An Improved 3rd-Order WENO-Z Type Scheme
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摘要: 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.Abstract: 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.
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Key words:
- WENO scheme /
- low dissipation /
- high resolution /
- global smoothness factor
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