一类耦合Burgers方程组的数值计算

Numerical Solution to Coupled Burgers’ Equations

本文基于有限体积格式,对于一类耦合Burgers方程组问题,在满足TVD (Total Variational Diminishing)准则的情况下,利用Hermite插值法建立了新的格式离散对流项,并利用三阶Runge-Kutta格式对时间项进行离散,通过经典的数值算例验证,该格式具有良好的计算效果。

This paper solves a class of coupled Burgers’ equations based on finite volume scheme in a uniform grid. A new scheme for discretizing convective term is constructed by Hermite interpolation method with satisfying TVD (Total Variational Diminishing) criterion, and the time discretization is fulfilled by using the third-order Runge-Kutta scheme. It is verified that this scheme has gained a good computational performance by several classical numerical examples.