https://hal-insu.archives-ouvertes.fr/insu-03846740Bloch, HélèneHélèneBlochUVSQ - Université de Versailles Saint-Quentin-en-YvelinesTremblin, PascalPascalTremblinUVSQ - Université de Versailles Saint-Quentin-en-YvelinesGonzález, MatthiasMatthiasGonzálezAIM (UMR_7158 / UMR_E_9005 / UM_112) - Astrophysique Interprétation Modélisation - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - INSU - CNRS - Institut national des sciences de l'Univers - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris CitéAudit, EdouardEdouardAuditUVSQ - Université de Versailles Saint-Quentin-en-YvelinesTowards a multigrid method for the M<SUB>1</SUB> model for radiative transferHAL CCSD2022Radiative transferMoment modelGeometric multigridMathematics - Numerical Analysis[SDU] Sciences of the Universe [physics]POTHIER, Nathalie2022-11-10 11:59:092022-11-12 03:26:552022-11-10 11:59:09enJournal articles10.1016/j.jcp.2022.1115741We present a geometric multigrid solver for the M<SUB>1</SUB> model of radiative transfer without source terms. In radiative hydrodynamics applications, the radiative transfer needs to be solved implicitly because of the fast propagation speed of photons relative to the fluid velocity. The M<SUB>1</SUB> model is hyperbolic and can be discretized with an HLL solver, whose time implicit integration can be done using a nonlinear Jacobi method. One can show that this iterative method always preserves the admissible states, such as positive radiative energy and reduced flux less than 1. To decrease the number of iterations required for the solver to converge, and therefore to decrease the computational cost, we propose a geometric multigrid algorithm. Unfortunately, this method is not able to preserve the admissible states. In order to preserve the admissible state states, we introduce a pseudo-time such that the solution of the problem on the coarse grid is the steady state of a differential equation in pseudo-time. We present preliminary results showing the decrease of the number of iterations and computational cost as a function of the number of multigrid levels used in the method. These results suggest that nonlinear multigrid methods can be used as a robust implicit solver for hyperbolic systems such as the M<SUB>1</SUB> model.