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-   -   Neumann Boundary Condition for Poisson Equation solution in Polar Coordinates (http://www.cfd-online.com/Forums/main/86665-neumann-boundary-condition-poisson-equation-solution-polar-coordinates.html)

 prapanj March 29, 2011 14:12

Neumann Boundary Condition for Poisson Equation solution in Polar Coordinates

I am attempting to solve the poisson equation in polar coordinates (2D). The problem domain is an annulus. At both 'r' boundaries, neumann homogenous boundary conditions. And theta is periodic.

I am attempting to solve this using BiCGStab solver, that I have written myself. For the above BCs the matrix is singular and hence my solution isn't converging.

To force an additive constant. I made 'nth' row of my matrix the nth row of identity matrix. And changed the correspoding b(n) to 0. Thus I attempted to make '0' the additive constant. When I did that, the solution at the nth position has a sharp peak in the solution. I have used the same strategy with CG solver on a symmetric system and it worked.

It is to be noted that this solution with the peak is a converged solution. When i change the additive constant at n to values other than 0, I am getting a scaled shift in my solutions. Also note that A matrix is nonsymmetric for such a problem in polar coordinates.

My BiCGSTAB is working fine with dirichlet BCs either wholly or partially on the boundary.

 Amir_Ghasemi July 29, 2011 10:55

Hello,
I have the same problem, any guidance is appreciated.