A simple approach to derive Riemann solvers for the compressible Euler equations in the ALE formulation from their Eulerian counterpart

In this paper, a new formula for the inviscid flux vector of the compressible Euler equations is proposed which links its Arbitrary Lagrangian-Eulerian (ALE) and Eulerian forms. On the one hand, this formula can be applied to compute approximate Riemann solvers in the ALE formulation starting from their Eulerian version. On the other hand, as shown, the same formula is also useful to verify the correctness of an Riemann solver in the ALE formulation once its Eulerian version is given. • Proposition of a bridge formula for Riemann solvers between their Eulerian and ALE formulation. • Investigation of its Galilean invariance. • Two examples of application to derive/verify Riemann solvers in the ALE formulation.