Scipedia: Journal's Papers

Smoothed surface gradients for panel methods

María Jesús Samper — Wed, 20 Feb 2019 11:55:04 +0100

A weak form to compute the dipolar and monopolar surface gradients, related to a low-order panel method, is shown. The flow problem is formulated by means of a three-dimensional potential model and the discretization is based on Morino's formulation for the perturbation velocity potential. On the body surface, this representation reduces to a boundary integral equation with the source (or monopolar) and the doublet (or dipolar) densities. The first of the two is found by application of the boundary flow condition, and the second one is the unknown over the body surface. A lower panel method is used for the analytic integrations of both the monopolar and dipolar influence coefficients. The surface velocity field is computed after solving the linear system, with a strong and a weak form of the Stokes theorem, which is oriented to fairly non-structured panel meshes. The proposed method is validated by comparing the numerical results with analytical ones for an isolated sphere and includes a prediction over a car-like configuration.

A closed form for low-order panel methods

María Jesús Samper — Wed, 20 Feb 2019 11:48:29 +0100

A closed form for the computation of the dipolar and monopolar influence coefficients related to a low-order panel method is shown. The flow problem is formulated by means of a three-dimensional potential model; the method of discretization is based on the Morino formulation for the perturbation velocity potential. On the body surface this representation reduces to an integral equation with the source (or monopolar) and the doublet (or dipolar) densities. The former is found by application of the boundary condition, and the latter is the unknown over the surface of the body. The lower panel method is used for the analytical integrations of the monopolar and dipolar influence coefficients, with special attention to avoid a logarithmic singularity in the monopolar matrix when flat fairly structured meshes that are common in ship-wave calculations are used.

A finite point method for incompressible flow problems

María Jesús Samper — Tue, 22 Jan 2019 11:47:07 +0100

A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment calculus (FIC) procedure developed by Oñate [14]. An enhanced fractional step procedure allowing the semi-implicit numerical solution of incompressible fluids using the FPM is described. Examples of application of the stabilized FPM to the solution of two incompressible flow problems are presented.

Finite element solution of free‐surface ship‐wave problems

María Jesús Samper — Wed, 12 Dec 2018 12:37:40 +0100

An unstructured finite element solver to evaluate the ship‐wave problem is presented. The scheme uses a non‐structured finite element algorithm for the Euler or Navier–Stokes flow as for the free‐surface boundary problem. The incompressible flow equations are solved via a fractional step method whereas the non‐linear free‐surface equation is solved via a reference surface which allows fixed and moving meshes. A new non‐structured stabilized approximation is used to eliminate spurious numerical oscillations of the free surface.

An unstructured grid-based, parallel free surface solver

María Jesús Samper — Mon, 04 Mar 2019 12:00:14 +0100

An unstructured grid-based, parallel-free surface solver is presented. The overall scheme combines a finite-element, equal-order, projection-type 3-D incompressible flow solver with a finite element, 2-D advection equation solver for the free surface equation. For steady-state applications, the mesh is not moved every timestep, in order to reduce the cost of geometry recalculations and surface repositioning. A number of modifications required for efficient processing on shared-memory, cache-based parallel machines are discussed, and timings are shown that indicate scalability to a modest number of processors. The results show good quantitative comparison with experiments and the results of other techniques. The present combination of unstructured grids (enhanced geometrical flexibility) and good parallel performance (rapid turnaround) should make the present approach attractive to hydrodynamic design simulations.

A mesh-free finite point method for advective-diffusive transport and fluid flow problems

María Jesús Samper — Thu, 20 Dec 2018 13:00:56 +0100

The finite point method (FPM) is a gridless numerical procedure based on the combination of weighted least square interpolations on a cloud of points with point collocation for evaluating the approximation integrals. In the paper, details of a procedure for stabilizing the numerical solution for advective-diffusive transport and fluid flow problems using the FPM are given. The method is based on a consistent introduction of the stabilizing terms in the governing differential equations. One example showing the applicability of the FPM is given.

Algebraic Discrete Nonlocal (DNL) Absorbing Boundary Condition for the Ship Wave Resistance Problem

María Jesús Samper — Mon, 04 Mar 2019 10:12:45 +0100

An absorbing boundary condition for the ship wave resistance problem is presented. In contrast to the Dawson-like methods, it avoids the use of numerical viscosities in the discretization, so that a centered scheme can be used for the free surface operator. The absorbing boundary condition is “completely absorbing,” in the sense that the solution is independent of the position of the downstream boundary and is derived from straightforward analysis of the resulting constant-coefficients difference equations, assuming that the mesh is 1D-structured (in the longitudinal direction) and requires the eigen-decomposition of a matrix one dimension lower than the system matrix. The use of a centered scheme for the free surface operator allows a full finite element discretization. The drag is computed by a momentum flux balance. This method is more accurate and guarantees positive resistances.

Boundary conditions for finite element simulations of convective flows with artificial boundaries

María Jesús Samper — Wed, 12 Dec 2018 11:21:07 +0100

We examine the use of natural boundary conditions and conditions of the Sommerfeld type for finite element simulations of convective transport in viscous incompressible flows. We show that natural boundary conditions are superior in the sense that they always provide a correct boundary condition, as opposed to the Sommerfeld‐type conditions, which can lead to a singular formulation and a great loss of accuracy. For the Navier–Stokes equations, the natural boundary conditions must be combined with a simple method to eliminate perturbations on the pressure at the open boundary, which is the source of most errors.

Petrov-Galerkin methods for the transient advective-diffusive equation with sharp gradients

María Jesús Samper — Wed, 12 Dec 2018 10:53:52 +0100

A Petrov–Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally exhibited by the numerical solution of the transient advective–diffusive equation in the vicinity of sharp gradients produced by transient loads and boundary layers. The formulation may be written as a generalization of the Galerkin Least‐Square method.

A stabilized finite point method for analysis of fluid mechanics problems

María Jesús Samper — Tue, 20 Nov 2018 16:09:05 +0100

flow type problems is presented. The method is based on the use of a weighted
least square interpolation procedure together with point collocation for evaluating the
approximation integrals. Some examples of application to convective trasport and
compressible flow problems are presented.

A finite point method in computational mechancis. Applications to convective transport and fluid flow.

María Jesús Samper — Mon, 18 Feb 2019 12:18:23 +0100

The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals. Some examples showing the accuracy of the method for solution of adjoint and non‐self adjoint equations typical of convective‐diffusive transport and also to the analysis of compressible fluid mechanics problem are presented.

Finite volumes and finite elements: Two ‘good friends’

María Jesús Samper — Wed, 19 Dec 2018 12:32:44 +0100

In this paper a comparison between the finite element and the finite volume methods is presented in the context of elliptic, convective–diffusion and fluid flow problems. The paper shows that both procedures share a number of features, like mesh discretization and approximation. Moreover, it is shown that in many cases both techniques are completely equivalent.

A simple hidden line algorithm for a structural model of planar elements

María Jesús Samper — Mon, 11 Mar 2019 11:03:58 +0100

A simple and efficient hidden line algorithm for finite element models is described here. The algorithm runs quickly, it has low computer storage and core size requirements. The method does not require any calculation of trigonometric functions and is able to treat planar quadrilateral polygons without subdividing them into triangles. Detailed flowcharts are presented for a better understanding.

Reduction methods and explicit time integration technique in structural dynamics

María Jesús Samper — Mon, 11 Mar 2019 10:53:38 +0100

A computer procedure for economically time-integrating large structural dynamics problems is presented. The main process is described as a two-step discretisation, the first one being performed by the finite element method. An error measure is proposed in order to check the validity of the results. The reduced system of equations is integrated by using the central differences explicit scheme. Linear and physical nonlinear examples of applications are shown.

The entire procedure seems to be particularly well-suited to be programmed in small computers, where the core and velocity characteristics impose severe restrictions on the problems to be directly solved.

Upwind parameters for the numerical solution of the compressible flow Euler equations

María Jesús Samper — Mon, 11 Mar 2019 12:10:27 +0100

The present work generalises the earlier work in which a variational principle technique was presented in order to evaluate the magnitude of upwind required to solve the compressible flow equations.

The technique proposed allows the choice of nodes where upwind is required in each of the relevant equations. It is a simple and mathematically consistent way of evaluating the amount of upwind or artificial viscosity to be introduced at every node and every equation involved.

Numerical implementation of a discontinuous finite element algorithm for phase-change problems

María Jesús Samper — Mon, 11 Mar 2019 11:16:26 +0100

This paper is devoted to the numerical solution of phase-change problems in two dimensions. The technique of finite elements is employed. The discretization is carried out using linear isoparametric elements and special attention is given to the accurate integration of functions presenting discontinuities at arbitrarily curved interfaces. This type of function arises in a natural way when dealing with phase-change problems because the enthalpy attains a discontinuity at the phase change temperature. To integrate the discontinuous functions in the phase-changing elements a second mapping is performed from the master element onto a new one for which the interface iis a straight line. The integrals are calculated using the Gaussian technique applied to each part of the divided element, which may be triangular or quadrilateral. The discontinuous integration technique improves the behaviour of the numerical method avoiding any possible loss of latent heat due to an inaccurate evaluation of the residual vector. Some important aspects of the solution of the nonlinear system of equations are discussed and several numerical examples are presented together with the details of the computational implementation of the algorithm.

On load interaction in the non linear buckling analysis of cylindrical shells

María Jesús Samper — Mon, 11 Mar 2019 12:26:13 +0100

The elastic stability of shells or shell-like structures under two independent load parameters is considered. One of the loads is associated to a limit point form of buckling, whereas the second is a bifurcation. A simple one degree of freedom mechanical system is first investigated, for which an analytical solution is possible. Next, a cylindrical shell under the combined action of axial load and localised lateral pressure is studied via a non linear, two-dimensional, finite element discretization. It is shown that both problems display the same general behaviour, with a stability boundary in the load space which is convex towards the region of stability. The results show the need of performing a full non-linear analysis to evaluate the stability boundary for the class of interaction problems considered.

Fluid flows around turbomachinery using an explicit pseudo‐temporal Euler FEM

María Jesús Samper — Wed, 06 Mar 2019 11:09:28 +0100

This work is devoted to the simulation by finite elements of nearly incompressible inviscid flows in real 3D geometries, by means of an Euler code based on the SUPG (streamline upwind Petrov–Galerkin) method, explicit forward Euler pseudo‐temporal time integration and periodic and absorbing boundary conditions, among other features. The main goal is the application to flow around turbomachinery, with special emphasis on the performance analysis of a given machine, that involves several numerical computations at different operation points. Finally, these results are summarized in the form of characteristic curves.

A Panel-Fourier Method for Free-Surface Flows

María Jesús Samper — Mon, 04 Mar 2019 12:11:25 +0100

A panel Fourier method for ship-wave flow problems is considered here. It is based on a three-dimensional potential flow model with a linearized free surface condition, and it is implemented by means of a low order panel method coupled to a Fourier series. The wave resistance is computed by pressure integration over the static wet hull and the wave pattern is obtained by a post-processing procedure. The strategy avoids the use of numerical viscosity, in contrast with the Dawson-like methods, widely used in naval panel codes, therefore a second centered scheme can be used for the discrete operator on the free surface. Numerical results including the wave pattern for a ferry along fifteen ship lengths are presented.

A general algorithm for compressible and incompressible flow. Stability analysis and explicit time integration

María Jesús Samper — Fri, 01 Mar 2019 11:48:19 +0100

Addresses two difficulties which arise when using a compressible code with equal order interpolation (non‐staggered grids in the finite‐difference nomenclature) to capture a steady‐state solution in the incompressible limit, i.e. at low Mach numbers. Explains that, first, numerical instabilities in the form of spurious oscillations in pressure pollute the solution and, second, the convergence to the steady state becomes extremely slow owing to bad conditioning of the different speeds of propagation. By using a stabilized method, allows the use of equal‐order interpolations in a consistent (weighted‐residual) formulation which stabilizes both the convection and the continuity terms at the same time. On the other hand, by using specially devised preconditioning, assures a rate of convergence independent of Mach number.