CFD Online Logo CFD Online URL
Home > Forums > Main CFD Forum

the criterium of convergence for the SIMPLE algo

Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Display Modes
Old   July 23, 2007, 08:22
Default the criterium of convergence for the SIMPLE algo
Posts: n/a
Hi all,

The SIMPLE algo is like that:

1. Set the boundary conditions.

2. Solve the discretized momentum equation to compute the intermediate velocity field.

3. Compute the mass fluxes at the cells faces.

4. Solve the pressure equation and apply under-relaxation.

5. Correct the mass fluxes at the cell faces.

6. Correct the velocities on the basis of the new pressure field.

7. Update the boundary conditions.

8. Repeat till convergence.

But what does "till convergence" mean?

norm[U_(n+1) - U_(n)]/norm[U_(n)] < tol is a good criterium?

I need some advice,

thanks in advance,


  Reply With Quote

Old   July 25, 2007, 09:08
Default Re: the criterium of convergence for the SIMPLE al
Lionel S.
Posts: n/a
Hi Lam,

I first thought that someone would have a good answer to give, but as nobody answered, I will try to help.

"But what does "till convergence" mean? " "norm[U_(n+1) - U_(n)]/norm[U_(n)] < tol "

Well... It's difficult to say, but I would think that that criterion is not really good.

Personally, I would think that the best way to evaluate the convergence of a CFD software is evaluating Navier Stokes and mass conservation FULLY EXPLICITLY.

I mean: you take every terms of NS at one side of the equality, which gives

rho . v . grad(v) + grad(p) - mu . laplacian(v) - rho . f

For an "exact" solution This shoud give zero. But if at some iteration you evaluate ALL these terms explicitly (with known values) it will give you a non null number, which is a good approximation of the error. Unfortunately, it strongly depends on your discretization scheme (finite volume finite elements or whatever)

In my personal CFD code, this gives some strong errors, even for a very good looking (physical) solution. But now it depends on how you evaluate the total error on the entire domain. Personally, I sum all these errors on each finite volume. Another possibility is to take

total error = sqrt ( sum(e_i) )

where e_i is the error of the i th control volume or finite element.

But actually, there is no perfect way to know if a numerical solution is a good approx. of the Navier Stokes continuous solution.

Hope it helps.

  Reply With Quote


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
SIMPLE algorithm in 3D cylindrical coordinates zouchu Main CFD Forum 1 January 20, 2014 18:02
Questions about the simple algo lam OpenFOAM Running, Solving & CFD 1 July 30, 2007 12:41
SIMPLE and energy equation convergence Fabio Main CFD Forum 0 June 1, 2007 06:06
Defect correction and convergence ganesh Main CFD Forum 4 June 30, 2006 14:20
SIMPLE for variable viscosity, poor convergence ? Anthony Ilaner Main CFD Forum 15 July 13, 2000 08:04

All times are GMT -4. The time now is 21:36.