Hugues Digonnet

Parallel meshing and remeshing

A parallel meshing technique using a combination between a local remeshing technique and repartitioning is presented. The meshing method is based on local mesh topology optimizations and is shown to work for all meshing applications from adaptive remeshing to mesh generation by using a minimal volume principle. Parallel remeshing is performed independently on each subdomain with fixed interfaces. A constrained repartitioning technique is introduced to move the interfaces between subdomains in an optimal way. Repartitioning and remeshing are iterated until a good mesh and a good partition are reached. Several examples are given for different meshing objectives. Application examples are shown with the commercial code Forge3, devoted to large deformation analysis and equipped with the proposed remeshing technique.

Stabilized finite element method for incompressible flows with high Reynolds number

In the following paper, we discuss the exhaustive use and implementation of stabilization finite element methods for the resolution of the 3D time-dependent incompressible Navier-Stokes equations. The proposed method starts by the use of a finite element variational multiscale (VMS) method, which consists in here of a decomposition for both the velocity and the pressure fields into coarse/resolved scales and fine/unresolved scales. This choice of decomposition is shown to be favorable for simulating flows at high Reynolds number. We explore the behaviour and accuracy of the proposed approximation on three test cases. First, the lid-driven square cavity at Reynolds number up to 50,000 is compared with the highly resolved numerical simulations and second, the lid-driven cubic cavity up to Re=12,000 is compared with the experimental data. Finally, we study the flow over a 2D backward-facing step at Re=42,000. Results show that the present implementation is able to exhibit good stability and accuracy properties for high Reynolds number flows with unstructured meshes.

Development of numerical tools for the multiscale modelling of recrystallization in metals, based on a digital material framework

This work is currently under development within the framework of an American‐European project (Digimat Project). The paper details the development of some numerical tools dedicated to the digital representation of metallic materials structures, to the finite element modelling of the polycrystalline microstructure deformation under large strains and to the subsequent recrystallization. The level set method used for the description of the microstructure interfaces is shown to represent a common base to all these developments.

Dynamic load-balancing of finite element applications with the DRAMA library

The DRAMA library, developed within the European Commission funded (ESPRIT) project DRAMA, supports dynamic load-balancing for parallel (message-passing) mesh-based applications. The target applications are those with dynamic and solution-adaptive features. The focus within the DRAMA project was on finite element simulation codes for structural mechanics. An introduction to the DRAMA library will illustrate that the very general cost model and the interface designed specifically for application requirements provide simplified and effective access to a range of parallel partitioners. The main body of the paper will demonstrate the ability to provide dynamic load-balancing for parallel FEM problems that include: adaptive meshing, re-meshing, the need for multi-phase partitioning.

Cimlib: A Fully Parallel Application For Numerical Simulations Based On Components Assembly

This paper presents CIMLIB with its two main characteristics: an Object Oriented Program and a fully parallel code. CIMLIB aims at providing a set of components that can be organized to build numerical simulation of a certain process. We describe two components: one treats the complex task of parallel remeshing, the other puts the focus on the Finite Element modeling. In a second part, we present some parallel performances and an example of a very large simulation (over a mesh of 25 millions nodes) that begins with the mesh generation and ends up writing results files, all done using 88 processors.

3D CAFE modeling of grain structures: application to primary dendritic and secondary eutectic solidification

A three-dimensional model is presented for the prediction of grain structures formed in casting. It is based on direct tracking of grain boundaries using a cellular automaton (CA) method. The model is fully coupled with a solution of the heat flow computed with a finite element (FE) method. Several unique capabilities are implemented including (i) the possibility to track the development of several types of grain structures, e.g. dendritic and eutectic grains, (ii) a coupling scheme that permits iterations between the FE method and the CA method, and (iii) tabulated enthalpy curves for the solid and liquid phases that offer the possibility to work with multicomponent alloys. The present CAFE model is also fully parallelized and runs on a cluster of computers. Demonstration is provided by direct comparison between simulated and recorded cooling curves for a directionally solidified aluminum?7?wt% silicon alloy.

Dynamic Parallel Adaption for Three Dimensional Unstructured Meshes: Application to Interface Tracking

The anisotropic mesh adaption techniques in the last decade have dramatically improved the numerical simulations accuracy of complex problems. An optimal anisotropic mesh adaption consists in refining and coarsening the mesh, by using a metric to specify stretching directions, in order to accurately capture physical anisotropy such as shock waves, contact discontinuities, vortexes, boundary layers and free surfaces. Thus, we propose in this paper, an anisotropic a posteriori error estimator that controls the error due to mesh discretization in all space directions. From the a posteriori error analysis, we obtain an optimal metric (optimal mesh) as a minimum of an error indicator function and for a given number of elements. The optimal metric obtained is used to build an optimal mesh for the given number of elements. Furthermore, solutions for the physical problems illustrated here are often more accurate on adapted meshes than those obtained on globally-refined meshes and at a much lower cost.

Optimized parallel computing for cellular automaton–finite element modeling of solidification grain structures

A numerical implementation of a three-dimensional (3D) cellular automaton (CA)?finite element (FE) model has been developed for the prediction of solidification grain structures. For the first time, it relies on optimized parallel computation to solve industrial-scale problems (centimeter to meter long) while using a sufficiently small CA grid size to predict representative structures. Several algorithm modifications and strategies to maximize parallel efficiency are introduced. Improvements on a real case simulation are measured and discussed. The CA?FE implementation here is demonstrated using 32 computing units to predict grain structure in a 2.08?m???0.382?m???0.382?m ingot involving 4.9 billion cells and 1.6 million grains. These numerical improvements permit tracking of local changes in texture and grain size over real-cast parts while integrating interactions with macrosegregation, heat flow and fluid flow. Full 3D is essential in all these analyses, and can be dealt with successfully using the implementation presented here.

Advanced parallel computing in material forming with CIMLib

This paper presents a fully parallel multi-component Library called CIMLib. CIMLib contains a set of components that allow to build efficiently numerical simulation of a various processes mainly in material forming. We describe in this paper the main components of the library: parallel mesh partitioning, parallel remeshing, the Finite Element modelling and the parallel storage and visualization. Two large numerical simulations are presented: the first one focuses on a multi-bodies contact problem, including friction, for complex 3D forming processes. The mesh is evolving during the simulation from 52K nodes to 7M nodes and 64 cores are used to handle this application. The second simulation concerns the multiphase problems involved in the manufacturing processes of full parts. The simulation is done using 88 processors and the mesh is refined during the simulation the final mesh has over 25M nodes.

Adaptive time-step with anisotropic meshing for incompressible flows

This paper presents a method of combining anisotropic mesh adaptation and adaptive time-stepping for Computational Fluid Dynamics (CFD). First, we recall important features of the anisotropic meshing approach using a posteriori estimates relying on the length distribution tensor approach and the associated edge based error analysis. Then we extend the proposed technique to contain adaptive time advancing based on a newly developed time error estimator. The objective of this paper is to show that the combination of time and space anisotropic adaptations with highly stretched elements can be used to compute high Reynolds number flows within reasonable computational and storage costs. In particular, it will be shown that boundary layers, flow detachments and all vortices are well captured automatically by the mesh. The time-step is controlled by the interpolation error and preserves the accuracy of the mesh adapted solution. A Variational MultiScale (VMS) method is employed for the discretization of the Navier-Stokes equations. Numerical solutions of some benchmark problems demonstrate the applicability of the proposed space-time error estimator. An important feature of the proposed method is its conceptual and computational simplicity as it only requires from the user a number of nodes according to which the mesh and the time-steps are automatically adapted.