Abstract

The largest runs up-to-now are usually performed for simple symmetric positive definite systems. It is a reasonable approach when measuring the overall scalability of an algorithm/implementation. However, in order to have an impact in science and industry, we must extend scalability to the most challenging applications, since these are the ones that really require extreme scale simulation tools, e.g., multiscale, multiphysics, nonlinear, and transient problems. In this talk, we will discuss some of our experiences in the development of FEMPAR, an in-house finite element multiphysics and massively parallel simulator.

On one hand, we will talk about how to deal in a parallel element-based environment with multiphysics simulations that involve interface coupling, e.g., fluid-structure interaction. Our approach is based on the partition of topological meshes, and ghost element information, in order to define locally the degrees of freedom and the unknowns that must be communicated among processors.

On the other hand, we will discuss how we deal with the resulting multiphysics (non)linear systems. We have two different approaches to the problem: block preconditioning and monolithic solvers. Block preconditioning techniques are interesting in the sense that they allow us to decouple complex multiphysics problems into simpler (probably) one physics simulations. However, in order for block preconditioners to be effective, we must define effective approximation of Schur complement systems, which can be a complicated (and very heuristic) task. We will show how we have implemented complex (recursive) block preconditioning strategies in FEMPAR using abstract definitions of operators, and how this framework has been applied to different multiphysics solvers.

We will also discuss how we can reach sustained scalability up to large core-counts (about 400,000 cores in a BG/Q). Our in-house numerical linear algebra solvers are based on multilevel domain decomposition techniques, and their very efficient practical implementations based on overlapped and asynchronous techniques. We will consider two different approaches, the first one being a combination of block-preconditioning and multilevel domain decomposition, whereas the second one will be a truly monolithic domain decomposition approach.

Many multiphysics simulations are also multiscale, and the use of adaptively refined meshes can reduce even orders of magnitude the computational cost of simulations with respect to uniformly refined meshes. The possibility to reach extremely scalable adaptive multiphysics solvers would open the door to unprecedented simulations of challenging problems that are out of reach nowadays. In this sense, we will show how we are dealing with scalable adaptive solvers in FEMPAR, via a combination of the p4est library for parallel mesh refinement and dynamic load balancing in our element-based framework. Further, we will show how we modify our solvers to deal with nonconforming meshes through interfaces, and the effect of cheap space-filling curve partitions on solver robustness. 

Abstract

In this paper, current developments on the coupled thermomechanical computational simulation of metal casting processes are presented A thermodynamically consistent constitutive material model is derived from a thermoviscoplastic free energy function. A continuous transition between the initial fluid-like and the final solid-like is modeled by considering a J2 thermoviscoplastic model. Thus, an thermoelastoviscoplastic model, suitable for the solid-like phase, degenerates into a pure thermoviscous model, suitable for the liquid-like phase, according to the evolution of the solid fraction function. A thermomechanical contact model, taking into account the insulated effects of the air-gap due to thermal shrinkage of the part during solidification and cooling, is introduced. A fractional step method, arising from an operator split of the governing differential equations, is considered to solve the coupled problem using a staggered scheme. Within a finite element setting, using low-order interpolation elements, a multiscale stabilization technique is introduced as a convenient framework to overcome the Babuska-Brezzi condition and avoid volumetric locking and pressure instabilities arising in incompressible or quasi-incompressible problems. Computational simulation of industrial castings show the good performance of the model. 

Abstract

Nowadays, many open-source numerical codes are available to solve physical problems in structural mechanics, fluid flow, heat transfer, and neutron diffusion. However, even if these codes are often highly specialized in the numerical simulation of a particular type of physics, none of them allows simulating complex systems involving all the physical problems mentioned above. In this work we present a numerical framework, based on the SALOME platform, developed to perform multiscale and multiphysics simulations involving all the mentioned physical problems. In particular, the developed numerical platform includes the multigrid finite element in-house code FEMuS for heat transfer, fluid flow, turbulence and fluid-structure modeling; the open-source finite volume CFD software OpenFOAM; the multiscale neutronic code DONJON-DRAGON; and a system-scale code used for thermal-hydraulic simulations. Efficient data exchange among these codes is performed within computer memory by using the MED libraries, provided by the SALOME platform.

Abstract

A partitioned iterative method based on hierarchical decomposition is proposed for providing numerical modeling and analysis of the piezoelectric energy harvester which is involved in coupled fluid-structure interaction, coupled electro-mechanical, and a controlling electrical circuit for piezoelectric structural applications in energy harvesting. This circuitintegrated piezoelectric structural application in energy harvesting surrounded by fluid media takes the form of natural four-way coupling of fluid flow, the structure, the electromechanical effect of the piezoelectric material, and the electrical circuit. This can be formulated exactly as a fluid-structure-piezoelectric-circuit interaction. These coupled four fields are hierarchically decomposed into the fluid-structure interaction, structure-piezoelectric interaction, and piezoelectric-circuit interaction interactions. Then these subsystems are decomposed into each field. The proposed finite element method enables to reuse of existing techniques because of its modularity. Furthermore, scalability to multiphysics and multisystem couplings is expected. There are some numerical approaches in particular monolithic coupling methods are studied which are computationally expensive and leads to an ill-conditioned coefficient matrix. Nevertheless, accurate modeling for predicting the characteristics of this four-way coupling using partitioned methods has not yet been developed. This method enables an investigation of piezoelectric structures in fluid with complex geometry, material composition, and attached electrical circuits to the harvester. A flexible piezoelectric bimorph harvester in the converging channel is analyzed to demonstrate the efficiency of the proposed method. The results indicate that the method captures the coupled effect accurately.

Abstract

The most commonly used coupling schemes in partitioned multiphysics simulations suffer from a decrease in the order of convergence, specifically in the time domain; a phenomenon we call order degradation. This paper discusses when this issue arises and how it can be studied with a simple example. We present a simple mass-spring system of ordinary differential equations (ODEs) to analyze accuracy and energy conservation of different coupling schemes. The ability to restore higher order of convergence by using Strang splitting or waveform iterations is verified in the context of the presented example. This paper provides details on some aspects of the talk titled 'Design and evaluation of a waveform iteration­based approach for coupling heterogeneous time stepping methods via preCICE' given at WCCM-APCOM 2022.

Abstract

In fluid-structure interaction (FSI), the fluid and solid domains are permantently changing, coupled along a time-dependent, moving fluid-structure interface. The update of the fluid domain, i.e., in the numerical context, the mesh update is critical for robust and efficient simulations. Herein, we propose to inherently embed the mesh generation into the simulation.The FSI domain is defined based on structured building blocks that imply all the relevant information needed for the automatic mesh generation: Topology, geometry, and grading information. Transfinite maps play a crucial role for the definition of sub-meshes with any desired order and resolution in each building block. In every time step, a new mesh is generated, taking into account the deforming FSI interface. This generation is fast compared to the overall work load in each time step which is still dominated by the (iterative) solutions of the systems of equations. It is also very robust and removes any mesh entanglement by construction provided that suitable building blocks are selected once initially. Numerical results confirm the success of the proposed FSI strategy with integrated mesh generation.

Abstract

Many multiscale simulation problems require a many-to-one coupling between different scales. For such coupled problems, researchers oftentimes focus on the coupling methodology, but largely ignore software engineering and high-performance computing aspects. This can lead to inefficient use of hardware resources, on the one hand, but also inefficient use of human resources as solutions to typical technical coupling problems are constantly reinvented. This work proposes a flexible and application-agnostic software framework to couple independent simulation codes in a many-to-one fashion. To this end, we introduce a prototype of a new lightweight software component called Micro Manager, which allows us to reuse the coupling library preCICE for two-scale coupled problems. We demonstrate the applicability of the framework by a two-scale coupled heat conduction problem.

Abstract

This paper presents two procedures, based on the numerical multiscale theory, developed to predict the mechanical non-linear response of composite materials under monotonically increasing loads. Such procedures are designed with the objective of reducing the computational cost required in these types of analysis. Starting from virtual tests of the microscale, the solution of the macroscale structure via Classical First-Order Multiscale Method will be replaced by an interpolation of a discrete number of homogenized surfaces previously calculated. These surfaces describe the stress evolution of the microscale at fixed levels of an equivalent damage parameter (). The information required for these surfaces to conduct the analysis is stored in a Data Base using a json format. Of the two methods developed, the first one uses the pre-computed homogenized surface just to obtain the material non-linear threshold, and generates a Representative Volume Element (RVE) once the material point goes into the nonlinear range; the second method is completely off-line and is capable of describing the material linear and non-linear behavior just by using the discrete homogenized surfaces stored in the Data Base. After describing the two procedures developed, this manuscript provides two examples to validate the capabilities of the proposed methods

Abstract

Abstract

In order to enhance safety assessments of Sodium Fast Reactors (SFR), some scenarios involving transient Fluid-Structure Interactions (FSI) are investigated using numerical simulation tools. SFRs are indeed quite sensible to mechanical deformations regarding their nuclear power (see [1] for more details). The originality of the scenario presented in the paper is to consider sufficient large mechanical interactions involving a large pressure decrease in the fluid domain. This decrease leads to vaporization of the fluid and then to a different impact on the structures. By means of the open-source software Code Saturne developed by EDF [2], this scenario is investigated in 2D using a 3-equation model derived from the Navier-Stokes equations while an harmonic model is applied for the mechanical structures. The code coupling is managed using the Newmark algorithm for the mechanical part and a damped fixed point algorithm in order to get a converged coupled FSI problem.