A novel GEEC (Geometry, Energy, and Entropy Compatible) procedure applied to a staggered direct-ALE scheme for hydrodynamics

Results on standard numerical test cases involving shocks and large deformations confirm the expected built-in properties of the scheme. In particular, the entropic compatibility leads to the preservation of entropy to second-order for isentropic flows, regardless of mesh motions and regardless of the first-order accuracy of the discrete mass transport equation. Indifference and versatility with respect to strenuous grid motion strategies are demonstrated in various situations - including supersonic shearing for new variants of Sod's shock tube and Sedov's blast wave - highlighting the advantages of the compatibility between velocity fields and volume variations in the presence of strong fluids advection.