CEMEF PhD 2017: Model Order Reduction for Interfacial Flows

The Centre for Material Forming (CEMEF) is one of the research laboratories of MINES ParisTech (top executive French engineering school).
CEMEF studies the materials processings in all their aspects: physics, chemical physics, thermal and mechanical analysis and numerical modelling. Researches are on a large range of materials: metals, synthetic and bio polymers, food stuff, composites and nanocomposites, glass, ceramics…

Thesis work description:
 
Fluid flows involving interfaces between different materials, or between different phases of a same material, are of paramount importance in many fields of science and engineering. Numerical simulation is often the only way for industrial companies to understand, predict and control these flows. Numerous numerical methods based on Finite Elements and Finite Volumes have been devised for the simulation of interfacial flows in the last decades. Many of them rely on local mesh refinement in the vicinity of the interface to compensate their inherent lack of accuracy. Because the interface evolves in time, the mesh has to be periodically adapted to follow it. This results in simulations that are computationally extremely intensive.

On the other hand, an alternative known as Model Order Reduction (MOR) is gaining interest. It aims to approximate a large-scale system with a reduced model that is much less computationally demanding. Applied to flow problems in industrial processes and products, such a fast prediction capability opens new possibilities for engineers. Up to now, however, little research has focused on developing MOR procedures that suit the type of mesh-adaptive simulation required for flows involving interfaces.

The goal of the PhD work, in the framework of the ANR project ROMINA, is to develop MOR techniques for mesh-adaptive, complex-physics simulation of interfacial flows. It will build on methods originating in two research labs of MINES ParisTech. The large-scale multi-phase problems will be solved through the Finite-Element CFD solvers of CEMEF. The MOR procedures will be based on the hyper-reduction techniques invented at the Centre des Matériaux. The new methods will be tested on academic test cases and assessed on cases that reflect industrial applications. The results are expected to be published in scientific journals and presented in international conferences.