Soutenance de thèse de Max Beckermann

Complex free-surface fluid flows at low-Reynolds number, such as free-surface flows, are of great interest for a wide range of engineering applications and natural phenomena. The main challenge of their simulation lies in the simultaneous computation of both the fluid solution and the evolving interface over time. The Particle Finite Element Method (PFEM) has proven particularly well suited to such problems, as its Lagrangian nature naturally captures interface evolution. The method combines a stabilized finite element fluid solver with efficient re-meshing algorithms. However, despite these advantages, PFEM remains computationally expensive, especially for large-scale simulations and parametric studies.

This thesis investigates the use of model-order reduction techniques to accelerate PFEM simulations and explores their practical implications. First, a novel time-global PFEM formulation is proposed, separating mesh propagation from field resolution and enabling a non-incremental framework better suited to model reduction strategies. 

We then introduce an expanded discretization with unique particle indexing, enabling data reduction for PFEM solutions. Several reduced basis construction strategies are developed, exploiting the Lagrangian displacement as a reduction map to improve the reducibility of PFEM solutions. We show that, for simple benchmarks, the velocity and pressure of particles with incomplete trajectories can be approximated by a low-dimensional linear manifold.

Finally, reduced formulations for the fluid problem itself are investigated. First, it is shown that efficient reduction requires the linearization the geometric nonlinearities to reduce the underlying computational cost.  A Proper Orthogonal Decomposition (POD)-based approach is then proposed, in which the reduced basis is generated from full-order snapshots, followed by multiple potential PGD strategies that eliminate the need for full-order solutions.  Particular attention is devoted to the stability of the reduced formulation, which proves to be a non-trivial issue; several solutions are proposed.

 

Composition du jury :

• David RYCKELYNCK, Professor, Mines Paris PSL University,  Rapporteur & Examinateur  
• Alessandro FRANCI, Associate Professor, Universitat Politècnica de Catalunya, Rapporteur & Examinateur
• Ronan Vicquelin, Professor, CentraleSupélec - Université Paris-Saclay,  Examinateur  
• Umberto PEREGO, Professor, Politecnico di Milano, Examinateur 
• Rodolfo André Kuche SANCHES, Associate Professor, Universidade de São Paulo, Examinateur
• Alexandre DABY-SEESARAM, Assistant professor, ENSTA - IP Paris,  Examinateur