TY - JOUR
T1 - A Well-Balanced Gas Kinetic Scheme for Navier-Stokes Equations with Gravitational Potential
AU - Chen , Songze
AU - Guo , Zhaoli
AU - Xu , Kun
JO - Communications in Computational Physics
VL - 3
SP - 902
EP - 926
PY - 2020
DA - 2020/07
SN - 28
DO - http://doi.org/10.4208/cicp.OA-2019-0067
UR - https://global-sci.org/intro/article_detail/cicp/17661.html
KW - Well-balanced, source term, gravity, gas kinetic scheme.
AB - <p style="text-align: justify;">The hydrostatic equilibrium state is the consequence of the exact balance between hydrostatic pressure and external force. Standard finite volume cannot keep this
balance exactly due to their unbalanced truncation errors. In this study, we introduce
an auxiliary variable which becomes constant at isothermal hydrostatic equilibria and
propose a well-balanced gas kinetic scheme for the Navier-Stokes equations. Through
reformulating the convection term and the force term via the auxiliary variable, zero
numerical flux and zero numerical source term are enforced at the hydrostatic equilibrium state instead of the balance between hydrostatic pressure and external force.
Several problems are tested to demonstrate the accuracy and the stability of the new
scheme. The results confirm that, the new scheme can preserve the exact hydrostatic
solution. The small perturbation riding on hydrostatic equilibria can be calculated accurately. More importantly, the new scheme is capable of simulating the process of
converging towards hydrostatic equilibria from a highly unbalanced initial condition.
The ultimate state of zero velocity and constant temperature is achieved up to machine
accuracy. As demonstrated by the numerical experiments, the current scheme is very
suitable for small amplitude perturbation and long time running under gravitational
potential.</p>