一种高阶数值通量的探讨
An Approach of High Order Numerical Flux
摘要: 参考MUSCL格式的构造思想，我们给出了一种高阶数值通量的构造方法。将高阶数值通量应用于有限体积(差分)ENO，WENO和DG等格式得到单步高阶Semi-Lagrangian格式。针对一维Euler方程组，本文在特征空间给出了一种新的特征线的处理方案，解决了Semi-Lagrangian方法难以推广到多维的难点。数值实验表明，新格式比原格式误差更小，效率更高，对激波的模拟效果也有较大提升。
Abstract: Referring to the construction idea of the MUSCL scheme, we present a construction method for high-order numerical fluxes. The higher order numerical flux is applied to the finite volume (dif-ference) ENO, WENO and DG schemes to obtain single step higher order Semi-Lagrangian scheme. For the one-dimensional Euler equations, this paper presents a new feature line processing scheme in the feature space, which solves the difficulty that the Semi-Lagrangian method is difficult to gen-eralize to multidimensional. Numerical experiments show that the new format is smaller than the original format, the efficiency is higher, and the simulation effect on the shock wave is also greatly improved.
文章引用：温燕静, 杨玉月, 魏雁霞. 一种高阶数值通量的探讨[J]. 应用数学进展, 2019, 8(5): 990-997. https://doi.org/10.12677/AAM.2019.85113

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