线性传输方程的Entropy-Monotone格式

Entropy-Monotone Scheme for Linear Advection Equation

在守恒律方程组的数值计算中,线性间断的磨损问题备受关注.为了减少线性间断的磨损,针对线性传输方程,提出了Entropy-Monotone格式.该格式属于Godunov型格式,包括重构、发展和求网格平均3个步骤.与传统的Godunov格式不同,该格式同时计算数值解和数值熵,并通过它们构造分片常数的台阶函数.数值实验表明,此格式对线性间断的模拟非常有效.

In numerical computation of conservation laws,the problem of the wear of linear discontinuity is of great concern.In order to decrease the wear of linear discontinuity,an entropy-monotone scheme was designed for the linear advection equation.This scheme is a Godunov scheme,which includes reconstruction,evolution,and cell-averaging.Different from the traditional Godunov scheme,this scheme simultaneously computes the numerical solution and numerical entropy,and uses them to reconstruction the＂step function＂in each cell.Numerical experiments show that this scheme is very effective for the simulation of linear discontinuity.