A 3D GCL compatible cell-centered Lagrangian scheme for solving gas dynamics equations

摘要: Solving the gas dynamics equations under Lagrangian formalism enables to simulate complex flows with strong shock waves. This formulation is well suited simulation of multi-material compressible fluid such as those encountered in domain High Energy Density Physics (HEDP). These types are characterized by 3D structures hydrodynamic instabilities (Richtmyer-Meshkov, Rayleigh-Taylor, etc.). Recently, extension different schemes has been proposed and appears be challenging. More precisely, definition cell geometry space through treatment its non-planar faces limiting a reconstructed field case second-order great interest. paper proposes two new methods solve these problems. A systematic symmetric geometrical decomposition polyhedral cells presented. method define discrete divergence operator leading respect Geometric Conservation Law (GCL). Moreover, multi-dimensional minmod limiter proposed. constructs, from nodal gradients, gradient which ensure monotonicity numerical solution even presence discontinuity. ingredients employed into cell-centered scheme. Robustness accuracy assessed against various representative test cases.