# NS on polar coordinate grid

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 May 31, 2005, 23:32 NS on polar coordinate grid #1 Brian Guest   Posts: n/a Hi, I am trying to solve the incompressible NS equations on a polar coordinate grid. I'm using a modified "stable fluid" method and am getting stable but strange results. After the pressure correction step the fluid flow is biased towards the angular direction and flows that should go horizontal are being curved. There is no divergence, however, and without the pressure correction the flow is as expected, but obviously not divergence free. Therefore I believe the pressure correction step is not maintaining conservation of momentum correctly. I have looked into coordinate transformations to set up the pressure poisson equation but the results are the same as the method I'm using now (divergence of the pressure gradient). Here's a rundown of the method: U0 = U^(n-1) U1 = U0 + dt*F // gravity, body forces U2 = transport(U1) // convection term U3 = U2 - (dt/rho)*del(p) // continuity U^n = U3 where pressure is found by solving this poisson equation: (dt/rho)del^2(p) = divergence(U2) and the del^2(p) matrix is set up as the divergence of the pressure gradient For the CFD experienced, does this sound like a resonable approach? I don't think I have everything quite right. Thanks in advance, Brian

 June 2, 2005, 05:35 Re: NS on polar coordinate grid #2 Alexander Starostin Guest   Posts: n/a I have not noticed a small detail maybe because it is undoubtely right in your scheme: For the polar coordinate system the additional terms come to NS equation due to the curvature of the coordinates.

 June 3, 2005, 20:39 Re: NS on polar coordinate grid #3 Brian Guest   Posts: n/a You're right, there are additional terms. However, the pressure correction step guarantees a divergence free field and not momentum. I'm wondering if I need to either find a momentum correction term or somehow tie this in when solving for pressure so the pressure gradient respects momentum?

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