Conservative and entropy controlled remap for multi-material ALE simulations with space-staggered schemes

Abstract

The remapping strategy is crucial in any Arbitrary Lagrangian-Eulerian (ALE) algorithm based on a Lagrange-plusremap paradigm. This step is particularly challenging for space-staggered schemes since inconsistencies may appear between cell centered and node centered fields after remap if no special care is taken [1][2][3]. We propose here a space-staggered remapping strategy focusing on conservation properties and entropy control. The proposed algorithm conserves mass, total energy and respects the Second Law of Thermodynamics (for robustness) up to round-off errors. This is achieved at a low computational cost by introducing a consistent, explicit and local post processing of the linear momentum after remap. This new method is then analyzed showing that the strict momentum conservation is sacrificed. It is now conserved to the scheme's order, such as entropy. Other classical properties such that the "DeBar consistency" [4], the continuity with the Lagrangian step and the monotonicity are also discussed. This work is developed in the context of the intersection-based (or overlay-based) remap. Therefore, the rezoned mesh does not have to be close to the Lagrangian one and, even if it is not considered here, our study can be easily extended to rezoning strategies which modify the mesh connectivity.