coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved on the CRAY XMP 12 at NRL. Several examples involving shock-shock interactions and the impact of shocks on structures demonstrate the performance of the method, indicating that considerable savings in CPU time and storage can be realized even for strongly unsteady flows.

Finite elements in CFD: What lies ahead

María Jesús Samper — Thu, 09 Jul 2020 16:00:40 +0200

The current state of the art of Finite Element Methods in Computational Fluid Dynamics is reviewed. The aim of this review is to point out what appear currently as the main shortcomings of Finite Element Methods, so as to concentrate the efforts to remove them. The analysis of flows using Finite Elements will only be successful if all steps involved in it are optimized. Therefore, I deem it necessary to describe explicit and implicit flow solvers, unstructured multigrid methods, adaptive refinement schemes, grid generation and graphics in 3‐D, the effective use of supercomputer hardware and memory, as well as the combination of structured and unstructured grids.

Finite Element Flux-Corrected Transport (FEM-FCT) for the Euler and Navier-Stokes equations

María Jesús Samper — Thu, 09 Jul 2020 15:52:20 +0200

A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux-corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady state examples are solved to illustrate the performance of the algorithm.

Some useful data structure for generation of unstructured grid

María Jesús Samper — Thu, 09 Jul 2020 15:44:37 +0200

Several data structures for the generation of unstructured grids are described. Their usefulness stems from the fact that they enable the necessary search operations to be performed in an optimal way. In particular, we describe heap lists, quad- and octrees, and linked lists. Combining these data structures, the important problem of interpolating information between unstructured grids is also solved.

Numerical simulation of shock-box interaction using an adaptive shock capturing scheme

María Jesús Samper — Thu, 09 Jul 2020 15:40:55 +0200

A recently developed transient, two-dimensional, finite-element shock capturing scheme is applied to the study of shock interaction with a box suspended above a rigid surface. The results demonstrate the excellent resolution of the captured shocks and the application of a newly developed adaptive refinement/coarsening algorithm. In addition to interesting shock propagation and interaction processes, the results demonstrate the capability of the new code to capture, and define in great detail, vortices shed from the downstream corners of the box. The ability of the new scheme to model such fluid dynamic phenomena as shock-shock, shock-surface, and shock-vortex interactions, as well as vortex dynamics, are demonstrated.

Adaptive Finite Element Flux Corrected Transport Techniques for CFD

María Jesús Samper — Thu, 09 Jul 2020 15:35:42 +0200

In previous papers [1,2] we have described an explicit finite element solution procedure for the compressible Euler and Navier-Stokes equations. The approach was a finite element equivalent of a two-step Lax-Wendroff scheme and was implemented on unstructured triangular or tetrahedral grids. An important feature of the work was the use of adaptive mesh refinement methods for the solution of steady state problems in two dimensions, using error indicators based upon interpolation theory.

Generation of three-dimensional unstructured grids by the advancing-front method

María Jesús Samper — Thu, 09 Jul 2020 15:31:13 +0200

The generation of three-dimensional unstructured grids using the advancing-front technique is described. This technique has been shown to be effective for the generation of unstructured grids in two dimensions.1,2 However, its extension to three-dimensional regions required algorithms to define the surface and suitable data structures that avoid excessive CPU-time overheads for the search operations involved. After obtaining an initial triangulation of the surfaces, tetrahedra are generated by successively deleting faces from the generation front. Details of the grid generation algorithm are given, together with examples and timings.

An adaptive finite element solver for transient problems with moving bodies

María Jesús Samper — Thu, 09 Jul 2020 15:23:30 +0200

The combination of adaptive remeshing techniques, flow solvers for transient problems with moving grids, and integrators for rigid body motion is presented. The resulting scheme allows the economic simulation of fully coupled fluid-rigid body interaction problems of arbitrary geometric complexity. Several results are given to demonstrate the capabilities developed.

FEM-FCT - Combining unstructured grids with high resolution

María Jesús Samper — Thu, 09 Jul 2020 15:19:58 +0200

We present the extension of flux‐corrected transport (FCT) schemes to unstructured grids. The spatial discretization is performed via finite elements. In particular, we have chosen triangular elements in two dimensions. The limiting procedure is based on Zalesak's extension to more than one dimension of the FCT schemes developed by Boris and Book. The resulting scheme, FEM‐FCT, is capable of resolving moving and stationary shocks within two elements, and several examples are given that demonstrate the accuracy attainable, even for complicated geometries.

Adaptive remeshing for transient problems

María Jesús Samper — Thu, 09 Jul 2020 15:09:01 +0200

Adaptive remeshing schemes for transient problems are presented. The main advantage of these schemes is the ease in incorporating directional refinement and body motion in the context of adaptive refinement. Practical numerical examples for the Euler equations, run on the CRAY-XMP-24 at NRL, show that the adaptive remeshing scheme by itself cannot compete with ordinary h-refinement for strongly unsteady flows that require a grid change every 5–10 timesteps. Therefore, we study the combination of adaptive remeshing and h-refinement. After generating a coarser grid with stretched elements, the whole grid is h-refined at once. Even with one level of h-refinement, the combined scheme easily out-performs ordinary h-refinement, yielding a very effective adaptive refinement method for this class of problems.

A vectorized particle tracer for unstructured grids

María Jesús Samper — Thu, 09 Jul 2020 14:57:26 +0200

A vectorized particle tracer for unstructured grids is described. The basic approach is to use elementary properties of the linear basis functions to search for particles on the grid using the element last occupied as an initial guess. To permit vectorization, a simple binary sort of the particles is performed every timestep such that all particles that have as yet not found their host element remain at the top of the list. In this way, vector-loops can be easily formed. Timings taken from a numerical example indicate that speed-ups of the order of 1:14 can be obtained on vector-machines when using this algorithm.

Numerical simulation of shock interaction with complex geometry canisters

María Jesús Samper — Thu, 09 Jul 2020 14:52:51 +0200

The objective of this research is to investigate shock interaction with complex geometry canisters suspended above a rigid elevated surface. Several geometries were examined in an effort to reduce the loads on the canisters during the shock diffraction phase. A new transient, two‐dimensional, finite‐element shock capturing scheme was utilized. Excellent shock resolution was demonstrated, as well as the efficiency of the newly developed adaptive refinement/coarsening algorithm. In addition to interesting shock wave propagation and interaction processes, the results demonstrated the capability of the new code to capture, and define in great detail, vortices shed from the downstream side of the canister.

Three-dimensional fluid-structure interaction using a finite element solver and adaptive remeshing

María Jesús Samper — Thu, 09 Jul 2020 14:23:05 +0200

The combination of adaptive remeshing techniques, flow solvers for transient problems with moving grids, and consistent rigid body motion integrators in three dimensions is presented. The resulting scheme allows the economical simulation of fully coupled fluid-rigid body interaction problems of arbitrary geometric complexity. Several results, showing three-dimensional store separation, are given to demonstrate the capabilities developed.

Electromagnetic PIC simulations using finite elements on unstructured grids

María Jesús Samper — Thu, 09 Jul 2020 14:14:09 +0200

There is an increasing demand to use kinetic plasma simulations to model real plasma devices such as e-beam diodes, plasma torches, opening switches, and so on. With this demands comes the realization that standard simulation tools based on rectangular structured meshes are often too inflexible to accommodate real device geometries. To gain geometric flexibility, one typically must abandon structured rectangular meshes. Some have had considerable success by distorting the grid to conform to boundary-fitted curvilinear coordinates. This gives substantial flexibility while retaining a logically rectangular data structure. However, to achieve the greatest flexibility, an unstructured mesh is necessary. For the last several years, we have been engaged in designing electromagnetic particle-in-cell (PIC) simulations that can be performed on unstructured grids of triangles. We feel this is a powerful strategy for matching kinetic plasma simulations to real problem geometries. Unstructured meshes not only accommodate complicated boundary shapes with ease, but also allow extreme local refinement without affecting resolution elsewhere. The basic challenges to overcome in formulating EM-PIC on these new meshes are: (1) grid generation; (2) particle interpolation and tracking, and (3) field solution. In this paper we briefly describe our techniques and give a simple example.

Simple Elements and Linelets for Incompressible Flows

María Jesús Samper — Thu, 09 Jul 2020 14:10:29 +0200

The current trends for the simulation of large-scale incompressible flow fields using finite elements are discussed. The main items are: a) the use of simple elements through stabilization and analogy with LBB-satisfying elements, and b) the development of fast solvers for general grids.

Three-dimensional space-marching algorithm on unstructured grids

María Jesús Samper — Thu, 09 Jul 2020 14:04:20 +0200

A three-dimensional space-marching algorithm using an unstructured discretization is proposed. The method utilizes a two-dimensional unstructured grid generator to construct grids in a crossflow plane while maintaining structure in the marching direction. The spatial discretization is obtained by applying a characteristic-based, upwind, finite volume scheme for the solution of the Euler equations. Solutions are presented for several different geometries comparing the results with existing numerical techniques and experiment.

Formation of shocks within axisymmetric nozzles

María Jesús Samper — Thu, 09 Jul 2020 13:55:08 +0200

The formation of shocks within axisymmetric supersonic nozzles has received considerable attention in the past, both experimentally and computationally. The presence of undesirable oblique shocks can significantly alter the downstream flowfield, reduce the thrust efficiency, and affect both the external acoustic signature and base pressure. In this paper numerical simulations of axisymmetric supersonic nozzle flow have been accomplished using an axisymmetric version of the finite element method/flux corrected transport algorithm. The adaptive unstructured gridding and the conservative nonlinear FCT scheme predicted shock formation that agreed with experimental data.

Parallel unstructured grid generation

María Jesús Samper — Thu, 09 Jul 2020 13:39:02 +0200

A parallel unstructured grid generation algorithm is presented and implemented on the INTEL hypercube. Different processor hierarchies are discussed, and the appropriate hierarchies for mesh generation and mesh smoothing are selected. A domain-splitting algorithm for unstructured grids, which tries to minimize the surface-to-volume ratio of each subdomain, is described. This splitting algorithm is employed both for grid generation and grid smoothing. Results obtained on the INTEL hypercube demonstrate the effectiveness of the algorithms developed.

Vorticity produced by shock wave diffraction

María Jesús Samper — Thu, 09 Jul 2020 13:34:15 +0200

Numerical simulations with a monotonicity preserving flow solver have been performed to study shock diffraction phenomena and shock wave generated vorticity. The computations were performed using the conservative Finite Element Method-Flux Corrected Transport (FEM-FCT) scheme, which has been shown to have an excellent predictive capability for various compressible flows with both strong and weak shocks. An adaptive unstructured methodology based on adapting to high density and entropy gradients was used in conjunction with a conservative shock-capturing scheme to adequately resolve strong and weak flowfield gradients. The chief interest was the formation of vorticity arising from shock wave propagation over a sharp corner and the high accuracy and resolution of the interacting compressible wave features. Numerical simulations were compared with previous experimental results and exhibited remarkably good agreement in terms of compressible wave propagation, as well as vorticity development and transport. The computations also allowed insight into the fundamental fluid dynamics, specifically shock diffraction, vortex convection and shock-vortex interactions.

Finite element methods in CFD: Grid generation, adaptivity, and parallelization

María Jesús Samper — Thu, 09 Jul 2020 13:24:42 +0200

Numerical methods for the solution of field problems using unstructured grids have reached a high degree of maturity. Although computational fluid dynamics (CFD) have been dominated by structured grids, with the increase in computational ability, unstructured grids have started to have an impact on complex geometrical problems in CFD. The following paper describes grid generation, adaptive refinement schemes, visualization and parallelization issues. It also includes a short chapter on CFD among related disciplines that will help the newcomer with flow simulation codes

Supersonic Flow over an Axisymmetric Backward-Facing Step

María Jesús Samper — Thu, 09 Jul 2020 13:07:38 +0200

Large eddy numerical simulations of supersonic flows over an axisymmetric backward-facing step have been completed using a recently developed axisymmetric version of the finite element method-flux corrected transport algorithm, FEM-FCT. The code is based on the mixing layer and recompression premises of the Chapman-Korst model. It solves the time-accurate Euler equations utilizing 1) adaptive unstructured gridding to resolve flow feature details and 2) a conservative nonlinear scheme to capture features in the compressible flowfield. This approach may be employed since the location of the separation point is fixed at the sharp corner. The simulation allows the large-scale structures present in the mixing layer to interact dynamically with the recompression region. Comparisons have been made with available experimental data for a range of Mach numbers and step height to step radius ratios for which boundary-layer effects are not pronounced. In general, good agreement between predictions and measurements was found for 1) the time-averaged surface pressure distributions along the backstep and the reattachment wall, 2) the flowfield structure in general, and 3) the downstream reattachment lengths. Effects of axisymmetry were noted in flowfield characteristics such as increased base pressure, curvature of expansion fans, stronger recompression shocks, and higher Mach number levels in the subsonic recirculating region.

Adaptive h‐refinement on 3D unstructured grids for transient problems

María Jesús Samper — Thu, 09 Jul 2020 13:02:07 +0200

An adaptive finite element scheme for transient problems is presented. The classic h‐enrichment/coarsening is employed in conjunction with a tetrahedral finite element discretization in three dimensions. A mesh change is performed every n time steps, depending on the Courant number employed and the number of ‘protective layers’ added ahead of the refined region. In order to simplify the refinement/coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved by pre‐sorting the elements and then performing the refinement/coarsening groupwise according to the case at hand. Further reductions in CPU requirements arc realized by optimizing the identification and sorting of elements for refinement and deletion. The developed technology has been used extensively for shock‐shock and shock‐object interaction runs in a production mode. A typical example of this class of problems is given.

Eulerian-Eulerian and Eulerian-Lagrangian methods in two phase flow

María Jesús Samper — Thu, 09 Jul 2020 12:52:28 +0200

This paper describes a Finite Element Method - Flux Corrected Transport (FEM-FCT) approach with an unstructured adaptive grid scheme to the simulation of two-phase flow. The gas equations are computed using an Eulerian frame of reference, while the particle transport is computed using both Eulerian and Lagrangian frames of reference. One dimensional shock wave attenuation was investigated to evaluate the performance of these methodologies and the gas-solid interphase transport models

An implicit three-dimensional finite element solver for unstructured meshes

María Jesús Samper — Thu, 09 Jul 2020 12:49:11 +0200

The development of an implicit 3D finite element algorithm for the solution of the compressible Euler and Navier-Stokes equations on unstructured meshes is reported. Numerical results for both inviscid and viscous flows are presented to demonstrate the proposed scheme's performance. The treatment of boundary conditions is found to be vital to the success of an implicit scheme

Some useful renumbering strategies for unstructured grids

María Jesús Samper — Thu, 09 Jul 2020 11:54:19 +0200

Several renumbering strategies for unstructured grids are discussed. They lead to a minimization of eache-misses and an optimal grouping of elements for different computer platforms, from superscalar workstations to multiprocessor register-to-register vector machines. Timings for a typical computational fluid dynamics (CFD) code that employs these renumbering strategies indicate that CPU requirements may be halved by applying them. The renumbering strategies discussed are all of linear time complexity, making them ideally suited for applications requiring frequent mesh changes. Furthermore, these renumbering strategies are not only valid for element-based codes but carry over to edge-based or face-based field solvers

Three‐dimensional parallel unstructured grid generation

María Jesús Samper — Thu, 09 Jul 2020 11:50:18 +0200

An algorithm for the parallel generation of 3-D unstructured grids is presented. The technique is an extension of the algorithm presented in Reference 21 for the 2-D case. The method uses a background grid as the means to separate spatially different regions, enabling the concurrent, parallel generation of elements in different domains and interdomain regions. The parallel 3-D grid generator was implemented and tested on the INTEL hypercube and Touchstone Delta parallel computers. The results obtained demonstrate the effectiveness of the algorithm developed. The methodology is applicable to the parallel implementation of a wide range of problems that are, in principle, scalar by nature, and do not lend themselves to SIMD parallelization.

Electromagnetics via the Taylor-Galerkin Finite Element Method on Unstructured Grids

María Jesús Samper — Thu, 09 Jul 2020 11:40:00 +0200

Traditional techniques for computing electromagnetic solutions in the time domain rely on finite differences. These so-called finite-difference time-domain (FDTD) methods are usually defined only on regular lattices of points and can be too restrictive for geometrically demanding problems. Great geometric flexibility can be achieved by abandoning the regular latticework of sample points and adopting an unstructured grid. An unstructured grid allows one to place the grid points anywhere one chooses, so that curved boundaries can be fit with ease and local regions in which the field gradients are steep can be selectively resolved with a fine mesh. In this paper we present a technique for solving Maxwell's equations on an unstructured grid based on the Taylor-Galerkin finite-element method. We present several numerical examples which reveal the fundamental accuracy and adaptability of the method. Although our examples are in two dimensions, the techniques and results generalize readily to 3D.

Numerical simulation of shock-box interaction using an adaptive finite element scheme

María Jesús Samper — Thu, 09 Jul 2020 11:35:19 +0200

A transient two-dimensional, finite elemnt shock capturing scheme on unstructured grids was applied to the study of a shock interacting with a box suspended above a rigid elevated surface. The area between the box and the surface was partially blocked by the box support beams, resulting in complex shock diffraction processes. The results demonstrate the capability of the developed adaptive refinement/corsening algorithm to properly adapt to weak shocks, expansions, and contact discontinuities, and highlight the resulting excellent resolution of the captured flow features. In addition to interesting shock diffraction and propagation phenomena, the results demonstrate the capability of the new code to capture, and define in great detail, vortex sheets shed from sharp corners. We show that the baroclinic effect, an inviscid process, controls the shedding phenomenon during the diffraction phase. Hence, the Eulerian model is able to correctly predict the process.

Edge-based element scheme for the Euler equations

María Jesús Samper — Thu, 09 Jul 2020 11:15:03 +0200

This paper describes the development, validation, and application of a new finite element scheme for the solution of the compressible Euler equations on unstructured grids. The implementation of the numerical scheme is based on an edge-based data structure, as opposed to a more element-based data structure. The use of this edge-based data structure not only improves the efficiency of the algorithm but also enables a straightforward implementation of the upwind schemes in the context of finite element methods. The algorithm has been tested and validated on some well documented configurations. A flow solution about a complete F-18 fighter is shown to demonstrate the accuracy and robustness of the proposed algorithm.

Unstructured Adaptive Remeshing Finite Element Method for Dusty Shock Flows

María Jesús Samper — Thu, 09 Jul 2020 11:06:07 +0200

The passage of planar shocks in a dusty gas was investigated to note effects due to particle loading and initial shock Mach number. Two-phase flow equations have been added to a conservative, monotonic flow solver to allow study of compressible particle and droplet flows, which are of importance for shock propagation in two-phase flows and spray propulsion systems. The formulation developed herein employed a conservative Eulerian treatment for the gas and particle phases. The computations were performed using the finite element method-flux corrected transport (FEM-FCT) scheme, which has shown excellent predictive capability of various compressible flows which include both strong and weak shocks. The flux limiting technique was modified to provide monotonic particle velocity fields to increase the scheme's computational stability. Adaptive unstructured methodology based on adapting to high gradients of both the fluid and particle densities was used in conjunction with the conservative shock-capturing scheme to adequately resolve strong flowfield gradients. The shock attenuation of this scheme was then compared with previous experimental and numerical results and was found to yield robust predictions. Various interphase coupling terms were also considered to note their effect on the shock attenuation.

Ray tracing with a space‐filling finite element mesh

María Jesús Samper — Thu, 09 Jul 2020 10:50:10 +0200

A new ray‐tracing technique is presented which does not work with ray–object intersections per se , but is based on the traversal of an unstructured tetrahedral mesh providing a convex enclosure of a scene of polyhedral objects. The tetrahedral mesh provides tight bounding and an adaptive subdivision of space. This non‐hierarchical data structure is traversed adaptively until one is led directly and unconditionally to the first object intersected. Rendering times are directly related to the average thickness of the enclosing mesh since all tetrahedra are traversed in constant time.

Since the proposed algorithm operates directly with volume elements, it allows for volumetric rendering effects. Volume rendering or anisotropic media can be implemented without any further effort. This is an important advantage as compared to usual techniques, which only operate on surface data.

Timings for several examples show that the use of this type of ray‐tracing technique, which is more suitable for general purpose visualization codes than traditional techniques, results in CPU times that are comparable with the best ray‐tracing techniques presently used. This is an unexpected and important result, as the vectorization and parallclization of the proposed technique are straightforward, in contrast with traditional ray‐tracing techniques

Edges, stars, superedges and chains

María Jesús Samper — Thu, 09 Jul 2020 10:32:31 +0200

Several possibilities for the reduction of indirect addressing operations within edge-based solvers are discussed. It is shown that indirect addressing operations may be reduced by a factor in excess of 1 : 4 if edges are grouped and linked together. Tests of benchmark loops on two common engineering computer platforms reveal that CPU saving factors ranging from 1.3 to 3.5 may be realized when switching from edge-based to superedge or chain-based loops.

Transient and steady heat conduction using an adaptive finite element cad-based approach

María Jesús Samper — Thu, 09 Jul 2020 10:20:02 +0200

A new heat transfer simulation capability is described. Non-traditional features of this capability include: a seamless link to CAD-CAM for rapid problem specification/description, integrated automatic grid generator tools for rapid mesh generation, nonlinear and/or varying material properties, source-terms and boundary conditions, a one-element type approach for simplicity and efficiency, automatic self-adaptive mesh refinement and coarsening with accurate error estimation, heavy reliance on iterative solvers, and on-line display on workstations for immediate visualization and user feedback. These innovations are documented on several examples that demonstrate the usefulness of the developed capability.

A Comparison Study of Two Finite-Element Schemes for Computation of Shock Waves

María Jesús Samper — Thu, 09 Jul 2020 10:07:59 +0200

This paper describes an extensive comparison study of two high-order-accuracy finite-element schemes: one of upwind type, the other of flux-corrected transport type, for the simulation of shock wave propagation on unstructured meshes. The performance of these two schemes for the solution of the Euler equations on unstructured meshes is compared on the basis of solution accuracy and computational efficiency for some well-known test cases. Advantages and disadvantages of the two schemes are discussed.

Mesh adaptation in fluid mechanics

María Jesús Samper — Thu, 09 Jul 2020 09:22:48 +0200

The development, application and impact of mesh adaptation procedures in the field of computational fluid mechanics (CFD) are reviewed. The discussion is restricted to unstructured (i.e. unordered) grids, such as those commonly encountered in finite element applications.

Finite element simulation of a turbulent MHD system: comparison to a pseudo-spectral simulation

María Jesús Samper — Wed, 08 Jul 2020 10:36:50 +0200

A finite element MHD algorithm is used to simulate a two-dimensional, viscous and resistive turbulent model, namely the Orszag-Tang vortex. The results are compared to a pseudo-spectral simulation of the same system reported by Dahlburg and Picone (Phys. Fluids B 1 (1989) 2153). The agreement of results from both methods supports the contention that the finite element method can appropriately simulate systems exhibiting turbulence, thus enabling the use of realistic geometries and boundary conditions, as well as adaptive refinement on simulations of turbulent systems. A short discussion on the behavior of ▿·B is presented. An inverse correlation between spatial resolution and the magnitude of ▿·B was found. The relevance of our findings to Adaptive Mesh Refinement is briefly discussed.

Robust, Vectorized Search Algorithms for Interpolation on Unstructured Grids

María Jesús Samper — Wed, 08 Jul 2020 10:28:47 +0200

Several search algorithms for the interpolation of data associated with unstructured grids are reviewed and compared. Particular emphasis is placed on the pitfalls these algorithms may experience for grids commonly encountered and on ways to improve their performance. It is shown how the most CPU-intensive portions of the search process may be vectorized. A technique for the proper interpolation of volumetric regions separated by thin surfaces is included. Timings for several problems show that speedups in excess of 1:5 can be obtained if due care is used when designing interpolation algorithms.

Simulation of complex incompressible flows using a finite element solver on MIMD machines

María Jesús Samper — Wed, 08 Jul 2020 10:24:38 +0200

An incompressible flow solver based on unstructured grids is implemented on parallel distributed-memory computer architecture. An important phase in the flow solver is the solution of the elliptic equations for the velocities and pressures. This elliptic solver is parallelized and incorporated into both the explicit and implicit versions of the incompressible flow solver. Performance and scalability studies are carried out on both Intel iPSC 860 and the Intel Delta prototype and show that the code is scalable. A parallelizable load balancing algorithm is developed to be used in conjunction with the incompressible flow solver. Steady and unsteady flows over a tri-element airfoil and NACA0012airfoil are computed using the parallel incompressible flow solver. The parallel flow solver is extended to 3D for simulation of flow past a fully appended submarine. The chapter concludes that the future developments will be focused on the incorporation of adaptive regridding in 2D and the parallel implementation of 3-D incompressible flow solver.

Computation of the unsteady flow past a tuna with caudal fin oscillation

María Jesús Samper — Wed, 08 Jul 2020 10:19:46 +0200

Only recently has a capability for computing three-dimensional, unsteady incompressible flow over a changing geometry become available. In that work, the flow field generated during a torpedo launch from a submarine was computed. This paper describes the extension of that work to carry out a direct computation, making no geometric simplifications, of the unsteady flow past a tuna, including the oscillatory caudal fin motion. In particular, described is the computation of the time variation of the pressure distribution over the entire body and the integration over all surfaces to obtain the unsteady thrust.

Large-Scale Blast Simulations

María Jesús Samper — Wed, 08 Jul 2020 10:12:40 +0200

This paper describes the application of FEFL096, a three-dimensional, adaptive, finite element, edge-based, ALE shock capturing methodology on unstructured tetrahedral grids, to large-scale simulations of blast wave interaction with structures. The first simulation applied the CFD methodology to the numerical simulation of blast wave diffraction within the B-2 level of the World Trade Center garage. This simulation modeled blast wave diffraction about hundreds of rigidly-modeled structures, spread over a large area. The second simulation applied a new loose-coupling algorithm that combined FEFL096 and DYNA3D, a state-of-the-art Computational Structural Dynamics (CSD) methodology, to the simulation of shock interaction with a structurally-responding truck.

A parallel implicit incompressible flow solver using unstructured meshes

María Jesús Samper — Wed, 08 Jul 2020 10:09:12 +0200

An incompressible flow solver based on unstructured grids is implemented on a parallel distributed memory computer architecture. An important phase in the flow solver is the solution of the elliptic equations for the velocities and pressure. This elliptic solver is parallelized and incorporated into both the explicit and implicit versions of the incompressible flow solver. Performance and scalability studies are carried out on both Intel iPSC 860 and the Intel Delta prototype, and these studies show that the code is scalable. A parallelizable load balancing algorithm is developed to be used in conjunction with the incompressible flow solver. Steady and unsteady flows over a tri-element airfoil and NACA0012 airfoil are computed using the parallel incompressible flow solver.

Dusty shock flow with unstructured adaptive finite elements and parcels

María Jesús Samper — Wed, 08 Jul 2020 09:49:03 +0200

Our objective is to formulate and develop an Eulerian-Lagrangian (E-L) method with an adaptive grid FEM-FCT flow solver that is computationally efficient. This method is used to predict a particle laden shock wave attenuation as a test case and to compare performance characteristics (computation speed, memory, and accuracy) with an E-E implentation that also includes adaptive unstructured grids

Regridding Surface Triangulations

María Jesús Samper — Wed, 08 Jul 2020 09:45:38 +0200

An advancing front surface gridding technique that operates on discretely defined surfaces (i.e. triangulations) is presented. Different aspects that are required to make the procedure reliable for complex geometries are discussed. Notable among these are (a) the recovery of surface features and discrete surface patches from the discrete data, (b) filtering based on point and side-normals to remove undesirable data close to cusps and corners, (c) the proper choice of host faces for ridges, and (d) fast interpolation procedures suitable for complex geometries. Post-generation surface recovery or repositioning techniques are discussed. Several examples ranging from academic to industrial demonstrate the utility of the proposed procedure forab initiosurface meshing from discrete data, such as those encountered when the surface description is already given as discrete, the improvement of existing surface triangulations, as well as remeshing applications during runs exhibiting significant change of domain.

Progress in grid generation via the advancing front technique

María Jesús Samper — Wed, 08 Jul 2020 09:41:12 +0200

We describe recent extensions and improvements to the advancing front grid generation technique. These improvements target a range of applicability, speed and user friendliness. The range of applicability is enlarged by the ability to produce volumetric grids around thin surfaces (such as shells, membranes, fabrics or surfaces with cusps), the generation of high aspect ratio grids for Navier-Stokes applications, the generation of higher order triangular and tetrahedral elements, and the generation of quadrilateral and hexahedral elements. Speed improvements are the result of reduced search overheads, as well as vectorization and parallelization. User friendliness is enhanced by the ability to grid directly discrete data and simpler ways of specifying the desired element size and shape in space. Numerous examples are included that demonstrate the versatility and maturity that advancing front grid generators have achieved.

Improved ALE mesh velocities for moving bodies

María Jesús Samper — Wed, 08 Jul 2020 09:37:11 +0200

A Laplacian smoothing of the mesh velocities with variable diffusivity based on the distance from moving bodies is introduced. This variable diffusivity enforces a more uniform mesh velocity in the region close to the moving bodies. Given that in most applications these are regions where small elements are located, the new procedure decreases element distortion considerably, reducing the need for local or global remeshing, and in some cases avoiding it altogether.

Extensions and improvements of the advancing front grid generation technique

María Jesús Samper — Tue, 07 Jul 2020 16:41:57 +0200

We describe extensions and improvements to the advancing front grid generation technique that have proven useful over the years. The following areas are treated in detail: situations with thin or crossing surfaces, meshing of surfaces defined by triangulations, and ease of user input to define the desired element size in space. The first extension is important if one considers the generation of volumetric grids around shells, membranes, fabrics, or CAD-data that exhibit cusps. Traditional advancing front generators are likely to fail in these situations. We propose the introduction of a crossing environment variable attached to faces and points in order to filter out undesired or incorrect information during the grid generation process. The second extension is required for situations where the surfaces to be gridded are not defined analytically, but via a triangulation. Typical cases where such triangulations are used to define the domain are geophysical problems, climate modelling and medical problems. The third topic deals with the reduction of manual labour to specify element size in space. Sources, element size attached directly to CAD-data, and adaptive background grids are discussed. Adaptive background grids, in combination with surface deviation tolerances, are used to obtain surface triangulations that represent the geometry faithfully, and at the same time enable a smooth transition to volumetric meshes.

Improved ALE mesh velocities for moving bodies

María Jesús Samper — Tue, 07 Jul 2020 16:36:55 +0200

Simulation of the magnetosphere with a new three dimensional MHD code and adaptive mesh refinement: Preliminary results

María Jesús Samper — Tue, 07 Jul 2020 16:25:22 +0200

We present the first results from a new unstructured mesh three dimensional finite element MHD code which uses dynamic solution-adaptive mesh refinement in a manner similar to our two dimensional finite element MHD code /31/. The problem being considered here is the interaction of the solar wind with the earth's magnetosphere, using a three-dimensional Cartesian approximation. Our results strongly indicate that such adaptive mesh techniques have the ability to resolve structures in the three dimensional MHD flow field that would otherwise be possible only with orders of magnitude greater cost and that are most likely beyond the capability of present supercomputers.

Comparisons of Preconditioned Iterative Methods in the Implicit Unstructured Solver of Compressible Flow

María Jesús Samper — Tue, 07 Jul 2020 16:19:28 +0200

Preconditioned iterative methods in an implicit unstructured grid solver of compressible flows are compared. The three-dimensional Euler and Navier-Stokes equations are discretized by the edge-based finite volume method. The artificial dissipation scheme for the inviscid numerical fluxes is developed for the unstructured grid from Jameson's scheme for the structured grid. The following methods are compared to the supersonic and transonic inviscid flows and subsonic viscous laminar and turbulent flows: the central difference methods with the scalar and matrix dissipation scheme and Roe's upwind method with the MUSCL scheme for the inviscid fluxes; the scalar and matrix dissipation method for the left-hand side operator in the implicit scheme; the ILU, DILU and SGS factorizations for the preconditioner; and GMRES and Bi-CGSTAB methods for the linear system solver. The results show that a combination of the matrix dissipation in the inviscid fluxes and the scalar dissipation in the left-hand side works better than the other *schemes. In the preconditioned iterative methods, a combination of DILU or SGS and the Bi-CGSTAB is recommended for the aspect of required memory.

Automatic unstructured grid generators

María Jesús Samper — Tue, 07 Jul 2020 16:11:07 +0200

A review of automatic unstructured grid generators is given. These types of grids have found widespread use in computational fluid dynamics, computational structural dynamics, computational electro-magnetics and computational thermodynamics. The following topics are treated: the methods most commonly used, the specification of desired element size/shape and surface definition/meshing. Finally, the use of automatic grid generators as an enabling technology for moving body simulations and adaptive remeshing techniques is discussed.

Conservative Load Projection and Tracking for Fluid-Structure Problems

María Jesús Samper — Tue, 07 Jul 2020 16:07:43 +0200

The loose coupling of computational fluid dynamics and computational structural dynamics solvers introduces some problems related to the information transfer between the codes. Some techniques developed to solve the problems of the load transfer and interface surface tracking are presented. The main criterion is to achieve conservation of total loads and total energy. The load projection scheme is based on Gaussian integration and fast interpolation algorithms for unstructured grids. The surface tracking algorithm, also based on interpolation, is important for many applications, including aeroelastic deformation of wings due to aerodynamic loads. The methodologies not only improve present fluid-structure interaction simulations, but also increase the range of their applicability. These techniques are of general character and can be used in other multidisciplinary applications as well.

On Some Outstanding Issues in CFD

María Jesús Samper — Tue, 07 Jul 2020 15:31:33 +0200

Against the general feeling that ‘CFD is solved’, I offer a few remarks from the trenches. When performing large-scale simulations of geometrically and physically complex flows, the notion of reliable, cost-effective, widely applicable and easy-to-use CFD still appears more as fiction than reality. The present monograph addresses some major areas where progress is urgently required. These areas are listed in the order a typical CFD run proceeds: model import/creation, grid generation, flow solvers, mesh adaptation and quality control. Finally, with a view towards the coming decade, code, data and project management are discussed.

Parallelizing the construction of indirect access arrays for shared‐memory machines

María Jesús Samper — Tue, 07 Jul 2020 15:26:21 +0200

A way has been found to form indirect addressing lists in parallel on shared-memory parallel machines. The maximum possible speed-up for typical tetrahedral grids is approximately 1:23. The algorithm requires an additional scratch array to shift from the serial ‘elements surrounding points’ to the parallel ‘elements surrounding processors surrounding points’ paradigm. The algorithm developed is general in nature, i.e. applicable to all indirect addressing lists. All numerical methods requiring the construction of indirect data structures, such as sparse matrix linear algebra procedures, field and particle solvers operating on unstructured grids, and network flow applications should see a benefit from this algorithm when running on shared-memory parallel machines

Renumbering strategies for unstructured-grid solvers operating on shared-memory, cache-based parallel machines

María Jesús Samper — Tue, 07 Jul 2020 15:19:36 +0200

Two renumbering strategies for field solvers based on unstructured grids that operate on shared-memory, cache-based parallel machines are described. Special attention is paid to the avoidance of cache-line overwrite, which can lead to drastic performance degradation on this type of machines. Both renumbering techniques avoid cache-misses and cache-line overwrite while allowing pipelining, leading to optimal coding for this type of hardware

Generalized Meshing Environment for Computational Mechanics

María Jesús Samper — Tue, 07 Jul 2020 15:14:03 +0200

One of the most time-consuming tasks in performing any discrete analysis the construction of a suitable mesh to represent the computational domain. Mesh generation today remains one of the pacing items in computational mechanics and consumes too many work hours and too many computers resources. This critical need for more progress in three-dimensional resources. This critical need for more progress in three-dimensional mesh generation certainly requires efficient geometry definition systems and advances in meshing methods. However, another major factor toward this progress is efficient methodology and computer software for automation of the meshing process. It is precisely this aspect of meshing that’s is the focus of this Note.

Distributed visualization in computational fluid dynamics

María Jesús Samper — Tue, 07 Jul 2020 14:59:00 +0200

The use of parallel computers and in particular distributed memory architectures imposes a number of requirements on the visualization systems for Computational Fluid Dynamics (CFD). We describe the design and capabilities of our distributed visualization software which can handle parallel multidisciplinary applications, can connect to a running solver for on-line display and steering, supports collaborative visualization and can be used as a tool for the automatic making of movies and animations. This discussion serves as an overview of the current trends and developments in visualization as applied to CFD and other computational sciences.

Computation of the 3-D Unsteady Flow Past Deforming Geometries

María Jesús Samper — Tue, 07 Jul 2020 14:51:13 +0200

A 3-D incompressible unsteady flow solver based on simple finite elements with adaptive remeshing and grid movement for both moving and deforming surfaces is described. We demonstrate the combination of adaptive remeshing techniques with the incompressible flow solver with the computation of flow past an eel in 2-D and a blue-fin tuna in 3-D. The flow past a swimming tuna was computed for two extreme cases of the caudal fin frequency and swimming speed. A grid refinement study was performed and a grid converged solution for the force produced by the caudal fin was obtained.

Parallel Advancing Front Grid Generation

María Jesús Samper — Tue, 07 Jul 2020 14:46:48 +0200

A parallel advancing front scheme has been developed. The domain to be gridded is rst subdivided spatially using a relatively coarse octree. Boxes are then identiied and gridded in parallel. A scheme that resembles closely the advancing front technique on scalar machines is recovered by only considering the boxes of the active front that generate small elements. The procedure has been implemented on the SGI Origin class of machines using the shared memory paradigm. Timings for a variety of cases show speedups similar to those obtained for ow codes. The procedure has been used to generate grids in excess of a hundred million elements.

Surface triangulation over intersecting geometries

María Jesús Samper — Tue, 07 Jul 2020 14:32:18 +0200

A method for the rapid construction of meshes over intersecting triangulated shapes is described. The method is based on an algorithm that automatically generates a surface mesh from intersecting triangulated surfaces by means of Boolean intersection/union operations. After the intersection of individual components is obtained, the exposed surface parts are extracted. The algorithm is intended for rapid interactive construction of non‐trivial surfaces in engineering design, manufacturing, visualization and molecular modelling applications. Techniques to make the method fast and general are described. The proposed algorithm is demonstrated on a number of examples, including intersections of multiple spheres, planes and general engineering shapes, as well as generation of surface and volume meshes around clusters of intersecting components followed by the computation of flow field parameters.

The numerical simulation of strongly unsteady flow with hundreds of moving bodies

María Jesús Samper — Tue, 07 Jul 2020 14:22:17 +0200

A methodology for the simulation of strongly unsteady flows with hundreds of moving bodies has been developed. An unstructured grid, high-order, monotonicity preserving, ALE solver with automatic refinement and remeshing capabilities was enhanced by adding equations of state for high explosives, deactivation techniques and optimal data structures to minimize CPU overheads, automatic recovery of CAD data from discrete data, two new remeshing options, and a number of visualization tools for the preprocessing phase of large runs. The combination of these improvements has enabled the simulation of strongly unsteady flows with hundreds of moving bodies. Several examples demonstrate the effectiveness of the proposed methodology.

A Navier-Stokes/Actuator Disc Simulation of Body-Ducted Propulsor Flow

María Jesús Samper — Tue, 07 Jul 2020 14:16:22 +0200

The interactions between a cylinder body and a ducted propeller is simulated using a coupled Navier-Stokes and actuator disc approach. The actuator disc approach raises the pressure of the fluid flowing through the propeller disc. Therefore, the finite number of blades, and the production of fluid rotation are ignored. An unstructured grid-based three-dimensional finite element method was used to solve the turbulent hydrodynamic flowfield. A Baldwin-Lomax turbulence model was used. The source strength was determined to match the thrust generated by propeller. The additional momentum due to the actuator disc is treated by a uniform distribution of sources over the propeller disc in momentum equation of Navier-Stokes equations. The three different momentum source strengths were used and the results from these cases and a no-source case are compared. It is shown that the source distribution can induce upstream separation if not properly chosen. (Work Sponsored by DoD HPCMO.)

Surface Gridding from Discrete Data

María Jesús Samper — Tue, 07 Jul 2020 14:06:09 +0200

An advancing front gridding technique that operates on discretely defined surfaces is presented. Different aspects that are required to make the procedure reliable for complex geometries are discussed. Notable among these are:

: a) the recovery of surface features and discrete surface patches from the discrete data; b) filtering based on point and side normals to remove undesirable data close to cusps and corners; c) the proper choice of host faces for ridges; d) fast interpolation procedures suitable for complex geometries. Post-generation surface recovery or repositioning techniques are discussed. Several examples ranging from academic to industrial demonstrate the utility of the proposed procedure for ab initio surface meshing from discrete data, such as those encountered when the surface description is already given as discrete, the improvement of existing surface triangulations, as well as remeshing applications during runs exhibiting significant change of domain.

A Fast, Matrix-free Implicit Method for Computing Low Mach Number Flows on Unstructured Grids

María Jesús Samper — Tue, 07 Jul 2020 13:58:05 +0200

A fast, matrix-free implicit method has been developed to solve low Mach number flow problems on unstructured grids. The preconditioned compressible Euler and Navier-Stokes equations are integrated in time using a linearized implicit scheme. A newly developed fast, matrix-free implicit method, GMRES + LU−SGS, is then applied to solve the resultant system of linear equations. A variety of computations has been made for a wide range of flow conditions, for both in viscid and viscous flows, in both 2D and 3D to validate the developed method and to evaluate the effectiveness of the GMRES + LU−SGS method. The numerical results obtained indicate that the use of the GMRES + LU−SGS method leads to a significant increase in performance over the LU−SGS method, while maintaining memory requirements similar to its explicit counterpart. An overall speedup factor from one to more than two order of magnitude for all test cases in comparison with the explicit method is demonstrated.

Flow and dispersion around buildings: An application with FLEFLO

María Jesús Samper — Tue, 07 Jul 2020 13:49:23 +0200

A series of simulations were performed in order to test the accuracy of FEFLO for problems of flow and dispersion around buildings. The major case was extracted from the Evaluation of Modelling Uncertainty (project EMU)[1]. The simulations were run in "black box" mode, i.e. no tuning of parameters was allowed. The results obtained were in very close agreement with the available wind-tunnel data for the case selected. The accuracy is comparable with other codes. The results show that an Euler run with proper profile yields a fairly accurate answer.

Measurement of stenosis from Magnetic resonance angiography using vessel skeletons

María Jesús Samper — Tue, 07 Jul 2020 13:28:18 +0200

Measurement of stenosis due to atherosclerosis is essential for interventional planning. Currently, measurement of stenosis from magnetic resonance angiography (MRA) is made based on 2D maximum intensity projection (MIP) images. This methodology, however, is subjective and does not take full advantage of the 3D nature of MRA. To address these limitations we present a deformable model for reconstructing the vessel surface with particular application to the carotid artery. The deformable model is based on a cylindrical coordinate system of a curvilinear axes. In this coordinate system, the location of each point on the surface of the deformable model is described by its axial, circumferential and radial position. The points on the surface deform in the radial direction so as to minimize discontinuity in radial position between adjacent points while maximizing the proximity of the surface to local edges in the image. The algorithm has no bias towards either narrower or wider cross- sectional shapes and is thus appropriate for the measurement of stenosis. Axes of the vessels are indicated manually or determined by axes detection methods. Once completed, the surface reconstruction lends itself directly to 3D methods for measuring cross-sectional diameter and area.

Generation of non‐isotropic unstructured grids via directional enrichment

María Jesús Samper — Tue, 07 Jul 2020 13:23:59 +0200

A procedure for the generation of highly stretched grids suitable for Reynolds‐averaged Navier–Stokes (RANS) calculations is presented. In a first stage, an isotropic (Euler) mesh is generated. In a second stage, this grid is successively enriched with points in order to achieve highly stretched elements. The element reconnection is carried out using a constrained Delaunay approach. Points are introduced from the regions of lowest stretching towards the regions of highest stretching. The procedure has the advantages of not requiring any type of surface recovery, not requiring extra passes or work to mesh concave ridges/corners, and guarantees a final mesh, an essential requirement for industrial environments. Given that point placement and element quality are highly dependent for the Delaunay procedure, special procedures were developed in order to obtain optimal point placement.

CFD Applications in Support of the Space Shuttle Risk Assessment

María Jesús Samper — Tue, 07 Jul 2020 13:20:11 +0200

The paper describes a numerical study of a potential accident scenario of the space shuttle, operating at the same flight conditions as flight 51L, the Challenger accident. The interest in performing this simulation is derived by evidence that indicates that the event itself did not exert large enough blast loading on the shuttle to break it apart. Rather, the quasi-steady aerodynamic loading on the damaged, unbalance vehicle caused the break-up. Despite the enormous explosive potential of the shuttle total fuel load (both liquid and solid), the post accident explosives working group estimated the maximum energy involvement to be equivalent to about five hundreds of pounds of TNT. This understanding motivated the simulation described here. To err on the conservative side, we modeled the event as an explosion, and used the maximum energy estimate. We modeled the transient detonation of a 500 lbs spherical charge of TNT, placed at the main engine, and the resulting blast wave propagation about the complete stack. Tracking of peak pressures and impulses at hundreds of locations on the vehicle surface indicate that the blast load was insufficient to break the vehicle, hence demonstrating likely crew survivability through such an event.

On the Computation of Compressible Turbulent Flows on Unstructured Grids

María Jesús Samper — Tue, 07 Jul 2020 12:30:42 +0200

An accurate, fast, matrix-free implicit method has been developed to solve compressible turbulent How problems using the Spalart and Allmaras one equation turbulence model on unstructured meshes. The mean-flow and turbulence-model equations are decoupled in the time integration in order to facilitate the incorporation of different turbulence models and reduce memory requirements. Both mean flow and turbulent equations are integrated in time using a linearized implicit scheme. A recently developed, fast, matrix-free implicit method, GMRES+LU-SGS, is then applied to solve the resultant system of linear equations. The spatial discretization is carried out using a hybrid finite volume and finite element method, where the finite volume approximation based on a containment dual control volume rather than the more popular median-dual control volume is used to discretize the inviscid fluxes, and the finite element approximation is used to evaluate the viscous flux terms. The developed method is used to compute a variety of turbulent flow problems in both 2D and 3D. The results obtained are in good agreement with theoretical and experimental data and indicate that the present method provides an accurate, fast, and robust algorithm for computing compressible turbulent flows on unstructured meshes.

Practical CFD Applications to Design of a Wave Cancellation Multihull Ship

María Jesús Samper — Tue, 07 Jul 2020 12:27:48 +0200

Four methods of analysis — a nonlinear method based on Euler's equations and three linear potential flow methods — are used to determine the optimal lo- cation of the outer hulls for a wave cancellation mul- tihull ship that consists of a main center hull and two outer hulls. The three potential flow methods corre- spond to a hierarchy of simple approximations based on the Fourier-Kochin representation of ship waves and the slender-ship approximation.

Time-Accurate Implicit ALE Algorithm for Shared-Memory Parallel Computers

María Jesús Samper — Tue, 07 Jul 2020 12:22:53 +0200

An unstructured grid matrix-free GMRES+LU-SGS scheme is used to simulate unsteady CFD problems with moving bodies. The method is applied on sharedmemory, cache-based parallel machines. A special grid renumbering technique is used for the parallelization rather than the traditional method of partitioning the computational domain. Moving mesh with recurrent remeshing models the body motion.

A Coupled CFD/CSD Methodology for Simulating Structural Response to Airblast and Fragment

María Jesús Samper — Tue, 07 Jul 2020 12:12:14 +0200

Several classes of important engineering problems require the concurrent application of CFD and CSD techniques. Currently, attempts to model these problems are solved either iteratively, requiring several cycles of CFD run followed by CSD run, or by assuming that the CFD and CSD solutions can be decoupled. The various efforts to develop a fluid/structure coupling can be classified according to the complexity level of the approximations used for each of the domains. These range from simple 6 DOF integration to finite elements with complex models for elasto-plastic materials with rupture laws and contact. Similarly, the fluid dynamics approximations range from the potential flow (irotational, inviscid, isentropic flows) to the full Navier-Stokes set of equations. The present research interests focus on non-linear applications, in particular, structures that experience severe deformations due to blast loads. Hence, the fluid applies either the Euler or Reynolds-Averaged Navier-Stokes equations, while elasto-plastic materials with rupture criteria are used for the structural modeling.

An accurate, fast, matrix-free implicit method for computing unsteady flows on unstructured grids

María Jesús Samper — Tue, 07 Jul 2020 12:05:14 +0200

An accurate, fast, matrix-free implicit method has been developed to solve the three-dimensional compressible unsteady flows on unstructured grids. A nonlinear system of equations as a result of a fully implicit temporal discretization is solved at each time step using a pseudo-time marching approach. A newly developed fast, matrix-free implicit method is then used to obtain the steady-state solution to the pseudo-time system. The developed method is applied to compute a variety of unsteady flow problems involving moving boundaries. The numerical results obtained indicate that the use of the present implicit method leads to a significant increase in performance over its explicit counterpart, while maintaining a similar memory requirement.

New methods for computational fluid dynamics modeling of carotid artery from magnetic resonance angiography

María Jesús Samper — Tue, 07 Jul 2020 11:56:36 +0200

Computational fluid dynamics (CFD) models of the carotid artery are constructed from contrast-enhanced magnetic resonance angiography (MRA) using a deformable model and a surface-merging algorithm. Physiologic flow conditions are obtained from cine phase-contrast MRA at two slice locations below and above the carotid bifurcation. The methodology was tested on image data from a rigid flow-through phantom of a carotid artery with 65% degree stenosis. Predicted flow patterns are in good agreement with MR flow measurements at intermediate slice locations. Our results show that flow in a rigid flow-through phantom of the carotid bifurcation with stenosis can be simulated accurately with CFD. The methodology was then tested on flow and anatomical data from a normal human subject. The sum of the instantaneous flows measured at the internal and external carotids differs from that at the common carotid, indicating that wall compliance must be modeled. Coupled fluid-structure calculations were able to reproduce the significant dampening of the velocity waveform observed between different slices along the common carotid artery. Visualizations of the blood flow in a compliant model of the carotid bifurcation were produced. A comparison between compliant and rigid models shows significant differences in the time-dependent wall shear stress at selected locations. Our results confirm that image-based CFD techniques can be applied to the modeling of hemodynamics in compliant carotid arteries. These capabilities may eventually allow physicians to enhance current image-based diagnosis, and to predict and evaluate the outcome of interventional procedures non- invasively.

Interpretation of arterial velocity waveforms

María Jesús Samper — Tue, 07 Jul 2020 11:51:20 +0200

Blood flow temporal waveforms change with position along an artery. The change in the flow waveforms can be accounted for by a transmission line model of flow. According to this model, pulse waves propagate at a finite velocity in both directions along the artery. In principle, given flow waveforms measured at three locations along an artery, the pulse-wave velocity, (c) can be determined from the wave equation (d2Q/dt2 equals c2d2Q/dz2, Q is flow, t is time, z is position). Given the vessel diameter, the vessel-wall compliance can be derived from pulse-wave velocity. However, direct solution of the wave equation for pulse-wave velocity is highly susceptible to flow-measurement error. Thus, we propose a new method for estimating pulse-wave velocity from arterial flow waveforms. In our method, ideal flow waveforms are reconstructed from three measured flow waveforms. The ideal waveforms are reconstructed by minimization of the total error between the ideal and measured waveforms subject to constraints of the wave equation. Ideal flow waveforms are reconstructed for a range of assumed pulse-wave velocities. The true pulse-wave velocity is considered to be that which produces the minimum total error. The method applied to blood flow measurements made with phase-contrast magnetic resonance imaging.

Unstructured Navier–Stokes grid generation at corners and ridges

María Jesús Samper — Tue, 07 Jul 2020 11:43:51 +0200

Problems related to automatic generation of highly stretched unstructured grids suitable for 3‐D Reynolds‐averaged Navier–Stokes computations are addressed. Special attention is given to treatment of such geometrical irregularities as convex and concave ridges as well as corners where the ridges meet. The existing unstructured grid generation approaches may fail or produce poor quality meshes in such geometrical regions. The proposed solution is based on special meshing of non‐slip body surfaces resulting in smooth and robust volume meshing and high overall quality of generated grids. Several examples demonstrate the efficiency of the method for complex 3‐D geometries.

CFD shape optimization using an incomplete-gradient adjoint formulation

María Jesús Samper — Tue, 07 Jul 2020 10:50:03 +0200

A design methodology based on the adjoint approach for flow problems governed by the incompressible Euler equations is presented. The main feature of the algorithm is that it avoids solving the adjoint equations, which saves an important amount of CPU time. Furthermore, the methodology is general in the sense it does not depend on the geometry representation. All the grid points on the surface to be optimized can be chosen as design parameters. In addition, the methodology can be applied to any type of mesh. The partial derivatives of the Row equations with respect to the design parameters are computed by finite differences. In this way, this computation is independent of the numerical scheme employed to obtain the Row solution. Once the design parameters have been updated, the new solid surface is obtained with a pseudo-shell approach in such a way that local singularities, which can degrade or inhibit the convergence to the optimal solution, are avoided. Some 2D and 3D numerical examples are shown to demonstrate the proposed methodology.

A parallel advancing front grid generation scheme

María Jesús Samper — Tue, 07 Jul 2020 10:46:59 +0200

A parallel advancing front scheme has been developed. The domain to be gridded is first subdivided spatially using a relatively coarse octree. Boxes are then identified and gridded in parallel. A scheme that resembles closely the advancing front technique on scalar machines is recovered by only considering the boxes of the active front that generate small elements. The procedure has been implemented on the SGI origin class of machines using the shared memory paradigm. Timings for a variety of cases show speedups similar to those obtained for flow codes. The procedure has been used to generate grids with tens of millions of elements.

Merging of intersecting triangulations for finite element modeling

María Jesús Samper — Tue, 07 Jul 2020 10:35:49 +0200

Surface mesh generation over intersecting triangulations is a problem common to many branches of biomechanics. A new strategy for merging intersecting triangulations is described. The basis of the method is that object surfaces are represented as the zero-level iso-surface of the distance-to-surface function defined on a background grid. Thus, the triangulation of intersecting objects reduces to the extraction of an iso-surface from an unstructured grid. In a first step, a regular background mesh is constructed. For each point of the background grid, the closest distance to the surface of each object is computed. Background points are then classified as external or internal by checking the direction of the surface normal at the closest location and assigned a positive or negative distance, respectively. Finally, the zero-level iso-surface is constructed. This is the final triangulation of the intersecting objects. The overall accuracy is enhanced by adaptive refinement of the background grid elements. The resulting surface models are used as support surfaces to generate three-dimensional grids for finite element analysis. The algorithms are demonstrated by merging arterial branches independently reconstructed from contrast-enhanced magnetic resonance images and by adding extra features such as vascular stents. Although the methodology is presented in the context of finite element analysis of blood flow, the algorithms are general and can be applied in other areas as well.

From medical images to anatomically accurate finite element grids

María Jesús Samper — Tue, 07 Jul 2020 10:30:02 +0200

Practical hydrodynamic optimization of a trimaran

María Jesús Samper — Tue, 07 Jul 2020 10:26:13 +0200

An illustrative application of practical CFD tools to a simple ship design problem is presented. Four methods of analysis – a nonlinear method based on Euler’s equations and three linear potential flow methods – are used to determine the optimal location of the outer hulls of a trimaran. The main center hull and the outer hulls of the trimaran are shown in the frontispiece, together with the parameters a and b that define the arrangement of the hulls. The three potential flow methods correspond to a hierarchy of simple approximations based on the Fourier-Kochin representation of ship waves and the slender-ship approximation.

Optimization of a Wave Cancellation Multihull Ship Using CFD Tools

María Jesús Samper — Tue, 07 Jul 2020 10:11:59 +0200

A simple CFD tool, coupled to a discrete surface representation and a gradient-based optimization procedure, is applied to the design of optimal hull forms and optimal arrangement of hulls for a wave cancellation multihull ship. The CFD tool, which is used to estimate the wave drag, is based on the zeroth-order slender ship approximation. The hull surface is represented by a triangulation, and almost every grid point on the surface can be used as a design variable. A smooth surface is obtained via a simplified pseudo-shell problem. The optimal design process consists of two steps. The optimal center and outer hull forms are determined independently in the first step, where each hull keeps the same displacement as the original design while the wave drag is minimized. The optimal outer-hull arrangement is determined in the second step for the optimal center and outer hull forms obtained in the first step. Results indicate that the new design can achieve a large wave drag reduction in comparison to the original design configuration.

Image-based finite element modeling of hemodynamics in stenosed carotid artery

María Jesús Samper — Tue, 07 Jul 2020 10:02:52 +0200

A methodology to construct patient-specific, anatomically and physiologically realistic finite element models of blood flows in stenosed carotid arteries is presented. Anatomical models of carotid arteries with stenosis are reconstructed from contrast-enhanced magnetic resonance angiography (MRA) images using a tubular deformable model along each arterial branch. A surface-merging algorithm is used to create a watertight model of the carotid bifurcation for subsequent finite element grid generation. A fully implicit scheme is used to solve the incompressible Navier-Stokes equations on unstructured grids in three-dimensions. Physiologic boundary conditions are derived from cine phase-contrast MRA flow velocity measurements at two locations below and above the bifurcation. The methodology was tested on image data of a patient with carotid artery stenosis. A finite element grid was successfully generated from contrast-enhanced MRA images, and pulsatile blood flow visualizations were produced. Visualizations of the wall shear stress distribution and of changes in both its magnitude and direction were produced. These quantities may become important in order to characterize healthy and diseased flow and wall shear stress patterns. We conclude that MRA can be used to obtain all the anatomical and physiologic data necessary for realistic modeling of blood flows in carotid arteries with stenosis. Our results confirm that image-based computational fluid dynamics techniques can be applied to the modeling of hemodynamics in carotid arteries with stenosis. These capabilities may be used to advance our understanding of the generation and progression of vascular disease, and may eventually allow physicians to enhance current image-based diagnosis, and to predict and evaluate the outcome of interventional procedures non-invasively.

A stabilized pseudo‐shell approach for surface parametrization in CFD design problems

María Jesús Samper — Tue, 07 Jul 2020 09:58:41 +0200

A surface representation for computational fluid dynamics (CFD) shape design problems is presented. The surface representation is based on the solution of a simplified pseudo‐shell problem on the surface to be optimized. A stabilized finite element formulation is used to perform this step. The methodology has the advantage of being completely independent of the CAD representation. Moreover, the user does not have to predefine any set of shape functions to parameterize the surface. The scheme uses a reasonable discretization of the surface to automatically build the shape deformation modes, by using the pseudo‐shell approach and the design parameter positions. Almost every point of the surface grid can be chosen as design parameter, which leads to a very rich design space. Most of the design variables are chosen in an automatic way, which makes the scheme easy to use. Furthermore, the surface grid is not distorted through the design cycles which avoids remeshing procedures. An example is presented to demonstrate the proposed methodology.

Minimization of indirect addressing for edge‐based field solvers

María Jesús Samper — Tue, 07 Jul 2020 09:54:55 +0200

A point renumbering scheme that halves the number of indirect addressing operations required for edge‐based field solvers has been developed. At the same time, an alternative (and entirely serendipitous) assembly of right‐hand side vectors was found to enhance performance considerably. The new loop structure is especially attractive for vector‐parallel machines with direct memory access. Timings on the CRAY‐SV1 and NEC‐SX5 show that for Laplacian loops, which appear in many CFD and CEM codes, CPU can be reduced considerably. The new renumbering scheme does not require any new data structures or arrays, allowing for progressive porting of loops in large‐scale production codes.

Calculation of Ship Sinkage and Trim Using a Finite Element Method and Unstructured Grids

María Jesús Samper — Tue, 07 Jul 2020 09:22:47 +0200

An unstructured grid-based, parallel free-surface flow solver has been extended to account for sinkage and trim effects in the calculation of steady ship waves. The overall scheme of the solver combines a finite-element, equal-order, projection-type three-dimensional incompressible flow solver with a finite element, two-dimensional advection equation solver for the free surface equation. The sinkage and trim, wave profiles, and wave drag computed using the present approach are in good agreement with experimental measurements for two hull forms at a wide range of Froude numbers. Numerical predictions indicate significant differences between the wave drag for a ship fixed in at-rest position and free to sink and trim, in agreement with experimental observations.

A feature‐preserving volumetric technique to merge surface triangulations

María Jesús Samper — Tue, 07 Jul 2020 09:13:08 +0200

Several extensions and improvements to surface merging procedures based on the extraction of iso-surfaces from a distance map defined on an adaptive background grid are presented. The main objective is to extend the application of these algorithms to surfaces with sharp edges and corners. In order to deal with objects of different length scales, the initial background grids are created using a Delaunay triangulation method and local voxelizations. A point enrichment technique that introduces points into the background grid along detected surface features such as ridges is used to ensure that these features are preserved in the final merged surface. The surface merging methodology is extended to include other Boolean operations between surface triangulations. The iso-surface extraction algorithms are modified to obtain the correct iso-surface for multi-component objects. The procedures are demonstrated with various examples, ranging from simple geometrical entities to complex engineering applications. The present algorithms allow realistic modelling of a large number of complex engineering geometries using overlapping components defined discretely, i.e. via surface triangulations. This capability is very useful for grid generation starting from data originated in measurements or images.

Comparisons of model simulations with observations of mean flow and turbulence within simple obstacle arrays

María Jesús Samper — Mon, 06 Jul 2020 16:56:45 +0200

A three-dimensional numerical code with unstructured tetrahedral grids, the finite element flow solver (FEFLO), was used to simulate the mean flow and the turbulence within obstacle array configurations consisting of simple cubical elements. Model simulations were compared with observations from a hydraulic water flume at the University of Waterloo. FEFLO was run in large eddy simulation mode, using the Smagorinsky closure model, to resolve the larger scales of the flow field. There were four experiment test cases consisting of square and staggered arrays of cubical obstacles with separations of 1.5 and 0.5 obstacle heights. The mean velocity profile for the incoming neutral boundary layer was approximated by a power law, and the turbulent fluctuations in the approach flow were generated using a Monte Carlo model. The numerical simulations were able to capture, within 40% on average, the general characteristics of the mean flow and the turbulence, such as the strong mean wind shears and the maximum turbulence at the elevation of the obstacles and the nearly constant mean wind and the 50% reduction in the turbulent velocity within the obstacle canopy. As expected, the mean wind speeds were significantly decreased (by about a factor of two or three) in the array with closer obstacle packing. It was found that, a “street canyon” effect was more obvious for the square arrays, with higher flow speeds in between the obstacles, than for the staggered arrays.

Fluid Dynamics of Flapping Aquatic Flight in the Bird Wrasse: Three-Dimensional Unsteady Computations With Fin Deformation

María Jesús Samper — Mon, 06 Jul 2020 16:49:30 +0200

Many fishes that swim with the paired pectoral fins use fin-stroke parameters that produce thrust force from lift in a mechanism of underwater flight. These locomotor mechanisms are of interest to behavioral biologists, biomechanics researchers and engineers. In the present study, we performed the first three-dimensional unsteady computations of fish swimming with oscillating and deforming fins. The objective of these computations was to investigate the fluid dynamics of force production associated with the flapping aquatic flight of the bird wrasse Gomphosus varius. For this computational work, we used the geometry of the wrasse and its pectoral fin, and previously measured fin kinematics, as the starting points for computational investigation of three-dimensional (3-D) unsteady fluid dynamics. We performed a 3-D steady computation and a complete set of 3-D quasisteady computations for a range of pectoral fin positions and surface velocities. An unstructured, grid-based, unsteady Navier-Stokes solver with automatic adaptive remeshing was then used to compute the unsteady flow about the wrasse through several complete cycles of pectoral fin oscillation. The shape deformation of the pectoral fin throughout the oscillation was taken from the experimental kinematics. The pressure distribution on the body of the bird wrasse and its pectoral fins was computed and integrated to give body and fin forces which were decomposed into lift and thrust. The velocity field variation on the surface of the wrasse body, on the pectoral fins and in the near-wake was computed throughout the swimming cycle. We compared our computational results for the steady, quasi-steady and unsteady cases with the experimental data on axial and vertical acceleration obtained from the pectoral fin kinematics experiments. These comparisons show that steady state computations are incapable of describing the fluid dynamics of flapping fins. Quasi-steady state computations, with correct incorporation of the experimental kinematics, are useful when determining trends in force production, but do not provide accurate estimates of the magnitudes of the forces produced. By contrast, unsteady computations about the deforming pectoral fins using experimentally measured fin kinematics were found to give excellent agreement, both in the time history of force production throughout the flapping strokes and in the magnitudes of the generated forces.

Blood Flow Modeling in Carotid Arteries with Computational Fluid Dynamics and MR Imaging

María Jesús Samper — Mon, 06 Jul 2020 16:39:40 +0200

The authors' goal was to develop a noninvasive method for detailed assessment of blood flow patterns from direct in vivo measurements of vessel anatomy and flow rates. The authors developed a method to construct realistic patient-specific finite element models of blood flow in carotid arteries. Anatomic models are reconstructed from contrast material-enhanced magnetic resonance (MR) angiographic images with a tubular deformable model along each arterial branch. A surface-merging algorithm is used to create a watertight model of the carotid bifurcation for subsequent finite element grid generation, and a fully implicit scheme is used to solve the incompressible Navier-Stokes equations on unstructured grids. Physiologic boundary conditions are derived from cine phase-contrast MR flow velocity measurements at two locations below and above the bifurcation. Vessel wall compliance is incorporated by means of fluid-solid interaction algorithms. The method was tested on imaging data from a healthy subject and a patient with mild stenosis. Finite element grids were successfully generated, and pulsatile blood flow calculations were performed. Computed and measured velocity profiles show good agreement. Flow patterns and wall shear stress distributions were visualized. Patient-specific computational fluid dynamics modeling based on MR images can be performed robustly and efficiently. Preliminary validation studies in a physical flow-through model suggest that the model is accurate. This method can be used to characterize blood flow patterns in healthy and diseased arteries and may eventually help physicians to supplement imaging-based diagnosis and predict and evaluate the outcome of interventional procedures.

On Incompressible Flow Solvers

María Jesús Samper — Mon, 06 Jul 2020 16:31:52 +0200

A family of low-order finite element solvers for incompressible flows is described. Both the advection and divergence terms are treated using consistent numerical fluxes along edges. Several techniques to accelerate convergence to steady state are explored and compared. The techniques are then used in a fully implicit time-marching scheme that solves a steady problem at every timestep. Several examples demonstrate the usefulness of the developed scehmes.

Development and Applications of a Coupled CFD/CSD Methodology Using an Embedded CSD Approach

María Jesús Samper — Mon, 06 Jul 2020 16:25:52 +0200

This paper describes recent algorithm developments and select applications of a program that couples parallel Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) methodologies. FEFL098 is the CFD code used while DYNA3D handles the CSD portion. FEFL098 solves the time-dependent, compressible Euler and Reynolds-Averaged Navier-Stokes equations on an unstructured mesh of tetrahedral elements. DYNA3D solves explicitly the large deformation, large strain formulation equations on an unstructured grid composed of bricks and hexahedral elements.

While the initial coupled algorithm used the so-called ”glued-mesh” approach, where the CFD and CSD faces match identically, failure of this approach to model severe structural deformation, as well as crack propagation in steel and concrete, led us to the development of the so-called ”embedded-mesh” approach. here, the CSD objects float through the CFD domain. While each approach has it’s own advantages, limitations and deficiencies, the embedded approach was proven to be superior for the class of problems modeled here. Critical applications of both approaches are described, including weapon detonation and fragmentation, fragment/airblast interaction with a steel wall, and an external airblast interaction with a generic steel ship hull.

Development And Applications Of An Embedded CSD Approach For Coupled CFD/CSD Modeling Of Blastlstructure Interactions

María Jesús Samper — Mon, 06 Jul 2020 16:20:59 +0200

This paper describes recent developments and select applications of a program that couples parallel Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) methodologies. FEFL098 is the CFD code used while DYNA3D handles the CSD portion. FEFL098 solves the time-dependent, compressible Euler and Reynolds-Averaged Navier-Stokes equations on an unstructured mesh of tetrahedral elements. DYNA3D solves explicitly the large deformation, large strain formulation equations on an unstructured grid composed of bricks and hexahedral elements. The initial algorithm constructed to model the coupled processes used the so-called "glued-mesh" approach, where the CFD and CSD faces match identically. Failure of this approach to model severe structural deformations in steel plates, as well as crack growth and propagation in steel and concrete, led us to the development of the so-called "embedded-mesh" approach, where the CSD mesh float through the CFD domain. While each approach has its own advantages, limitations and deficiencies, the embedded approach was proven to be superior for the class of problems modeled here. Critical applications of both approaches are described, including weapon detonation and fragmentation, airblast interaction with a reinforced concrete wall, and fragment/airblast interactions with steel wall structures including a generic steel ship hull and a steel tower.

Coupling of CFD and CSD methodologies for modeling blast and structural response

María Jesús Samper — Mon, 06 Jul 2020 16:15:02 +0200

This paper describes recent algorithm developments and applications of a program that couples parallel Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) methodologies. FEFL098 is the CFD code used while DYNA3D handles the CSD portion. FEFL098 solves the time-dependent compressible Euler and Reynolds-Averaged Navier-Stokes equations on an unstructured mesh of tetrahedral elements. DYNA3D solves explicitly the large deformation, large strain formulation equations on an unstructured grid composed of bricks and hexahedral elements. While the initial coupled algorithm used the so-called "glued-mesh" approach, where the CFD and CSD faces match identically, failure of this approach to model severe structural deformation, as well as crack propagation in steel and concrete, led us to the development of the so-called "embedded-mesh" approach. Here, the CSD objects float through the CFD domain. While each approach has its own advantages, limitations, and deficiencies, the embedded approach was proven to be superior for the class of problems modeled here. Critical application of both approaches are described, including weapon detonation and fragmentation, airblast interaction with a reinforced concrete wall, and fragment/airblast interaction with a steel wall. The final application models the interaction of an external airblast with a generic steel ship.

Fluid-structure interaction using adaptive embedded unstructured grids

María Jesús Samper — Mon, 06 Jul 2020 15:27:44 +0200

Fluid-structure interaction cases with severe topological change due to fragmentation or rupture in the structure have prompted the development of flow solvers using a so-called embedded mesh approach. A simple embedded domain method for node-based unstructured grid solvers is presented. Edges crossing embedded surface faces are either removed or duplicated. Several techniques to improve the treatment of boundary points close to the immersed surfaces are explored. Adaptive mesh refinement based on proximity to the curvature or corners of the embedded CSD surfaces is used to enhance the accuracy of the solution. User-defined or automatic deactivation for the regions inside immersed solid bodies is employed to avoid unnecessary work. Several examples are included that show the viability of this approach for coupled fluid-structure problems.

On The Modeling Of Boundary Conditions For Embedded Schemes

María Jesús Samper — Mon, 06 Jul 2020 15:22:52 +0200

A simple embedded method for an unstructured grid is presented. An enhancement of the boundary treatments using ghost points is then described. Several examples are used to demonstrate the viability of the approach for inviscid flow simulations.

Adaptive Embedded Unstructured Grid Methods

María Jesús Samper — Mon, 06 Jul 2020 15:16:37 +0200

A simple embedded domain method for node-based unstructured grid solvers is presented. The key modification of the original, edge-based solver is to remove all geometry-parameters (essentially the normals) belonging to edges cut by embedded surface faces. Several techniques to improve the treatment of boundary points close to the immersed surfaces are explored. Alternatively, higher-order boundary conditions are achieved by duplicating crossed edges and their endpoints. Adaptive mesh refinement based on proximity to or the curvature of the embedded CSD surfaces is used to enhance the accuracy of the solution. User-defined or automatic deactivation for the regions inside immersed solid bodies is employed to avoid unnecessary work. Several examples are included that show the viability of this approach for inviscid and viscous, compressible and incompressible, steady and unsteady flows, as well as coupled fluid–structure problems.

Computation of Compressible Flows using a Two-equation Turbulence Model on Unstructured Grids

María Jesús Samper — Mon, 06 Jul 2020 15:11:59 +0200

This paper presents a numerical method for solving compressible turbulent flows using a k - l turbulence model on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multi-stage Runge-Kutta time stepping scheme, while the turbulence equations are advanced using a multi-stage point-implicit scheme. The positivity of turbulence variables is achieved using a simple change of dependent variables. The developed method is used to compute a variety of turbulent flow problems. The results obtained are in good agreement with theoretical and experimental data, indicating that the present method provides a viable and robust algorithm for computing turbulent flows on unstructured meshes.

A Linelet preconditioner for incompressible flows

María Jesús Samper — Mon, 06 Jul 2020 15:05:17 +0200

A parallel linelet preconditioner has been implemented to accelerate finite element (FE) solvers for incompressible flows when highly anisotropic meshes are used. The convergence of the standard preconditioned conjugate gradient (PCG) solver that is commonly used to solve the discrete pressure equations, greatly deteriorates due to the presence of highly distorted elements, which are of mandatory use for high Reynolds-number flows. The linelet preconditioner notably accelerates the convergence rate of the PCG solver in such situations, saving an important amount of CPU time. Unlike other more sophisticated preconditioners, parallelization of the linelet preconditioner is almost straighforward. Numerical examples and some comparisons with other preconditioners are presented to demonstrate the performance of the proposed preconditioner.

Applications of patient-specific CFD in medicine and life science

María Jesús Samper — Mon, 06 Jul 2020 15:01:41 +0200

Recent advances in medical image segmentation, grid generation, flow solvers, realistic boundary conditions, fluid–structure interaction, data reduction and visualization arc reviewed with special emphasis on patient‐specific flow prediction. At the same time, present shortcomings in each one of these areas are identified. Several examples are given that show that this methodology is maturing rapidly, and may soon find widespread use in medicine.