求解双曲守恒律方程的WENO-AO型熵稳定格式

WENO-AO Type Entropy Stable Scheme for Solving Hyperbolic Conservation Law Equations

摘要: 通过在单元交界面处进行WENO-AO重构，构造了一种求解双曲守恒律方程的高分辨率熵稳定格式。该格式有三个优势：1) 该格式在光滑区域是五阶精度的，同时在间断附近无伪振荡产生；2) 在对称条件下，线性权值可以是任意和为1的正数；3) 该格式可以避免极值的裁剪。数值实验表明，该格式具有良好的鲁棒性、高分辨率等特性。

Abstract: By performing WENO-AO reconstruction at the interface of the cells, a high-resolution entropy stable scheme for solving hyperbolic conservation law equations is constructed. This scheme has three advantages: 1) The scheme has fifth-order accuracy in the smooth area, and there is no spurious oscillation near the discontinuity. 2) Under the condition of symmetry, the linear weight can be any positive number with the sum of 1. 3) This scheme can avoid extreme clipping. Numerical experiments show that the scheme has good robustness, high resolution and so on.