Dear Alexander,

could you please be a little more specific in your question. Is your model non-linear or linearized? Is it time-dependent or do you consider the stady-state of your problem?

To which iterations do you refer in your question? Which parameter?

Best regards,

Pascal Omnes

Pascal,

vector potential equation is always steady like Poisson equation for stream function. I'm using locally one scheme of Samarskiy for equation approximation. Thus the iteration parameter is added. It is analogous to time and in 2D problem i can calculate it through the dimension grid. But this formula is not suited for 3D. If you can give me some advices, i'll be indebted to you

Dear Alexander,

so after discretization by finite differences, you're solving a linear equation for your vector potential (is it a vector Laplacian, or a -grad (div) + curl (curl)?).

And you are using an iterative method to solve the discrete system of equations?

Which type of iterative method? Can you describe it so that we know what you actually use, and where the parameter you want to optimize for comes into play?

With simple equations and on regular rectangular finite difference grids, it is sometimes possible to compute the eigenvalues / eigenvectors of the system matrix and use this knowledge to study the convergence of the iterative process you use.

Pascal

Pascal,

You can see the vector potential equation on figure 2. Then i replace steady equation to unsteady(Figure 3, i used this method in 2D problem and it is suitable here too). And finally you can see iteration parameter (tau) on figure 4 (finite - difference scheme). I solve it by iteration sweep method. So when I change iteration parameter, the results change too. I think it should be between 1e-4 and 1e-5. But how can i calculate the optimal value?

I know, that would be wiser to swap on finite volume method. But it will take much time for me to understand it.

Look for multigrid methods