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laliong April 22, 1999 09:04

incompressible NS equation

I'm trying to solve incompressible NS equations. However, the pressure equation is a laplacian equation with Neumann boundary condition. Does anybody know how to solve this equation since the matrix of the system of linear equations is a singular matrix ?

Thanks a lot.

Jim Park April 22, 1999 12:15

Re: incompressible NS equation
If I remember this correctly, the singularity indicates that the pressure can be determined to within a constant value. In other words, your solution will be adequate to correct the velocity field to insure continuity but you won't actually know the pressure level.

The folks at the Los Alamos Nat'l Lab who invented this approach (MAC, SMAC, ICE, ...) solved the LaPlace eqn iteratively, by over-relaxation. As an alternative, I think you can specify the pressure at one point, making the matrix non-singular so it can be solved by elimination, etc. But your solution is still only known to within a constant (the value you specified).

Good Luck!

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