Conservative multi-material remap for staggered multi-material Arbitrary Lagrangian–Eulerian methods

Abstract

Remapping is one of the essential parts of most multi-material Arbitrary Lagrangian–Eulerian (ALE) methods. In this paper, we present a new remapping approach in the framework of 2D staggered multi-material ALE on logically rectangular meshes. It is based on the computation of the second-order material mass fluxes (using intersections/overlays) to all neighboring cells, including the corner neighbors. Fluid mass is then remapped in a flux form as well as all other fluid quantities (internal energy, pressure). We pay a special attention to the remap of nodal quantities, performed also in a flux form. An optimization-based approach is used for the construction of the nodal mass fluxes. The flux-corrected remap (FCR) approach for flux limiting is employed for the nodal velocity remap, which enforces bound preservation of the remapped constructed velocity field. Several examples of numerical calculations are presented, which demonstrate properties of our remapping method in the context of a full ALE algorithm.