Thierry Coupez

Finite element solution of the 3D mold filling problem for viscous incompressible fluid

A general solution for the 3D mold filling by incompressible viscous fluid is described. It is based on the combination of an extended flow solver and the solution of a transport equation governing the flow front position. The flow solver uses tetrahedral elements, a first order stable mixed velocity pressure formulation entering in the family of the MINI-element, and a global iterative solution. The characteristic function of the fluid domain is shown to follow a conservative law and the moving fluid description is transformed into a transport equation in the whole domain to be filled. An explicit discontinuous Taylor-Galerkin scheme is introduced to solve this fluid motion equation. This scheme is shown to be consistent and conservative. The calculated shape of the fountain flow front is compared to the reference one. The flexibility and the robustness of this approach is demonstrated through complicated flows and geometries examples.

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.

Metric construction by length distribution tensor and edge based error for anisotropic adaptive meshing

Metric tensors play a key role to control the generation of unstructured anisotropic meshes. In practice, the most well established error analysis enables to calculate a metric tensor on an element basis. In this paper, we propose to build a metric field directly at the nodes of the mesh for a direct use in the meshing tools. First, the unit mesh metric is defined and well justified on a node basis, by using the statistical concept of length distribution tensors. Then, the interpolation error analysis is performed on the projected approximate scalar field along the edges. The error estimate is established on each edge whatever the dimension is. It enables to calculate a stretching factor providing a new edge length distribution, its associated tensor and the corresponding metric. The optimal stretching factor field is obtained by solving an optimization problem under the constraint of a fixed number of edges in the mesh. Several examples of interpolation error are proposed as well as preliminary results of anisotropic adaptation for interface and free surface problem using a level set method.

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.

Finite element model of primary recrystallization in polycrystalline aggregates using a level set framework

The paper describes a robust finite element model of interface motion in media with multiple domains and junctions, as is the case in polycrystalline materials. The adopted level set framework describes each domain (grain) with a single level set function, while avoiding the creation of overlap or vacuum between these domains. The finite element mesh provides information on stored energies, calculated from a previous deformation step. Nucleation and growth of new grains are modelled by inserting additional level set functions around chosen nodes of the mesh. The kinetics and topological evolutions induced by primary recrystallization are discussed from simple test cases to more complex configurations and compared with the Johnson–Mehl–Avrami–Kolmogorov theory.

Génération de maillage et adaptation de maillage par optimisation locale

ABSTRACT The need of meshing informing processes motivated the development of the meshing method which is described in this paper. A new definition for a mesh is introduced using minimal volume principle which is proven. It is shown that non conform meshes can be improved to recover a conform mesh. The generic form of the global optimization algorithm is given, based on the combination of local improvement of the neighborhood of the nodes and the edges. A layer of virtual boundary elements is introduced in order to couple the surface and the volume remeshing. A mesh size map can be introduced directly in the shape factor of elements. The mesh optimization of the modified shape factor provides implicitly the adapted mesh. Finally the adaptation cycle is presented, which consists in computing a mesh size map on the current mesh, to adapt the mesh, to compute again the mesh sie map and to adapt again until a convergence state is reached. Examples in static and dynamic adaptation are given.

3-D finite element modelling of the forging process with automatic remeshing

Abstract The purpose of this paper is to illustrate the interest of using a finite element program to simulate the forging process of industrial parts. The forge3 code, which can simulate hot forging of industrial parts, is presented: thermo-mechanical formulation, numerical resolution. It is well known that, in an updated lagrangian approach using a convective mesh, the degeneracy of the mesh occurs very rapidly and stops the simulation. An automatic mesh generation procedure for 3-D complex geometries has been developed with which it is possible to create the initial mesh of the billet as well as to remesh it after its degeneracy. This technique enables to simulate the whole forging process of complex industrial parts using quadratic tetrahedra. In order to show the effectiveness of the method, the example of the forging of a tripod has been computed. The simulation results show that the computation can be carried out using the described remeshing procedure and that it can be applied with success to even more complex geometries.

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.

A Taylor discontinuous Galerkin method for the thermal solution in 3D mold filling

Abstract In continuity with the work of the authors, a Taylor discontinuous Galerkin method is introduced to solve the thermal problem in the context of the 3D mold filling by viscous incompressible fluid. This numerical scheme is designed to deal with the physical phenomena of shear and temperature dependent viscosity, viscous heat generation and heat transfer by conduction and convection. A mixed temperature/heat flux formulation is introduced which enables to capture high temperature gradients without any polluting oscillations of the solution. The temperature and the heat flux are interpolated by a constant per element (P0 element) and an explicit solution based on the recursive time derivation of the equations is described. This approach aims to simulate non-isothermal flows of viscous fluid with moving free surfaces and more particularly the injection molding process involving thermal shocks at the interface between the cold mold wall and the hot polymer. The extension of the method in the context of the mold filling problem is given and several examples are proposed. The thermal solver is coupled to the mechanical solver which is based on a first order mixed finite element method for the kinematic and the solution of a transport equation for the flow front motion description. The proposed 3D technic is validated with known solutions and it is compared to 2D calculation obtained by different approaches.