A Cell-Centered Godunov Method Based on Staggered Data Distribution, Part I: One-Dimensional Case

Abstract

This paper presents a cell-centered Godunov method based on staggered data distribution in Eulerian framework. The motivation is to reduce the intrinsic entropy dissipation of classical Godunov methods in the calculation of an isentropic or rarefaction flow. At the same time, the property of accurate shock capturing is also retained. By analyzing the factors that cause nonphysical entropy in the conventional Godunov methods, we introduce two velocities rather than a single velocity in a cell to reduce kinetic energy dissipation. A series of redistribution strategies are adopted to update subcell quantities in order to improve accuracy. Numerical examples validate that the present method can dramatically reduce nonphysical entropy increase.