满足最大值原理的熵格式计算线性传输方程

On MaximumPrincipleSatisfying Entropy Scheme for Linear Advection Equation

摘要:

茅德康等发展了熵格式计算一维双曲守恒型方程，熵格式具有超收敛性并且适合长时间计算．但是熵格式不满足最大值原理，在最值点处会出现过高或者过低现象．发展了满足最大值原理的熵格式并且对一维和二维线性传输方程进行了数值模拟，数值结果表明该格式在最值点不会出现过高过低现象而且不会发生非物理振荡．

Abstract:

Mao Dekang et al developed an entropy scheme for computing one dimensional hyperbolic conservation equations, which has a super convergence property and is suitable for long time numerical computation. But the entropy scheme does not satisfy the maximum principle. Overshooting or undershooting may occur in the vicinity of maximum or minimum points. In this work, numerical simulations of one dimensional and two dimensional linear advection equations are carried out. The numerical results show that the proposed scheme does not lead to overshooting or undershooting, moreover, nonphysical oscillations do not occur.