Outlet BC
 

In some flow situations like viscous flow over a cylinder, the outlet BC in FVM is taken as a zero-normal-gradient condition i.e.,

d(rho)/dn = 0

d(vel)/dn = 0

dp/dn = 0

First of all is this correct ? Secondly how do you implement this in practice in a 3d unstructured grid finite volume formulation ? I would be interested to know if there are differences for cell-centered and node-centered schemes.

Re: Outlet BC
 

Dear Praveen,

1. The conditions that you have mentioned are all extrapolation bc's which are not correct simply because they do not look into whether the flow is subsonic/supersonic. A full extrapolation of all variables is correct only when the flow is supersonic, although with a genuinely large farfield radii, the above mentioned BCs could work. However, I would suggest that a Reimann invariant or solver based NRBC would be the more ideal choice. The farfield normally being free of viscous activity, the BC would be the same for Euler/NS cases. This NRBC is capable of handling both subsonic/supersonic flows.

2. If you had to implement the BCs mentioned in a 3D framework, you would have to use a suitable generalised gradient finding strategy. One possibility would be to use LS/GG to find the x-- and y-- gradients and then compute the normal derivatives using these and the unit normals nx and ny as,

d(rho)/dn = d(rho)/dx *nx + d(rho)/dy * ny and so on ...

3. As far as node- and cell- centered schemes are concerned, I do not see any major differences, except in the construction of a dual volume being necessary for the node-centered approach.

Hope this helps.

Regards,

Ganesh

Re: Outlet BC
 

I am currently using a Reimann bc. But it does not allow the flow to pass through the outlet without perturbing it. Well, I have put the outlet bc at 20*diameter which is probably too close. But I would prefer not to enlarge the domain. The flow conditions are M=0.1 and Re=40. Reimann bc is not very appropriate since the flow is strongly parabolic due to the wake. There are some sophisticated methods but I have not tried them, see for example, http://citeseer.ist.psu.edu/622061.html

I was hoping there was some extrapolation-type bc which could be implemented within the FVM framework, but maybe its not possible.