一个改进的三阶WENO-Z型格式

在WENO-Z型格式框架下，基于高阶全局光滑因子，在非线性权建立过程中引入参数，通过收敛性分析确定参数取值范围，兼顾精确性与不振荡性，得到参数最佳取值.最终得到一个低耗散、高分辨率的三阶WENO差分格式，该格式在函数一阶极值点处仍保持预期三阶精度.最后通过精确解算例验证了格式在各种类型极值点处精度恢复情况，并通过一、二维Euler方程组经典算例测试了格式的低耗散、高分辨特性.结果表明，该文格式是一个性能优良的激波捕捉格式.

An Improved 3rd-Order WENO-Z Type Scheme

Based on the high-order global smoothness factor, a low-dissipation and high-resolution 3rd-order WENO difference scheme was obtained under the WENO-Z scheme framework. A parameter was introduced in the nonlinear weight, the parameter range was determined by convergence analysis, and the optimal parameter value was obtained with combined accuracy and non-oscillation. The scheme can maintain expected 3rd-order accuracy at the 1st-order extremum of the function. Finally, the accuracy recovery of the scheme at various extremum points was verified with exact solution examples, and the low-dissipation and high-resolution characteristics of the scheme were tested with the 1D and 2D Euler equations. The results show that, the proposed scheme is a good shock-capturing method.