关键词: 数值方法, 高分辨率格式, TVD理论

Abstract: 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.

Key words: numerical method, schemes, TVD theory