Wall boundary conditions for the Navier-Stokes Equations
I am doing finite volume Navier-Stokes Computations for external flows in 2D, both cell-centered and cell-vertex based methods. I would like to get some information regarding the implementation of wall boundary conditions, and some references on the same. Thanks in advance.
Re: Wall boundary conditions for the Navier-Stokes Equations
You can implement convective flux terms and viscous terms separatly. For the convective terms, all you need on the wall is the pressure, and the mass/heat flux terms are zero everywhere on the wall (except for heat transfer calculations using non-adiabatic wall, in that case, the heat flux is not zero). In the viscous terms, the velocity on the wall is zero.
For cell-vortex based method, the control points are on the wall itself, so the pressure and velocity conditions can be dirctly applied. For cell-center based method, the pressure on the wall needs to be extrapolated from the interior control points. You may read the following artical to get useful hint: Rizzi, A. "Numerical Implementation of solid-body boundary conditions for the Euler equations." ZAMM, Vol. 58, pp. 301-304. (1978).
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