WENO格式权重分析与改进

为了优化WENO格式计算性能,在对Jiang和Shu的经典WENO格式(记为WENO-JS)加权方法分析的基础上,通过引入间接光滑指数,构造出一种新的WENO格式——WENO-E格式,取得减小间断区耗散的效果。理论分析表明,该格式与WENO-JS格式计算效率基本相同,可达到相同阶的计算精度;但在相同网格下,较之WENO-JS格式,该格式对光滑区域的求解有更小的截断误差,对间断的捕捉有更高的分辨率。与WENO-JS格式相比,采用WENO-E格式进行线性迁移方程、非线性Burgers方程、欧拉方程等相关问题的数值实验,均能取得更好的数值结果。

Analysis and improvement of weights in WENO schemes

The WENO scheme is of great significance for the accurate calculation of complex flow fields, which has high precision and high resolution. In order to improve the computational performance of the WENO scheme, a new WENO scheme named WENO-E scheme is constructed, which decreases dissipation close to discontinuities. The new scheme is constructed by introducing indirect smooth indicator, based on the analysis of the algorithm of weighted factors in the classical WENO scheme which is named WENO-JS for proposed by Jiang and Shu. The theoretical analysis shows that the WENO-E scheme can reach the same convergence order of WENO-JS, with the same computational efficiency; but obtain smaller truncation errors at smooth parts of the solution, and higher resolution close to discontinuities, with the same grids. Subsequently, numerical experiments with the linear transport equation, the nonlinear Burgers equation and the one dimensional Euler system of equations are conducted; compared with the classical WENO scheme, the WENO-E scheme has achieved better numerical solutions.