Research on hybrid method based on CPR and high-resolution second order scheme

Correction Procedure via Reconstruction (CPR) is a compact and efficient numerical method, but it still has drawbacks in capturing strong shocks. However, Weighted Compact Nonlinear Scheme (WCNS) can capture shocks well. By introducing second-order scheme based on high-order interpolation of WCNS into high-order CPR method, an efficient hybrid shock-capturing method with high resolution property is proposed. Firstly, shock detection indicator based on the deviation of nonlinear weights from linear weights is used to judge troubled cells. Buffer cells are introduced in the neighbors of troubled cells, and other cells are marked as smooth cells. Therefore we use the second-order scheme to calculate in troubled cells and buffer cells, and CPR to calculate in smooth cells, which is the main idea of the proposed hybrid method. By calculating several numerical problems including isentropic vortex, shock and shock-vortex interaction, the accuracy, shock capturing ability and efficiency of hybrid method are validated with reference results. Numerical results show that the proposed hybrid method has satisfying shock-capturing ability, and has high-resolution property in smooth areas, which can be efficiently applied to numerical simulations of supersonic flows. Moreover, the method is more efficient compared with the second-order scheme based on high-order interpolation of WCNS.