间断陡削化方法Ⅰ : 人为刚性源项方法——刚性常微分方程的计算方法的应用

A Discontinuity Sharpenning Technique Ⅰ: Adding Artificial Stiff Source Term Approach ——An Application of Stiff ODE Solver

本文针对界面运动的计算提出了适当附加人为刚性源项计算接触间断的方法。数值实验表明了这一方法是有效的。

As is well known that the discontinuity of the solution of linear advection equation likeut+aux=0, a= const >0is difficult to be preserved using capturing methods.The situation becomes even worse if the equation contains a stiff source term likeut+aux=ψ(u)In this case wrong speed of the discontinuity propagation will be observed if the stiff source term ψ(u) is not handled in an appropriate way. In this paper we are successed in solving this problem.The method of adding artificial stiff source term is introduced for resolving contact discontinuities of linear advection equations.So called highly fidelity algorithms of ODEs with stiff source terms are presented as the fundamental elements of the PDE solvers.Correct wave speed is obtained by using a special modification of the source term ψ(u) as (u j)=(1-θ j)ψ(u j) with some kind of switch function θ j. Comparative numerical results are presented.