Triangular metric-based mesh adaptation for compressible multi-material flows in semi-Lagrangian coordinates

Abstract

In this paper, we propose an adaptive mesh refinement method for 2D multi-material compressible non-viscous flows in semi-Lagrangian coordinates.The mesh adaptation procedure is local and relies on a discrete metric field evaluation. The remapping method is second-order accurate and we prove its stability. We propose a multi-material treatment using two ingredients: the local remeshing is performed in a way that reduces as much as possible the creation of mixed cells and an interface reconstruction method that can be used to avoid the diffusion of the material interfaces.The obtained method is almost Lagrangian and can be implemented in a parallel framework. We provide some numerical tests which attest the validity of the method and its robustness.