High Order B.C. for Finite Difference Method
 

Hello, could anybody tell me how to implement higher order (more the 2nd order) accurate B.C. at a solid wall boundary. I need to appximate velocity components for three ghost cells out of the flow domain.

For v = tangential velocity; u = normal velocity, I tried this: v[-1] = -v[1]; v[-2] = v[2]; v[-3] = -v[3]; u[-1] = u[1]; u[-2] = u[2]; u[-3] = u[3]; It is based on the same mass-conservation idea originally suggested by Harlow and Welch in MAC paper for one ghost-cell.

Another approach seems to be to get a polynomial based on the values inside the flow-domain and then estimate ghost-cell-values using this polinomial. For one ghost-cell, this approach matches with what is suggested in the above MAC apprach if linear approximation.

I think this is not a big deal for personals experienced in CFD. Please suggest me. I tried internet but couldn't get it!

Thanks a lot in anticipation!

-Chandra

Re: High Order B.C. for Finite Difference Method
 

Chandra,

Without spending much time on this, I'd say you should not extrapolate information beyond 1/2 a grid point into a wall or everything will go berserk. At least, in the case of higher-order methods. Stay within the fluid. You can close 4th-order, interior first-deriviatives to third-order and be fine. Higher than that, life gets difficult. You can read about these topics in the following paper and those in the bibliography. Good luck!

Ken Mattsson, Boundary Procedures for Summation-by-Parts Operators, Journal of Scientific Computing, v.18 n.1, p.133-153, February 2003

Re: High Order B.C. for Finite Difference Method
 

Hey, thanks a lot for the info. I will look into the paper you mentioned!!

-Chandra