基于映射函数的三阶WENO改进格式及其应用

低耗散、高分辨率激波捕捉格式对含激波流场的数值模拟具有重要意义.在传统三阶WENO格式（WENO-JS3）和三阶WENO Z格式（WENO-Z3）基础上，基于映射函数，给出WENO-M3、WENO MZ3格式.选用Sod激波管、激波与熵波相互作用、双爆轰波碰撞及双Mach(马赫)反射等经典算例，考察上述格式的计算性能.数值结果表明，WENO-MZ3格式相较其他格式具有耗散低、对流场结构分辨率高的特性.为了进一步扩展WENO-MZ3格式的应用范围，采用该格式数值研究封闭方形舱室内柱形高压、高密度气体爆炸波传播过程，波系演化规律以及壁面典型测点压力载荷.数值计算结果表明WENO-MZ3格式能够较好地模拟包含高压比、高密度比的爆炸波且给出数值耗散较小的壁面压力载荷.

An Improved rd-Order WENO Scheme Based on Mapping Functions and Its Application

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.