A Cell-Centered Godunov Method Based on Staggered Data Distribution, Part I: One-Dimensional Case (Journal of Computational Mathematics, 2024)
This paper presents a cell-centered Godunov method based on staggered data distribution in Eulerian framework. The motivation is to reduce the intrinsic entropy dissipationof classical Godunov methods in the calculation of an isentropic or rarefaction flow. Atthe same time, the property of accurate shock capturing is also retained. By analyzing thefactors that cause nonphysical entropy in the conventional Godunov methods, we introducetwo 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 toimprove accuracy. Numerical examples validate that the present method can dramaticallyreduce nonphysical entropy increase.