An eXtreme Mesh deformation method to follow sharp physical interfaces

This project will develop an innovative approach,

X-MESH, to overcome a major difficulty associated with engineering

analysis: we aim to provide a revolutionary way to track physical

interfaces in finite element simulations using extreme deformation of

the meshes.

Unprecedented low computational cost, high robustness and

accuracy are expected as the proposed approach is designed to avoid

the pitfalls of the current methods, especially for topological changes.

The key idea of the project

has emerged in a synergistic brainstorming between J.-F. Remacle

(meshing methods) and N. Moës (computational methods). This key idea

is to allow elements to deform up to zero measure. For example, a

triangle can deform to an edge or even a point. This idea is rather

extreme and totally revisits the interaction between the meshing

community and the computational community who, for decades, have

striven to interact through beautiful meshes.

Six areas in fluid and solid mechanics as well as heat

transfer are targeted. Interfaces will be either (i) material,

i.e. attached to particles of matter (the interface between two

immiscible fluids or the dry interface in a wetting and drying model)

(ii) immaterial, i.e. migrating through the material (a

solidification front, contact front, yield front in yield stress fluid

flow or a crack front).

Successes brought by X-MESH are expected in the following engineering

areas: safety design and maintenance, manufacturing processes, coastal

engineering, energy efficiency, ocean modeling to cite a few. The

project takes place in a stimulating environment mixing senior staff

with PhDs and Post-docs to produce and disseminate publications with

open source pieces of software. It also intends to create a synergy at

large with the computational communities dealing with interfaces and

fronts in all fields of science: topology optimization,

superconductivity, tissue growth, hydrogel swelling, crystal growth,

ferroelectric crystal etc.