
[Sponsors] 
February 26, 2008, 17:24 
specify a reference pressure point in FD method?

#1 
Guest
Posts: n/a

Hi everyone,
I had a problem to specify a reference pressure point in finite difference method cases. We are use laplacian(P)=div(U)*rho/dt to calculate the pressure. In a fully wall bounded case, we allpied homogeneous Nuemman boundary condition at the wall for the Poisson equation. But because it is a fully wallbounded case, we cannot get a unique results without specify a reference pressure point in the domain. We can do some operation to the Laplacian coeffecient matrix to get a specified pressure value at the reference point. But how we can update the pressure value at this point? Any reply will be highly appreciated! Cheers, Rui 

February 26, 2008, 21:53 
Re: specify a reference pressure point in FD metho

#2 
Guest
Posts: n/a

At one node on your grid, replace the finite difference approximation to the LaPlace equation with P = P_reference.
In other words, you don't update it, you freeze it. For direct methods, I think you must do this to avoid a singular coefficient matrix. For an iterative solution (relaxation for example), you'll obtain a value for the reference node, p = p_rn. Use this to correct the entire pressure field by p_node = p_reference  p_rn . You'll probably get other suggestions ... 

February 27, 2008, 05:05 
Re: specify a reference pressure point in FD metho

#3 
Guest
Posts: n/a

Thank you very much, otd! Freeze it? You mean using the matrix, changing the diagonal entry into 1, and other entry into 0? But in this way, when I calculate the pressure gradient, I will have trouble. I need the pressure gradient to correct the velocity, which is the projection method to couple velocity and pressure.
For an iterative solution, what is it? Can you provide more details?? 

February 27, 2008, 09:13 
Re: specify a reference pressure point in FD metho

#4 
Guest
Posts: n/a

Change the diagonal to 1, the RHS to P_reference (which could of course be 0). Then use the calculated value (P_reference) at that point for your corrections.
I'm not on top of the latest relaxation schemes (including multigrid). My experience is that relaxation is tolerant of what would be a singular matrix. You can learn a lot about these things with small 2d heat conduction simulations. Numerical analysis books (maybe online course notes) will tell you a lot about relaxation schemes, which you can try out on a PC with a relatively small investment of your time. When you're done, you'll know as much as most of the rest of us! Good luck. 

February 27, 2008, 10:04 
Re: specify a reference pressure point in FD metho

#5 
Guest
Posts: n/a

Thank you very much!!!!!


February 28, 2008, 07:59 
Re: specify a reference pressure point in FD metho

#6 
Guest
Posts: n/a

But the thing is I am using projection method to update velocity from pressure field, which means I calculate a intermedia velocity, U*, from momentum equation, but without pressure gradient, and then solve poisson euqation to get the pressure, afterwards use the pressure gradient to correct U* to get U(n+1).
So if I cannot update the pressure at the reference point, I cannot get an accurate U(n+1). The error will turned to be very big, even I use interpolation to update the pressure very time step. Is there any other way to update the pressure at the reference point?? Many thanks in advance! 

February 28, 2008, 11:42 
Re: specify a reference pressure point in FD metho

#7 
Guest
Posts: n/a

In my experience, the pressure equation can be solved using iterative methods such as SOR (successive overrelaxation), ADI (alternating direction implicit) WITHOUT pinning a reference pressure. What counts is the gradient (numerically the difference in pressure between neighboring nodes).
I haven't tried multigrid but someone in the cfdonline community surely has. My level of linear algrebra experience (solution of simultaneous equations using direct solvers) requires passing a nonsingular matrix the solver (pinning one value for instance) to obtain a unique solution. Perhaps someone else on the forum has some suggestions for you. 

February 28, 2008, 11:54 
Re: specify a reference pressure point in FD metho

#8 
Guest
Posts: n/a

Yes. But in FD, for a fully wallbounded case, if we do not specify a pressure reference point, the linear problem will be illconditioned. Poisson equation is a second derivative equation, but at the boundary, we only have dp/dn = 0, the homogeneous Neumann boundary condition. So we need a reference point to get a unique result.
I think we are talking about different things, otd. thank you very much for the suggestion!!! 

February 29, 2008, 10:48 
Re: specify a reference pressure point in FD metho

#9 
Guest
Posts: n/a

I've assumed that you're interested in incompressible flows here  you're not solving for energy transport and an equation of state. In particular, you have a fluid/flow combination in which density variation is negligible. Is this the case?
If so, the pressure LEVEL is arbitrary. Only the pressure GRADIENT is unique. To show this, assume that you calculate a pressure field that satisfies the Poisson equation grad p = D*rho/delt. Call that solution p*(x,y). Add ANY constant to that, PP(x,y) = p*(x,y) + p_const. Because grad p_const = 0, PP(x,y) also satisfies the Poisson equation. If you are comparing to data (a tranducer reading at one point in the flow for example), use that to determine p_const. If in fact you have a compressible fluid/flow problem, that's a whole different discussion. 

February 29, 2008, 13:34 
Re: specify a reference pressure point in FD metho

#10 
Guest
Posts: n/a

But the thing is for finite difference method, in a fully wallbounded domain, you cannot solve the Poisson equation without any Dirichlet boundary condition. So we need specify a point with a guessed pressure. The problem arises here that how we can update the pressure at this point?


August 30, 2010, 08:50 
Did you find out what to do with the reference pressure point?

#11 
New Member
Join Date: Aug 2010
Posts: 2
Rep Power: 0 
Hello,
I followed your discussions. I have exactly the same problem with the Poisson equation of the projection method for incompressible NavierStokes. @Rui: How did you solve the problem? Thanks in advance 

Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
It would be wonderful if a tool for FoamToTecplot is available  luckyluke  OpenFOAM PostProcessing  165  November 27, 2012 07:54 
Compiling new Solver with wmake  lin123  OpenFOAM  3  April 13, 2010 14:18 
TwoPhase Buoyant Flow Issue  Miguel Baritto  CFX  4  August 31, 2006 12:02 
Building OpenFoAm on SGI Altix 64bits  anne  OpenFOAM Installation  8  June 15, 2006 09:27 
How to apply negtive pressure to outlet  bioman66  CFX  5  June 3, 2006 01:40 