Convergence of a multidimensional Glimm-like scheme for the transport of fronts

Thierry Gallouët (1) , Olivier Hurisse (2)

1 AMU - Aix Marseille Université
2 EDF R&D MFEE - Mécanique des Fluides, Energies et Environnement

This paper is devoted to the numerical analysis of a numerical scheme dedicated to the simulation of front advection (see https://hal.archives-ouvertes.fr/hal-02940407v1 for a preprint version presenting this scheme and some numerical results). The latter has been recently proposed and it is based on the ideas used for the Glimm's scheme. It relies on a two-step approach: a convection step is followed by a projection step which is based on a random choice. The main advantage of this scheme is that it applies to multi-dimensional problems. In the present paper a convergence result for this scheme is provided for a particular class of multi-dimensional problems. This work has been accepted for publication in IMA Journal of Numerical Analysis: https://doi.org/10.1093/imanum/drab053.

Mots clés: Glimm’s scheme; front propagation; multidimensional problem; random choice

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Thierry Gallouët, Olivier Hurisse. Convergence of a multidimensional Glimm-like scheme for the transport of fronts. IMA Journal of Numerical Analysis, 2021. ⟨hal-02940407v2⟩