A well-balanced gas kinetic scheme for Navier-Stokes equations with gravitational potential

Understand

The hydrostatic equilibrium state is the consequence of the exact hydrostatic balance between hydrostatic pressure and external force.

• Standard finite volume or finite difference schemes 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 equilibrium state and propose a well-balanced gas kinetic scheme for the Navier-Stokes equations with a global reconstruction.
• 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.