A Well-balanced Gas Kinetic Scheme

doi:10.19596/j.cnki.1001-246x.8158

Abstract

Abstract: Hydrostatic equilibrium is a static state that the fluid pressure is balanced with gravity. Classic finite difference and finite volume methods cannot maintain this equilibrium state on discrete scales, and produce non-physical phenomena often such as spurious currents. In this work, volume integral of the source term is implemented at cell interface, so that the balance of pressure and gravity under discrete conditions is achieved on discrete scales. A well-balanced gas kinetic scheme of the Navier-Stokes(NS) equation is therefore constructed. The scheme maintains accurately the static equilibrium state under isothermal conditions and captures small perturbation propagation near equilibrium state at machine precision. At the same time, the scheme solves non-isothermal stratified flow near equilibrium state. Apart from the non-isothermal equilibrium described by Euler's equation, the scheme can also represent balance of thermal conduction in addition to force balance. It is shown that the scheme preserves second-order accuracy with respect to both density and temperature distribution when simulating an non-isothermal equilibrium state. Numerical examples reveal that the scheme is a potential tool in simulating stratified flow of temperature and density under gravitational field.

Key words: well-balanced, gas kinetic scheme, spurious current, hydrostatic equilibrium

CLC Number:

O357.3

ZOU Xing, CHEN Songze, GUO Zhaoli. A Well-balanced Gas Kinetic Scheme[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(6): 653-666.

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