一种改进的五阶WENO-Z格式
An Improved Fifth-Order WENO-Z Scheme
DOI: 10.12677/aam.2026.153085, PDF,    科研立项经费支持
作者: 于春泷, 张玲玲*：太原理工大学数学学院，山西 太原
关键词: WENO格式；模板重组；光滑因子；精度分析；WENO Scheme； Stencil Reorganization； Smoothness Indicator； Precision Analysis
摘要: 本文从WENO-Z格式的模版重组出发，提出了一种全局光滑因子，并对其进行加权处理，进而得到了一种改进的五阶WENO-Z格式。该格式保证了在一阶极值点处的计算精度不降低，并在理论推导上满足收敛精度的充分条件。选取了波动方程、一、二维欧拉方程组等经典算例进行数值测试。研究结果表明，新格式在满足相同五阶精度的情况下，不仅拥有更好的激波捕捉能力，而且提高了对复杂流场结构的分辨率。
Abstract: Starting from the template reconstruction of the WENO-Z scheme, we introduce a global smoothness indicator and apply a weighted treatment to obtain an improved fifth-order WENO-Z scheme. This formulation guarantees that the computational accuracy at first-order extreme points does not degrade, and its theoretical derivation satisfies the sufficient conditions for convergence order. Classical test problems, including the linear equation and the two-dimensional Euler equations, are employed to assess the method. The results demonstrate that, at the same nominal fifth-order accuracy, the proposed scheme not only exhibits enhanced shock-capturing capability but also provides improved resolution of complex flow-field structures.
文章引用：于春泷, 张玲玲. 一种改进的五阶WENO-Z格式[J]. 应用数学进展, 2026, 15(3): 34-47. https://doi.org/10.12677/aam.2026.153085

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