求解二维双曲守恒律方程的自适应人工粘性熵稳定格式

采用熵守恒格式求解双曲守恒律方程组时,通过加入适当的人工粘性,能使格式达到熵稳定,从而使得到的数值解能收敛于满足物理特性的解。自适应人工粘性在不同的计算区域上,能根据解的特性变化而改变其大小。本文将自适应人工粘性添加到熵守恒格式上,使得新格式满足熵稳定条件。并通过调节系数C使得格式整体达到高分辨率。最后以熵稳定ERoe格式和高分辨率EYee格式作为参照,通过几个二维数值实验,说明新格式的特性。

Adaptive Artificial Viscosity Entropy Stable Scheme for Two- Dimension Hyperbolic Conservation Laws

When using entropy conservative schemes to solve the equations of hyperbolic conservation laws, wecan add some appropriate artificial viscosity to make the scheme meet the entropy stable conditions. Adaptiveartificial viscosity can adjust its own amount according to the character of solution. In this paper, we add adap-tive artificial viscosity to entropy conservative schemes to meet the entropy stable conditions, and then adjustthe coefficient C to achieve high resolution. Finally, we compare this method with entropy -stable ERoe andhigh - resolution EYee scheme to show the characteristics of the new method.