The repair paradigm: New algorithms and applications to compressible flow

The repair paradigm leads to several algorithms for redistributing mass, momentum and energy, while adhering to local maximum principles, as an adjunct to the remapping step in certain compressible flow codes that use remapping, such as Arbitrary–Lagrangian–Eulerian codes, or for just redistributing mass in advection codes. In the case of advection of a concentration, repair keeps the newly computed concentration in a cell between the maximum and minimum concentrations in neighboring old cells, thus guaranteeing at least that the new concentration is between zero and one. For compressible flow, density, velocity and internal energy are similarly constrained while maintaining conservation of mass, momentum and total energy. In this way, positive density and internal energy are achieved as a side effect. We propose a new algorithm, combining both local and global repair, that maintains causality and is efficient in a parallel computational setting. The local/global algorithm is independent of the order in which the distribution is performed, and it maintains 1D symmetry. This is applied to advection in two dimensions, and to, among others, the LeBlanc problem, the Sedov problem, and an interacting 2D blast wave problem. The latter is done with a Lagrangian code for which rezoning, remapping and repair are essential.