Mattéo Couplet
PhD student
Ir. MAP at UCLouvain in 2020

Main project: Three-dimensional multi-block decomposition for automatic hexahedral mesh generation and application to fluid flow simulations.
Funding: FNRS
Supervisor(s): Jean-François Remacle, Philippe Chatelain

In computational physics, the vast majority of Partial Differential Equation (PDE) solvers rely on a spatial discretization of the bulk of the domain, typically a mesh. Thus far, geometrically complex domains are discretized predominantly using unstructured meshes, on which the PDE is subsequently solved using the Finite Element Method. Methods based on unstructured meshes are however inherently penalized in their computational efficiency. On the contrary, the regularity of block structured meshes can be leveraged to build efficient algorithms. For this reason, automatic generation of block-structured meshes is the holy grail of mesh generation.

A first objective of the research project is therefore to explore new approaches for generating multiblock decompositions of general 3D domains. We will build on the recent developments in 3D frame fields and aim at improving formulations based on the constrained minimization of an energy function. A second lead that will be explored is based on the decomposition of the domain in convex sub-regions, on which existing methods are more robust.

Constructing a new class of meshes is only relevant if those meshes are endowed with a true benefit in terms of CPU/GPU time and accuracy. A second objective is therefore to extend existing Computational Fluid
Dynamics technologies for Cartesian grids to multiblock grids. In particular, we want to take advantage of the conformal map-like nature of the mesh to increase computational performance, and also show how our methodology can be applied to models with moving or deforming boundaries.

IMMC main research direction(s):
Computational science

computational geometry
finite elements
mesh generation

Research group(s): MEMA