二维线性传输方程满足两个守恒律的数值格式

The Numerical Scheme Satisfying Two Conservation Laws for Two Dimensional Linear Advection Equations

摘要: 在本文中，我们针对二维线性传输方程设计了满足两个守恒律的数值格式。该格式不仅能保持数值解守恒，同时能保持数值能量守恒。通过数值算例验证格式的有效性，数值结果表明该格式在远离极值点的区域内具有误差相互抵消的超收敛性质，并且能够很好的保持解的结构。

Abstract: In this paper, we develop an improved numerical scheme satisfying two conservation laws for two-dimensional linear advection equations, which satisfying both the numerical solution and numerical energy conservative. The numerical results show that the scheme has the super-con- vergence property away from the extreme points, and can keep the structure of the solution well.