Capturing contact discontinuities using the unified coordinates

TLDR: In this article, a unified coordinate system was proposed to resolve contact discontinuities for unsteady viscous flow, as well as the special case of steady flow when h = k. The functions h and k are determined by requiring that fluid pathlines coincide with coordinate lines and the grid angles are preserved.

Abstract: Publisher Summary This chapter introduces a coordinate system, which moves with velocity Q = (hu,kv), where q = (u,v) is fluid velocity. It includes the Eulerian coordinates as a special case when h = k = 0 and the Lagrangian when h = k = 1. The functions h and k are determined by requiring that fluid pathlines coincide with coordinate lines and the grid angles are preserved. This unified coordinate system is shown to be superior to the Eulerian one in resolving contact discontinuities for unsteady viscous flow, as well as the special case of steady flow when h = k. It also avoids computation breakdown associated with Lagrangian coordinates.