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Pressure correction in cylindrical coordinates

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Old   April 12, 2012, 01:47
Default Pressure correction in cylindrical coordinates
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I am trying to write a code for the equivalent of a lid driven cavity in cylindrical coordinates. As a reference, I have adapted a 2D cartesian lid driven cavity code written by Seibold which can be found at:

The non linear terms are calculated using an explicit upwind method and the viscosity terms are implicit. I think I am having problems with the pressure corrections step in cylindrical coordinates.

Right now, I am finding P by solving the following equation where ** denotes the velocity field after a partial step for the nonlinear and viscosity terms.:

\frac{1}{r}\frac{\partial P}{\partial r} + \frac{\partial^2 P}{\partial r^2}+\frac{\partial^2 P}{\partial z^2} = \frac{u_r^{**}}{r}+\frac{\partial u_r^{**}}{\partial r} +  \frac{\partial u_z^{**}}{\partial z}

Could some one give me some tips? My u_z velocity profiles look like this and I expect the profile at 0.5L to be similar to a poiseuille profile.
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