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Hi, I have a problem with my SIMPLER routine. The residuum for the pressure equation is always the same. Has anybody an idea? I use FVM, collocated grid and SIMPLE is already working, so I think the errors must come from the pressure solution. If anybody had un easy to understand free C or Fortran Code with SIMPLER it would also help very much. Thanks!

I think is should be the same.The residual in SIMPLER will not get zero values at convergence,but as you said a constant value.

Thanks for your answer! But can you also give a mathematical explication of this behaviour?!

In the residual of the pressure equation (not pressure correction) the velocities that are being used are actually pseudovelocities (Ups=(SUM(Ai*Ui)+Su-(dP/dXi))/Ap ), that do not satisfy the continuity equation. Also the residual (or else the source of the pressure equation, Su ) must take an non-zero value, because also the pressure is not zero but a much larger value. In the pressure correction equation, when the residual is almost zero, also the P' is almost zero. Hope I have helped

Thanks for your help, George. This seems to be logical.. But I have problems yet with boundary conditions in the pressure equation. I want to fix pressure at outlet (100000 Pa), but this doesn't work. The pressure in the whole field seems to be much too low?! What can I do?! Till now I am solving the pressure equation with following boundary conditions: At the cells next to boundary I add AE*p to the source terms and AE to the central coefficients. After solving the pressure equation I do not extrapolate solved pressure to the outlet. What have I forgotten?! Please answer!

After you add AE*P and AE to the source term and the central coefficient respectively, then you should set AE equal to zero,so that your final algebraic equation will be: (AP+AE)*P=AN*PN+AS*PS+AW*PW+(SU+AE*PE) Also when you compute dP/dx at the cell next to the boundary you should include the outlet pressure in this formulation,for example: dP/dx=(P(outlet)-P)/dx ,so that the information of the specified pressure at the outlet will be incorporated to your computations. Because the pressure is much too low,are you sure that your pressure at t=0 is around 1 bar? Try these things and if it doesn't work let me know

Hi George!

This things I have already done... but it does not work... Perhaps there is an error in the basics: 1. Firstly I solve the Momentums without pressure contribution for getting the pseudo velocities. 2. Then I solve the pressure equation. 3. Then I solve the Momentums again with the pressure contribution (gradients). 4. After this the pressure correction is solved but only the velocities are corrected.

The Residuals for velocities and pressure correction are remaining high, the mass defect is getting low. Have you any idea for me?! Thanks a lot!

Dear Michael,

I have not run the SIMPLER algorithm for years, but I recall that the sequence of step is a bit different..Hopefully is just semantics:

1 - Assemble the coefficients (AP,AE,AW,AN,AP, DP) for the momentum equations. There is nothing to solve at this time, and you need to store them for use at a second time.. See (4)

2 - Create the pressure equation using the coefficients from the momemtum equation.. The coefficient multiplying the unknowns are a function of Dp, while you right hand side is a function of the Ap's and the initial guess for velocity. Apply pressure bc's as needed.

3 - Solve the pressure equation using a suitable linear solver.

4 - Complete the right hand side of the momemtum equations using the pressure field from (3).

5 - Solve the momemtum equations using a linear solver as appropriate.

6 - Assemble the pressure correction equation (which uses the same coefficients as in (2), but the right hand side is obtained using true velocities from (5)

7 - Solve for p'

8 - Correct the velocity field using solution from (7)

Do not relax the pressure field, and do not add the pressure correction to it either..

Good luck, Opaque..

PS. Have you read about SIMPLE X? I think it behave better than SIMPLER for very fine meshes..

Hi,

It is working better now, but yet not really well. The residuals for u,v and pressure correction are not falling under certain values. Also the massdefect is not really falling down. Can it be that there are yet problems resulting from the collocated grid arrangement?! What's about Rhie Chow Correctors. How do they differ in pressure and pressure correction equation?!

Can you help me?!

PS: The first solving of momentum equation I use only to get the pseudo velocities... for the right hand side of the pressure equation!

Dear Michael,

The important assumption of the pressure equation right hand side is that the velocity field satisfy continuity. The solution of the momemtum equations do not satisfy the continuity equation; therefore the need for the pressure correction equation.

I recall that SIMPLER should start from an initial guess that satisfy continuity,so pressure field is "physical", you solve for momemtum, and correct the momemtum velocities via p'. P' is not longer a pressure correction, but a mass correction field.

As a Rhie-Chow corrections, I never did the collocated arrangement..

Good luck, Opaque..