MUSCL格式TV性质的非线性分析

分析求解非线性双曲型守恒律的MUSCL类格式的TV性质。首先从该类格式的一般形式出发,提出和证明了该类格式实现TVD的需求。所提TVD需求直接表示为对变量变差符号和量值限制,体现了双曲型方程解的依赖域原理,为分析MUSCL格式的TV性质提供了理论工具。同时提出了基于TVD需求再构数值解分布,以降低数值耗散从而提高接触面及膨胀波头/波尾分辨率的基本思路。

NON-LINEAR ANALYSIS OF TV PROPERTIES OF MUSCL TYPE SCHEMES

The TV properties of MUSCL type schemes for hyperbolic conservation laws are discussed.From the general form of MUSCL type schemes,the requirements to keep the schemes TVD are proposed and verified.They can be presented directly as the limitation to the sign and magnitude of the variable variations,and fully reflect the principle of region dependence of solution to hyperbolic equations,so as to provide a theoretical tool to analyze the MUSCL type schemes.The paper also presents the basic ideas on reconstruction of numerical solution distribution,based on the proposed TVD requirements,to reduce numerical dissipation and improve resolution of the contact discontinuities and head/tail of rarefaction waves.