Simulation of compressible flows on unstructured meshes using Lagrange-Remap-like approach: stability for large time steps, towards an all-Mach-regime solver.

We present a discretization strategy for compressible fluids systems for unstrutctured grids based a Lagrange-Remap approach that does not involve any moving mesh. We present the stability properties of this solver and present a natural semi-implicit extension of the method that allows to remain stable under a CFL condition involving only the material velocity. We present another modification of the solver that allows to provide an accurate and stable solver for simulation involving low-Mach regions in the flow. This work is a collaboration with Christophe CHALONS and Mathieu GIRARDIN.