Mot d'introduction

• Jean-Paul Caltagirone (Bordeaux INP)

Room: 2ème étage de la FRUMAM

Efficient Solution Strategies for Coupled Stokes–Darcy Problems

• Iryna Rybak (University of Stuttgart)

Room: 2ème étage de la FRUMAM

From finite volume and finite element methods to discontinuous Galerkin approach -- applications in fluid dynamics

• Vít Dolejší (Charles University in Prague)

Room: 2ème étage de la FRUMAM The discontinuous Galerkin (DG) method exhibits an amazing technique for the numerical solution of partial differential equations. DG method employs the advantages of more classical finite element (FE) and finite volume (FV) methods, particularly the high order of accuracy and discontinuous approximation. The later property significantly improves the stability of numerical scheme which is beneficial namely for problems of fluid dynamics when the convection is dominating. We briefly mention the conection of DG method to FV and FE discretization sand discuss additional favourable properties of this approach: the realization of boundary conditions through boundary penalty, the hp-mesh adaptation, the use of dynamically changing grids for time dependent problems and two-level domain decomposition preconditioners. Finally, we present several numerical examples for practical problems arising in porous media flows and non-hydrostatic mesoscale atmospheric modeling.

Calibration of stress--jump conditions for arbitrary flow directions in fluid--porous systems

• Joscha Nickl (Aix-Marseille université et University of Stuttgart)

Room: 2ème étage de la FRUMAM The coupling of Stokes and Darcy's equations for simulating flow in porous media and adjacent free-flow regions has led to various coupling conditions being developed. Notably, Angot et al. [Phys. Rev. E 95 (2017) 063302-1–063302-16] introduced stress jump conditions that accommodate arbitrary flow directions at the interface. These conditions incorporate a friction tensor whose values remain unknown. While calibration has been achieved for one-dimensional flow, validation of the stress jump conditions in two-dimensional scenarios remains absent. Through comprehensive analysis of multiple porous medium configurations and flow regimes, we determine the unknown parameters in these conditions by comparison with reference solutions derived from pore-scale simulations. Our investigation compares various optimization methods for calibration purposes. Despite having three unknown parameters, we demonstrate that leveraging the porous-medium structure allows reduction to a two-dimensional problem without compromising model performance. Finally, a regional sensitivity analysis reveals how susceptible the simulation results are to variations in the friction tensor components.

Mot d'introduction

• Kai Schneider (Aix-Marseille Université)

Room: 2ème étage de la FRUMAM

Immersed boundary methods for numerical simulation of confined fluid and plasma turbulence in complex geometries

• Kai Schneider (Aix-Marseille Université)

Room: 2ème étage de la FRUMAM

Méthodes de pénalisation volumique pour la résolution numérique du plasma de bord dans un tokamak

• Thomas Auphan (Centre de Physique des Particules de Marseille)

Room: 2ème étage de la FRUMAM Dans cette exposé on traitera d'un des thèmes de recherche cher à Philippe Angot : les méthodes de pénalisation volume pour le traitement des conditions aux limites dans ces domaines complexes. Je présenterai les travaux qui ont fait partie de ma thèse de doctorat co-dirigée par Philippe Angot et Olivier Guès : l'étude théorique et numérique de méthodes de pénalisation volumique dans le cadre de la simulation numérique du plasma proche de la paroi d'un réacteur à fusion de type tokamak.

Convergence of the fully discrete incremental projection scheme for incompressible flows

• Thierry Gallouët

Room: 2ème étage de la FRUMAM The aim of this talks is to prove the convergence of the approximate solutions, given by a first order in time incremental projection scheme, to a weak solution of the time-dependent incompressible Navier-Stokes equations, without any assumption of existence or regularity assumptions on the exact solution.