求解双曲守恒律方程的自适应人工黏性熵稳定格式

采用熵守恒格式求解双曲守恒律方程不满足熵稳定条件.为了达到熵稳定,需要在熵守恒格式的基础上增加黏性机制,使总熵耗散.鉴于自适应人工黏性在不同的计算区域上其黏性大小的变化特点,在熵守恒通量的基础上添加经过修正的自适应人工黏性通量构造出一种新的结构简单的熵稳定格式.根据自适应人工黏性的自适应性,并经过简单调节黏性比例系数C之后,该格式可以在不使用限制器的情况下达到整体的高分辨率,表现出:在间断区域有足够的数值耗散保证稳定;在光滑区域,黏性很小,不会影响格式在此的高精度.最后的几个数值算例以熵稳定ERoe格式和高分辨率熵稳定EYee格式的数值结果作为参照,分析说明这种格式的特性.

Adaptive artificial viscosity entropy stable scheme for hyperbolic conservation laws

The entropy stable conditions may not be met if entropy conservation schemes are used to solve the equations of hyperbolic conservation laws. To achieve entropy stability, the total entropy of a numerical scheme must be dissipative. The frequently-used method is to add a viscosity mechanism to an entropy conservative scheme. By considering the change characteristics of the size of adaptive artificial viscosity in different parts of the computational domain, a new simple entropy stable scheme was proposed by combining the flux of entropy conservation with the corrected flux of adaptive artificial viscosity. According to the adaptivity of adaptive artificial viscosity, this scheme can achieve the overall high resolution without using any limiters but adjusting the viscosity proportional coefficients C. So the computed solution was stable at its discontinuous parts with enough numerical dissipation while maintaining the high order accuracy at smooth parts with very small viscosity. At the end, several numerical examples were performed to analyze the characteristics of the proposed scheme with reference to the numerical results of entropy stable ERoe scheme and high resolution entropy stable EYee scheme.