A Godunov Method with Staggered Lagrangian Discretization Applicable to Isentropic Flows

doi:10.19596/j.cnki.1001-246x.8144

Abstract

Abstract: In cell-centered Godunov method,unphysical overheating problem exists in rarefaction flows.We develop a Godunov method with staggered Lagrangian discretization which is applicable to isentropic flows. Velocity and thermodynamic variables are defined in staggered discretization. The velocity averaging process in a cell is avoided,so that the kinetic energy dissipation due to the momentum averaging process is removed. In contrast to the traditional von Neumann staggered grid method, the face flux is provided by a node multidimensional Riemann solver. The difficulty in selecting multidimensional artificial viscosity is overcome. In order to reduce unphysical entropy production of multidimensional Riemann solver in rarefaction problems,we give a reasonable criterion of rarefaction appearance to satisfy the thermodynamic relation. Numerical results show that the method removes overheating problem in rarefaction problems, and retains the property of accurate shock capturing of the original Lagrangian Godunov method as well.

Key words: staggered grid, Riemann solver, rarefaction wave, Godunov method

CLC Number:

O354

SUN Chen, LI Xiao, SHEN Zhijun. A Godunov Method with Staggered Lagrangian Discretization Applicable to Isentropic Flows[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(5): 529-538.

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