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.
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?
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:
Here is book, where the discretization of the projection method is described with even more detail:
Wow, those are great resources!
Thanks for your help.
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