[Zach_uky]

Hi, I know there are a lot of thread about pressure poisson equation, I ve read all of them, but I haven't found a solution for my problem. Next let me tell you the details of my problem.

First, I have compressible flow solver, after several years of work, it can solve turbulent problem well. But my adviser think it is too slow to solve an extra energy equation, want me write a incompressible solver based on this frame.

I works several weeks now. This code is a finite volume code. all of the value is in the cell center. I choose projection method for the incompressible solver. First solve NS equation without pressure to get the velocity u* which does not satify divergence free filed u. Then solve the pressure poisson equation and project the velocity to divergence free field. The pressure poisson equation is
Δp=(▽• u*)/t
which could be discretized as
∑A*n• (lr)(p_l-p_r)/(lr)^2=V*(▽• u*)/t
where p_l and p_r is the left and right side pressure, t is time step length, V is volume, A is the face area, n is the normal of the face, (lr) is the vector from left cell center to right cell center. we also can set
AoverH= A*n• (lr)(p_l-p_r)/(lr)^2

Then the projection part is
u=u*-t▽p

Then go to next time step. When I solve the pressure poisson equation, I use
divergence in the cell center as the right hand side(rhs) of my solver, then put the jacobian AoverH into the martix(C).
Then the problem is
C * P=rhs
For the boundary condition, I use neumann condition for inlet, wall, symmetry, but 0 pressure for outlet.
My solver is a domain splitting MPI code. I use GMRES in petsc to solver this problem, the grid I use is a 100000 grid mesh, it is a quarter pipe.

my problem 1: for the neumann boundary face, whether AoverH should be zero? When I set AoverH to zero at the boundary, the iteration number is huge about 1000, the result is right. When AoverH is not zero, the iteration is no more than 20. after converge, the result is wrong.

Problem 2: if AoverH on the neumann boundary should be zero, how to decrease the iteration number.

problem 3: I have not use stagger grid, p and u are in the cell center, is that ok?

Can any one give me some guidance? Thank you in advance