基于改进的三阶SPWENO重构方法求解浅水波方程
Solving the Shallow Water Equation Based on the Improved Third-Order SPWENO Reconstruction Method
摘要: 计算了离散情况下跨越间断时的具体熵增量，给出相应的耗散项，从而修正了求解浅水波方程的熵守恒格式。结合Roe的迎风耗散项，构造了一阶精度的熵稳定格式。为了提高格式的精度，利用改进的三阶SPWENO重构方法对熵变量进行了重构，得到了一类高精度高分辨率的熵稳定格式，并通过数值算例验证了新格式的有效性。
Abstract: In discrete situation, the specific entropy production when crossing the discontinuities is calculated, and the corresponding dissipation term is given, thus correcting the entropy conservation scheme for shallow water equation. Adding the Roe-type upwind dissipation term, the first-order entropy stable scheme is constructed. In order to improve the accuracy of the scheme, the entropy variable is reconstructed by the improved third-order SPWENO reconstruction to obtain a kind of high-precision high-resolution entropy stable scheme. Finally, the validity of the new scheme is verified by numerical experiments.
文章引用：李雅蓉, 沈亚玲. 基于改进的三阶SPWENO重构方法求解浅水波方程[J]. 应用数学进展, 2021, 10(9): 2967-2975. https://doi.org/10.12677/AAM.2021.109311

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