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

In this paper, we propose an adaptive mesh refinement method for 2D multi-material compressible nonviscous flows in semi-Lagrangian coordinates. The mesh adaptation procedure is local and relies on 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 to reduce as much as possible mixture creation and an interface reconstruction method is used to avoid material diffusion in mixing cells. 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.