Positivity preserving and entropy consistent approximate Riemann solvers dedicated to the high-order MOOD-based Finite Volume discretization of Lagrangian and Eulerian gas dynamics

In this paper we propose to revisit the notion of simple Riemann solver both in Lagrangian and Eulerian coordinates following seminal work Gallice ”Positive entropy stable Godunov-type schemes for gas dynamics MHD equations or coordinates” Numer. Math., 94, 2003. We provide relation between forms systems conservation laws 1D. Then an approximate (simple) is derived based on notions positivity preservation control. Its counterpart further deduced. Next build associated 1D first-order accurate cell-centered Finite Volume scheme show numerically its behaviors classical test cases. using Lagrangian–Eulerian relationships, derive scheme, which inherits by construction properties terms well-defined CFL condition. At last extend arbitrary orders accuracy a Runge–Kutta time discretization, polynomial reconstruction posteriori MOOD limiting strategy. Numerical tests are carried out assess robustness, accuracy, essentially non-oscillatory numerical methods.