CFD Online Logo CFD Online URL
Home > Forums > Main CFD Forum

Poisson Solver or suitable scheme

Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Display Modes
Old   August 3, 2006, 16:49
Default Poisson Solver or suitable scheme
Posts: n/a
Hi, I'm programing a 2D(it would be 3D later) incompressible viscous internal flow code recently(Re~1000-3000). I use franctional-step method(by Kim and Moin 1985) and adaptive grid. However, I have trouble with soving Poisson equation. Because I'll deal with complicate geometry later, therefore fast Fourier sovler doestn't work in my case.

Anyone can suggest me which numerical scheme I can use to solve the Poisson equation or where I can find the existing code online??!!

Another small question is the boundary of pressure. By the paper, it said that we don't need ad hoct boundary for pressure by adaptive grid. However, when I solve the Poisson equation of phi, I do need the boundary condition, rihgt? What should I do with that?

It's a long question. Thanks for your patience and attention.

  Reply With Quote

Old   August 4, 2006, 06:47
Default Re: Poisson Solver or suitable scheme
Posts: n/a

Ultimately the discretized Possion Equation leads you to a system of equations Ax=B. You can then use standard open source solvers like PETSc or LAPACK. You just need to input the coefficient Matrix A and B in a specific order. Im not sure of the adaptive case but you can have a look at it.

Pressure b.c in physical sense is not required. However you need a b.c for phi since it forms the poisson eqn. It comes like this :

If the intermediate solution is 'us', then, we know, it is decomposed as:

us = u_n+1_ + dt*grad(phi). Taking the normal component,

gives rise to: = n.u_n+1_ + dt* n.grad(phi).

mostly, it is assumed that at the boundary, 'us' assumes the value of u_n+1_ . So the above eqn bcomes : n.grad(phi)=0. And it so happens that in this case by virtue of the 1st order time discretization, phi has to be equal to 'p' so that the splitting is exact. When its a second order crank nicholson discretisation, using phi=p will give a wrong splitting.

This sort of b.c for pressure is argued in literature as the formation of numerical boundary layers, since this boundary condition is numerical and not physical.

There are higher order methods in which phi = p + f( and in this case you never say that you are having a b.c for pressure, but phi instead.


  Reply With Quote


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
Working directory via command line Luiz CFX 4 March 6, 2011 21:02
Poisson solver nikwin OpenFOAM Running, Solving & CFD 1 April 17, 2009 16:59
why the solver reject it? Anyone with experience? bearcat CFX 6 April 28, 2008 14:08
Poisson Solver oevermann OpenFOAM Running, Solving & CFD 1 April 12, 2006 06:05
Which scheme is suitable for NS under vacuum? Zhihang Zhang Main CFD Forum 1 January 21, 2004 20:47

All times are GMT -4. The time now is 19:31.