Remapping, recovery and repair on a staggered grid Original Research Article

An accurate remapping algorithm is an essential component of many arbitrary Lagrangian–Eulerian (ALE) methods. In previous work, we have described a local remapping algorithm for a positive cell-centered scalar function that is second-order accurate, conservative, and sign preserving. However remapping in the context of high speed flow introduces new issues, which include the consistent treatment of the kinetic and internal energies, compatible remapping of mass and momentum on the staggered mesh, and the generalization from sign preservation to monotonicity preservation. We describe a remap strategy that deals with each of these issues. Although the theoretical development of this strategy is intricate, the resulting scheme is both simple to implement and efficient. We provide numerical examples to illustrate the individual steps of the remap and its overall performance.