On the Geometric Conservation Law for Unsteady Flow Simulations on Moving Mesh

When using the dynamic mesh method to deal with moving boundary problems, the Geometric Conservation Law (GCL) must be considered carefully. This paper reviews the study on GCL problem of dynamic grid in finite volume framework based on Arbitrary Lagrangian-Eulerian (ALE) methods. Several common approaches to satisfy discretized geometric conservation law (DGCL) are studied and simplified to a uniform form. The uniform flow and the isentropic vortex are tested to validate the geometric conservation property and the temporal-accuracy. Numerical results illustrate that although the violating of GCL does not pollute the original time-accuracy of numerical schemes for the governing equations, it may introduce extra artificial errors. When the “Adding Source Term” methods are adopted, the temporal accuracy order of face velocity scheme must match the temporal accuracy order of numerical schemes for the governing equations, otherwise it will pollute the original temporal accuracy.