带源项浅水波方程的高分辨率熵稳定格式

An Entropy Stable Scheme for Shallow Water Equations With Source Terms

提出了一种求解带源项浅水波方程的熵稳定格式.新格式利用通量限制函数将一阶熵稳定格式和高阶熵守恒格式结合,具有熵守恒格式和熵稳定格式的优点:在解的光滑区域具有高精度,在解的间断区域避免了非物理现象的产生,同时可以准确地捕捉激波,从而达到高分辨率的效果.利用新格式计算了一维和二维的经典算例,数值结果表明,新格式是模拟带源项浅水波方程的理想方法.

An entropy stable scheme was developed for the shallow water equations with source terms,and a 1 st-order entropy stable scheme and a high-order entropy conservation scheme were combined with a flux limiter function. The new entropy scheme preserves advantages of both the entropy conservation scheme and the entropy stable scheme,having higher accuracy in the regions of the smooth solutions and capturing shocks accurately while avoiding non-physical phenomena in the regions of the discontinuous solutions,thus achieves high resolution. The new scheme was successfully applied to calculate the classical1 D and 2 D problems. The numerical results show that the new scheme does be an ideal method to simulate the shallow water equations with source terms.