Pressure from Particle Image Velocimetry Measurements
 

Hello to everyone,

I got the instantaneous 2D velocity measurements from Particle Image Velocimetry inside the region of a hydraulic jump.

I want to calculate the mean time pressure field from the mean time velocity measurements by the numerical solution of the Reynolds averaged Poisson Pressure equation.

I solve the resulting system with the Jacobi method but the iterative algorithm does not converge as the absolute difference between the updated pressure field and the pressure field calculated from the previous iteration is not getting smaller.

Any ideas for the problem ?

Thank you.

Could you give the details? I suppose you want to solve

Div Grad p = source,

the LHS being in your case?
But to state the full Poisson problem you need to prescribe the BCs, how did you prescribe that?
Are you working on a cartesian structured grid?

Yes I want to solve Div Grad p=source. The equation follows the Reynolds average approach, so Poisson equation for pressure also contains the Reynolds shear stress terms in the RHS.
All BCs are Newmman conditions regarding the grad(p) calculated from the two dimensional Reynolds averaged Navier Stokes equations.
I work on a cartesian structured grid which is the same with the grid that the velocity has been measured with PIV.

Tu ensure convergence of an iterative method, you have to fulfill the compatibility condition. Thus, I suppose you prescribed the Neumann conditions in a non correct way.

Check for similar discussions in this forum.

Please can you propose me papers regarding the compatibility condition ?

Thank you.

That is a classic topic in mathematical anaysis of PDE. Just search on Google:
https://www.google.com/search?client...eumann+problem