An arbitrary lagrangian eulerian strategy to solve compressible fluid flows

In this paper, we consider an Arbitrary Lagrangian Eulerian (ALE) alternative to the computation of bi-dimensional compressible fluid dynamics written in La-grangian frame. In this formulation, the conservation laws are solved on a mesh moving at the speed of the flow. In the context of multi-material flows, this La-grangian description allows the exact preservation of the interface between different species. Originally, Lagrangian schemes considered a staggered discretization of unknowns (density, velocity, energy), the velocity is located at nodes and density, pressure are cell centered, [33] and more recently, with some improvements [5]. Recently, new schemes have been designed as a full centered version [7] [22]. These two schemes can be seen as an extension of Godunov scheme to fully multi-dimensional flux (at nodes). Each one verifies a local discrete vertex centered entropy inequality. Despite all efforts to obtain robust simulations for Inertial Confinement Fusion (ICF) computations, nowadays, the pure Lagrangian frame mode does not ensure a good cell quality during the calculation: for example non convex cell and/or tangled cell may appear. A commonly used alternative is to consider an ALE formulation [15]. A pure Lagrangian phase is followed by a two step process: the rezoning of the Lagrangian mesh followed by a remapping step. The aim of this paper is to propose some schemes for each step. In the first one, we will introduce a strategy that controls the quality of the rezoned mesh for arbitrary polygonal conformal mesh under the constraint of being close to the La-grangian grid. For the second one, we propose an extension of [23] swept volume based remapping method. We propose also a local way to impose a discrete maxi-mum principle (local bound preservation) for arbitrary second order limiter (or high order method) without any repair process [21]