[tchitchas]

Hello Guys, I developed a code in fortran to solve the 2D lid-cavity problem using the FVM.

I used the SIMPLE algorithm with staggered grid and to solve the linear equations resuting from the momentum (x,y) and continuity, i used the Gauss-Seidel method.

With a coarse refining, the results converge very quickly. However, when I refine the mesh (something like 150x150 volumes), the result continues to converge, but it takes soooo many iterations for the convergence of the system of equations from the continuity (to find p correction). It took almost 20 hours to finish the simulation.

I used a residual of 1.10^-8

The results are close to expected (comparing with benchmark)

Is this behavior normal? Or is something wrong?

Thank you in advance.

[AliE]

Hello,

Gauss-seidel has a very slow convergence comparered to krilov subspace solvers. Try a preconditioned conjugate gradient for the pressure-correction equation. It is straightforward to implement.

[FMDenaro]

Originally Posted by tchitchas

Hello Guys, I developed a code in fortran to solve the 2D lid-cavity problem.

I used the SIMPLE algorithm with staggered grid and to solve the linear equations resuting from the momentum (x,y) and continuity, i used the Gauss-Seidel method.

With a coarse refining, the results converge very quickly. However, when I refine the mesh (something like 150x150 volumes), the result continues to converge, but it takes soooo many iterations for the convergence of the system of equations from the continuity (to find p correction). It took almost 20 hours to finish the simulation.

I used a residual of 1.10^-8

The results are close to expected (comparing with benchmark)

Is this behavior normal? Or is something wrong?

Thank you in advance.

First, the convergence velocity depends on the spectral radius of the matrix. The BC.s can change the structure of the matrix. I am not sure about what you are doing, you wrote "linear system", thus have you linearized the momentum equation?

Finally, think to use the SOR with a proper acceleration factor.

[LuckyTran]

Yes, slowness should be expected. You need an accelerator.

See also multigrid methods (i.e. algebraic multigrid and geoemtric multigrid).

Slow convergence on finer grids is the price you pay for discretizing the gov. eqns. The short-wavelength errors converge quickly (cell to cell changes) but the long-wavelength ones don't (say from an interior cell to the boundary). When you make the grid finer, you make this convergence rate slower for the long wavelengths.

[tchitchas]

Originally Posted by FMDenaro

First, the convergence velocity depends on the spectral radius of the matrix. The BC.s can change the structure of the matrix. I am not sure about what you are doing, you wrote "linear system", thus have you linearized the momentum equation?

Finally, think to use the SOR with a proper acceleration factor.

Hello FMDenaro, thanks for the reply, sorry for the lack of information. Yes, I linearized the convective term of the momentum equation with the SIMPLE method. I will try the SOR to accelerate the convergence.

Thanks for the answer.