# Projection Methods

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 June 8, 2011, 22:25 Projection Methods #1 New Member   Felipe Hernandez Join Date: Apr 2011 Posts: 13 Rep Power: 7 I've got a incompressible Navier-Stokes code that works reasonably well (compared to the taylor-green vortex) that uses a pressure-correction time integration method. I want to implement a projection method now, both as a learning experience and to compare the accuracies. I'm just trying to get a gist of how it works and how it compares to the pressure correction method. From what I understand, I get an intermediate velocity (probably from the old pressure) and then I project the velocity onto divergence-free vector field (by projecting the vector onto the null-space of another matrix?!), then I solve for pressure, and then I make it divergence-free again. Is this correct? If not, could you describe projection methods to me? Are there any good (and free?!) articles you could point me to? I have a strict \$0 budget for learning CFD. EDIT: I also want the method to be accurate at the no-slip boundary conditions so that I can calculate the drag/lift forces. I was reading that projection methods may have a problem with this. Should I look at other options? Last edited by Petrov; June 8, 2011 at 22:53.

 June 10, 2011, 03:32 pjm #2 Member   Hans Bihs Join Date: Jun 2009 Location: Trondheim, Norway Posts: 36 Rep Power: 9 Hi, you got the projection almost right, except that the intermediate velocity is calculated with the pressure not included. This is the major difference to SIMPLE type methods: There you include the pressure gradient in the Navier-Stokes equation, so you only need to solve the poisson equation for the pressure correction. The procedure for the projection method is (with explicit time treatment for the velocities): - calculate intermediate velocity u* without the pressure gradient - calculate the divergence of the velocity field, this term will be the right hand side of the poisson equation for the pressure - discretize the poisson equation for the pressure (trivial for constant density) - solve the poisson equation iteratively - correct the velocities (explicitly) with the pressure gradient - go to next timestep Here is a link to a paper, where the projection method is used and explained with some detail: http://wissrech.ins.uni-bonn.de/rese.../croce/lsm.pdf Here is book, where the discretization of the projection method is described with even more detail: http://books.google.com/books?id=ehu...page&q&f=false Cheers Hans

 June 10, 2011, 09:50 #3 New Member   Felipe Hernandez Join Date: Apr 2011 Posts: 13 Rep Power: 7 Wow, those are great resources! Thanks for your help.

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