线性传输方程满足3个守恒律的差分格式

A Finite Difference Scheme for Linear Advection Equation Satisfying Three Conservation Laws

考虑单个线性传输方程,对其设计了一种满足3个守恒律的差分格式.此格式为3阶Godunov型的,用的是分片2次重构,重构函数的系数由3个守恒量来确定.虽然微分方程是线性的,但所设计的格式是非线性的.数值实验结果表明,此格式是非线性稳定的,并且对长时间的数值模拟有很好的保结构性质.

This paper is concerned with scalar linear advection equation. A difference scheme satisfying three conservation laws is proposed, which is of the third-order Godunov type with piecewise parabolic reconstruction. Coefficients of the reconstructed function in each grid are determined by three conservation quantities. Although the equation is linear, the proposed scheme is nonlinear. Numerical experiments show that the scheme is nonlinearly stable and has good structure-preserving property in long-time numerical simulations.