A high-resolution TVD finite volume scheme for the Euler equations in conservation form

Abstract

A finite-volume numerical algorithm using nonuniformly distributed skewed, quadrilateral cells is developed to solve the Euler equations in conservation form. Fluxes across the cell boundaries are computed using the total variation diminishing (TVD) methodology developed by Harten. Proof of the TVD property for nonuniform grid systems and a truncation error analysis are presented along with a discussion of the treatment of boundary conditions. Four test cases are given to examine the efficacy of the present scheme using a system of skewed and nonuniform cells. The excellent agreement of the numerical results with exact solutions and carefully designed experiments demonstrates the ability of the present scheme to accurately resolve complicated wave developments and interactions using highly nonuniform multiblock zonal cell distributions.