Showing papers on "MUSCL scheme published in 1985"

A Direct Eulerian MUSCL Scheme for Gas Dynamics

Abstract: We present a second order extension of Godunov’s method for gas dynamics in Eulerian coordinates patterned after van Leer’s MUSCL scheme for gas dynamics in Lagrangian coordinates. The present method performs the Eulerian calculation in a single step by solving Riemann problems and characteristic equations for the fluxes in the Eulerian frame. We also make several modifications in the formulation of MUSCL, applicable to both this scheme and to the original Lagrangian scheme, all aimed at making a more robust and accurate scheme. We present the results of test caclulations in one and two space variables.

Convergence of Generalized MUSCL Schemes

Abstract: Semidiscrete generalizations of the second order extension of Godunov’s scheme, known as the MUSCL scheme, are constructed, starting with any three point “E” scheme. They are used to approximate scalar conservation laws in one space dimension. For convex conservation laws, each member of a wide class is proven to be a convergent approximation to the correct physical solution. Comparison with another class of high resolution convergent schemes is made.