# Deriving pressure from velocity

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 August 14, 2014, 09:42 Deriving pressure from velocity #1 Member   Join Date: Aug 2014 Posts: 58 Rep Power: 4 Hello everybody, I am currently trying to implement a CFD code for deriving pressure from velocity in 2D. It's not a problem which has been solved a lot. Problem : " I have a velocity field on a structured mesh but not necessarily rectangular..and I have to find the pressure field." First I have tried to solve this problem on a rectangular fully populated grid and then on any grids with the Finite Element method. I try different methods for solving this problem: an iterative method and the Pressure Poisson equation. I haven't good results with both. But I focused on the pressure poisson equation. Do you think this method could give some good results for different kind of flows ? ( not too turbulent ) I compute F=Ux^2 + 2 UxUy + Uy^2 and then solve the linear system AP=F where P is the pressure and A the 2D-laplacian matrix. I implemented Neumann or dirichlet boundaries inside A and F depending on the problem. No relevant results..So I tried to do the same with a staggered grid with P on the center of the cell and U and V on the edges. But no good results or the A matrix was singular . So finally I want to know if I am on the right way or if I should choose an other method ? I am quite lost at the time being.. Thank you very much, I can clarify some points if necessary ! Samy

 August 18, 2014, 16:41 Pressure from velocity #2 Member   Join Date: Aug 2014 Posts: 58 Rep Power: 4 Hi again, Is everyone had already compute the pressure field from velocity field ? What the more accurate method ? Thank you very much, Best, Samuel

 August 21, 2014, 13:31 #3 Senior Member   Sebastian Engel Join Date: Jun 2011 Location: Germany Posts: 139 Rep Power: 9 Hi samycfd, unfortunately i don't have any helpful advice for this topic. Iin my studies abroad, i met a Professor of Niigata University, Prof. Fujisawa. His laboraty was working on a simular topic. I recalled the following paper "Measurement of Pressure Field around a NACA0018 Airfoil from PIV Velocity Data", Journal of Visualization. http://iospress.metapress.com/content/x13646u580l57uh8/ There is a preview page of this short paper. Maybe all relevant information for you is included in that paragraph. With regards, Sebastian

 August 22, 2014, 04:44 #4 Member   Join Date: Aug 2014 Posts: 58 Rep Power: 4 Thank you for your answer. I know this method but it doesn't work for me. Have you ever solved the Pressure Poisson equation ?

 August 22, 2014, 11:20 #5 Senior Member   Sebastian Engel Join Date: Jun 2011 Location: Germany Posts: 139 Rep Power: 9 No, i haven't.

August 25, 2014, 12:03
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Shenren Xu
Join Date: Jan 2011
Location: London, U.K.
Posts: 63
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Solving the Poisson equation the way you described seems okay. Could you post the velocity field you used and one pressure solution you computed just for the readers to get an idea how good/bad your pressure solution is?

Poisson eqn. might be stiff to solve, so it'll help if you could show the convergence of your Poisson solve.

Quote:
 Originally Posted by samycfd Hello everybody, I am currently trying to implement a CFD code for deriving pressure from velocity in 2D. It's not a problem which has been solved a lot. Problem : " I have a velocity field on a structured mesh but not necessarily rectangular..and I have to find the pressure field." First I have tried to solve this problem on a rectangular fully populated grid and then on any grids with the Finite Element method. I try different methods for solving this problem: an iterative method and the Pressure Poisson equation. I haven't good results with both. But I focused on the pressure poisson equation. Do you think this method could give some good results for different kind of flows ? ( not too turbulent ) I compute F=Ux^2 + 2 UxUy + Uy^2 and then solve the linear system AP=F where P is the pressure and A the 2D-laplacian matrix. I implemented Neumann or dirichlet boundaries inside A and F depending on the problem. No relevant results..So I tried to do the same with a staggered grid with P on the center of the cell and U and V on the edges. But no good results or the A matrix was singular . So finally I want to know if I am on the right way or if I should choose an other method ? I am quite lost at the time being.. Thank you very much, I can clarify some points if necessary ! Samy

 August 26, 2014, 03:45 #7 Member   Join Date: Aug 2014 Posts: 58 Rep Power: 4 I compute the Lid-driven cavity case in FLUENT ( pressure and velocity) and then with my algorithm I get the following pressure field( blue ) https://drive.google.com/folderview?...EU&usp=sharing

 August 26, 2014, 08:28 #8 Member   Join Date: Aug 2014 Posts: 58 Rep Power: 4 Do you think it would be better solving the PPE with the Finite Volume method ? Ps: I often have Neumann BC on each edges so I define one reference point on an edge as Dirichlet value to avoid the matrix to be singular ( as discussed in many other threads... ) And the particular point in the pressure field is the point I defined.. If i change the location we will able to see it in the pressure field. So something is apparently wrong !

 August 26, 2014, 09:37 update ! #9 Member   Join Date: Aug 2014 Posts: 58 Rep Power: 4 I have found an error ! So my pressure field is , for this velocity field :

 August 28, 2014, 19:51 #10 New Member   Join Date: Aug 2014 Posts: 2 Rep Power: 0 May I ask if the flow problem of the thread's author has an incompressibility constraint? Nobody mentioned so far if incompressibility is assumed or not. So I just wanted to know. (I was in the believe that the Poisson Equation can be only derived, if incompressibility is assumed, but I may be wrong such that my question is of no relevance). Last edited by 12er; September 2, 2014 at 07:40.

August 29, 2014, 02:46
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Join Date: Aug 2014
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Quote:
 if the flow problem of the thread's author has an incompressibility constraint?
Yes you're right. I assume that the constraint is verified and I checked if it's true. If not I know that results could be wrong.

Do you know if I can reconstruct the velocity field in order it satisfy the constraint? As in the pressure correction algorithm ?(SIMPLE)

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