High-Order Hybrid WCNS-CPR Schemes on Hybrid Meshes with Curved Edges for Conservation Laws I: Spatial Accuracy and Geometric Conservation Laws

Abstract

A type of hybrid WCNS and CPR method for solving conservation laws on hybrid structured and unstructured meshes is proposed. WCNS on structured grid is conjoined with CPR on unstructured grid through CPR on structured grid. The main hybrid technique becomes coupling WCNS and CPR on curvilinear structured grid. Calculation of grid metrics, interpolation methods of physical coordinates and state variables, and computation of Riemann flux near coupling interface are designed to maintain the expected high order accuracy and to satisfy discrete geometric conservation laws in the whole computational domain. Third-order schemes and fifth-order schemes are considered. Numerical simulations show that the proposed hybrid WCNS-CPR schemes can obtain designed accuracy, satisfy geometric conservation law and have good balance of computational efficiency and grid flexibility.