基于映射函数的三阶WENO改进格式及其应用
摘要
Low-dissipation and high-resolution shock-capturing schemes are of great significance for numerical simulation of flow fields containing shock waves. The WENO-M3 and WENO-MZ3 schemes were proposed with mapping functions based on the classical 3rd-order WENO scheme (WENO-JS3) and the 3rd-order WENO-Z scheme (WENO-Z3). Several classical 1D Riemann problems and double Mach reflection cases were simulated with the above schemes. The simulation results indicate that the WENO-MZ3 scheme has better characteristics of low numerical dissipation and high resolution for the flow features among all the schemes. To expand the application scope of the WENO-MZ3 scheme, the propagation and evolution of blast waves generated by cylindrical high pressure gas in a closed square cabin were investigated. Moreover, 2 typical pressure gauging points on the walls were monitored during the simulation. It is indicated that the WENO-MZ3 scheme is suitable for simulating the evolution of blast waves containing high pressure ratios and high density ratios. The WENO-MZ3 scheme gives lower-dissipation results than the WENO-JS3 scheme for the pressure load on the walls.