BC for 2D ns solver
 

Hi, Could anyone help me out by giving me a list of possible BC's that can be applied to a 2D ns solver.It uses rectangular cartesian mesh.

Thanking you Thampy

Re: BC for 2D ns solver
 

At solid wall, you can set both the veolcity components to zero ( u = v = 0 ). You can prescribe isothermal or adiabatic wall conditions for temperature(T)(you have to be a bit more careful if the flow is compressible). Pressure (p) can be extrapolated from the interior.

Assuming the far-field boundary is a rectangle, comprising of inlet, exit and top and bottom portions, one can prescribe freestream u,v & T at the inlet and extrapolate pressure from the interior. For the other three boundaries, you can do exactly opposite of what is done for the inlet. i.e prescribe freestream p and extrapolate u,v & T from the interior.

This is one of the several ways of prescribing BCs for laminar viscous flow past a body.

Can you give some references where one can find 2D compressible N-S computations on Cartesian grids ?

Good Luck,

Jawahar

Re: BC for 2D ns solver
 

(I) You have a density equation - first order derivative in space, and 2 or 3 velocity equations of second order (due to the viscous term) and maybe an energy equation (say for P) or the first order. Consequently, you have to specify the density and pressure at only one boundary each, while the velocities have to be specified at both boundaries.

(II) The best way to impose the boundary conditions is not on the primitive variables themselves (i.e. not on the density, pressure and velocities) but on the characteristics of the flow at the boundaries. This will automatically take care of (I). Imposed values from outside are specified for the incoming characteristic at the boundaries, and computed (or extrapolated) values from the computational domain are specified for the outgoing characteristics of the flow at the boundaries. One then obtains the values of the primitives variables at the boundaries through the characteristics of the flow there. This makes sure the free boundaries are not reflective. See e.g. Givoli, 1991, Journal of Computational Physics, 94, page 1 (review article).

(III) The values that you chose to impose 'from outside' (inflow, pressure, etc..) are the physical boundary conditions, and are the ones imposed on the inflowing characteristics of the flow at the boundaries. These can be e.g. giving the velocities, the pressure or their derivatives, etc... (message of P.Jawahar).

PG.