(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
A new high-order conservative patched grid strategy is developed with the concept of collapsed edge. Different from the traditional patched grid algorithm, where the patched interface is a line in two-dimensional space, the new strategy employs a transition region, where a collapsed edge is located within to form four point matched blocks. The introduction of the collapsed edge ensures that the grid generation of neighbouring blocks connected by the transition region is independent. The biggest advantage of this new strategy is that conservation is satisfied automatically since the numerical flux at the collapsed edge is zero. Furthermore, when applied in the framework of high-order finite difference methods based on the coordinate transformation, no essential modifications are needed. Some typical numerical examples are simulated with the new patched grid strategy combined with the fifth-order Weighted Compact Nonlinear Schemes (WCNS) to verify the capability of this new method.