High-Order Hybrid WCNS-CPR Schemes on Hybrid Meshes with Curved Edges for Conservation Laws I: Spatial Accuracy and Geometric Conservation Laws (Communications in Computational Physics, 2018)
A type of hybrid WCNS and CPR method for solving conservation laws onhybrid structured and unstructured meshes is proposed. WCNS on structured gridis conjoined with CPR on unstructured grid through CPR on structured grid. Themain hybrid technique becomes coupling WCNS and CPR on curvilinear structuredgrid. Calculation of grid metrics, interpolation methods of physical coordinates andstate variables, and computation of Riemann flux near coupling interface are designedto maintain the expected high order accuracy and to satisfy discrete geometric conservationlaws in the whole computational domain. Third-order schemes and fifth-orderschemes are considered. Numerical simulations show that the proposed hybridWCNS-CPR schemes can obtain designed accuracy, satisfy geometric conservation lawand have good balance of computational efficiency and grid flexibility.
Keywords: Weighted compact nonlinear scheme (WCNS); Correction procedure via reconstruction (CPR); hybrid schemes; hybrid grid; high-order accuracy.