Change of Poisson solver in a predictor-corrector scheme gives inaccurate results

oyrabl · December 7, 2016, 16:16

Hi.

I'm implementing a new higher order method for the Poisson equation, to do the pressure correction in a predictor-corrector scheme.
The rest of the code is discretized with FDM on a staggered grid.

The code is tested for the flow around a square cylinder, in the laminar regime. With the old, second order solver, I'm able to reproduce benchmarks from the literature. However, the new Poisson solver is not able to reproduce the same results. The drag coefficient obtained with the new method is too high, and the wake is not properly reproduced. The results are not improving when the grid is refined.

The only thing that is changed is the routine for the solving the Poisson equation. I'm using Neumann BC at all boundaries (dp/dn=0), except for one corner where the pressure is fixed.

I've tested that the volume integral of the RHS is zero.

The developer of the originally code is on vacation, and I've not access to the entire source code. My code is implemented with matlab engine in a fortran code.

Any ideas what the problem could be? I've attached the streamlines and contour plots of the pressure for the two methods(for a very coarse grid). The Reynolds number is 40.

Thanks!

FMDenaro · December 7, 2016, 16:48

If you are using a fractional-step method, the Poisson equation must enforce the divergence-free constraint. It means you have to discretize the equation

Div Grad p = q ,

not the equation

Lap p = q .

The Grad p term that you discretize in the pressure equation must then be used in the correction of the momentum.

Said that, if your solver fulfill the integral of the RHS to be zero, your solver must converge also without fixing te value, thus I suggest to check that. Furthermore, check if the divergence-free constraint is satisfied as the same way as for the second order code.

Are you sure that the figures are taken at the same steady state threshold?

Santiago · December 20, 2016, 18:15

Why you enforce a dirichlet BC in for the poisson solver? Remember that the 'pressure' expressed in the laplacian equation is a lagrange multiplier that 'optimizes' the velocity field towards a divergence-free space. No physical BCs should be imposed to it, except those coming from a normal projection of the momentum equation. Try to use homogeneous neumann everywhere

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December 7, 2016, 16:48		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,897 Rep Power: 73	If you are using a fractional-step method, the Poisson equation must enforce the divergence-free constraint. It means you have to discretize the equation Div Grad p = q , not the equation Lap p = q . The Grad p term that you discretize in the pressure equation must then be used in the correction of the momentum. Said that, if your solver fulfill the integral of the RHS to be zero, your solver must converge also without fixing te value, thus I suggest to check that. Furthermore, check if the divergence-free constraint is satisfied as the same way as for the second order code. Are you sure that the figures are taken at the same steady state threshold? psakievich likes this.

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December 20, 2016, 18:15		#3
Santiago Senior Member Santiago Lopez Castano Join Date: Nov 2012 Posts: 354 Rep Power: 16	Why you enforce a dirichlet BC in for the poisson solver? Remember that the 'pressure' expressed in the laplacian equation is a lagrange multiplier that 'optimizes' the velocity field towards a divergence-free space. No physical BCs should be imposed to it, except those coming from a normal projection of the momentum equation. Try to use homogeneous neumann everywhere Sent from my GT-I8190L using CFD Online Forum mobile app