Strcture of pressure correction equation in PISO stable over time ?

sebi · October 26, 2010, 05:09

Hello everybody,

I have a problem in understanding why the things I'm doing work. I'm using the PISO algorithm to solve the Navier-Stokes equations. In there I have to solve the Poisson-like pressure equation which I'm solving with an algebraic multigrid solver.
Unfortunatly my PISO algorithm does not use a real Poisson pressure equation like -/LAPLACE/ p= RHS, but it includes the flux a caused by this correction into the operator.
This is, I have - /DIV/ a /DIV/ p = RHS.

For the standard PISO with a real Poisson pressure equation it is pretty clear that the structure of the matrix resulting from discretising this will never change over the time steps. But how is this in my case ?
I see that the matrix' structure doesn't really change so I can use the AMG coarsening once and once again without giving a new setup. But this is too heuristic in my eyes.

So my question is: Can I argue from any physical point of view that the structure of my matrix stays as it is ?
Does anyone have an idea or a hint where I could read about this ?

KIndest regards,

Sebi

harishg · October 26, 2010, 22:19

PISO algorithm was a method proposed for pressure-velocity coupling of incompressible flows. There are many ways in which the algorithm has been used in the literature. Check the paper based on which the code was written. It might be a good starting point to understand.

October 26, 2010, 05:09	Strcture of pressure correction equation in PISO stable over time ?	#1
sebi New Member Join Date: Feb 2010 Posts: 7 Rep Power: 16	Hello everybody, I have a problem in understanding why the things I'm doing work. I'm using the PISO algorithm to solve the Navier-Stokes equations. In there I have to solve the Poisson-like pressure equation which I'm solving with an algebraic multigrid solver. Unfortunatly my PISO algorithm does not use a real Poisson pressure equation like -/LAPLACE/ p= RHS, but it includes the flux a caused by this correction into the operator. This is, I have - /DIV/ a /DIV/ p = RHS. For the standard PISO with a real Poisson pressure equation it is pretty clear that the structure of the matrix resulting from discretising this will never change over the time steps. But how is this in my case ? I see that the matrix' structure doesn't really change so I can use the AMG coarsening once and once again without giving a new setup. But this is too heuristic in my eyes. So my question is: Can I argue from any physical point of view that the structure of my matrix stays as it is ? Does anyone have an idea or a hint where I could read about this ? KIndest regards, Sebi

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October 26, 2010, 22:19		#2
harishg Senior Member N/A Join Date: Mar 2009 Posts: 189 Rep Power: 17	PISO algorithm was a method proposed for pressure-velocity coupling of incompressible flows. There are many ways in which the algorithm has been used in the literature. Check the paper based on which the code was written. It might be a good starting point to understand.