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February 23, 2007, 19:11 
convergence criterion

#1 
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hi, i've asked this question on a previous thread, but its so far back that i dont think anyone will see it. I'm a third year student currently doing my 3rd year project and i'm using fluent to analyse fluid over a submerged submarine fin. now i'v manage to get some results from it, but its just a matter of interpreting them. i know this will sound really stupid. But what is the convergence criterion? I understand what the word means, but i dont know how it relates to CFD. Also, when iterating, a graph is plotted of the residuals against no of iterations which i am unsure about. Please, if anyone can help me leave a message


February 24, 2007, 04:58 
Re: convergence criterion

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Hi,
Well, first I should say that I don't know precisely what Fluent is plotting as "residual". But more generally, in CFD: You have two types of iterations. One point is to understand that you have to solve linear systems (Ax=b), which is done by an iterative way (direct methods would be very time and memory expensive). So the solvers iterates to solve Ax=b, and the residual at one time the "linear" residual is norm(Axb) where x is the current solution (to be improved from one interation to another). The second point is the fact that when you solved one linear system Ax=b, you have NOT finished your job. Each linear system represents the linearisation of NavierStokes equations around ONE point, and this point will change, as we get more and more accruate solutions from time to time. So another residual is the difference between two consecutive solutions: norm(xx_prev) where x is the current solution of current linear system and x_prev is the solution of previous linear system, which represents differential equations linearized at another point. If you have converged to the right solution, then the two types of iterations should converge, IE the residual should be very small. By a very practical point of view, I don't know what Fluent means by "residual" (is is linear residual, differences between consecutive solutions or probably a mix of them) but usually you take 1e3 as convergence criterion for all values for a first calculation, and then you can lower it to 1e4 or 1e5 to get a much more precise solution. But it shouldn't change the solution very much. Hope it's clear, but sorry I'm not an expert of Fluent, even I work on it sometimes Bye Lionel 

February 24, 2007, 06:14 
Re: convergence criterion

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you point to a critical point.
Generally when we have a wellpose numerical model, under stability/consistency bound of numerical method, we expect convergence. I think that your questin is that when we cut simulation or adjust convergence criteria of various solvers (in fluent: xmom, ymom, continuty, energy, ...) to what treshold (is it?) I think that answer to this at first needs some prior information about behavior of solution (need atleast some numerical experiments) and then we must indicate what is our aim from simulation. For example you answer lift or drag, so you must change convergence criteria and monitor its effect on the parameter under study then decide to what treshold is sufficient. More details: It is ideal to automate this task, fortunately some effort were done for this, in clear: automatic adjusting simulation parameters to acheive desirable accuracy for parameter under study. Using error recovery, error estimation and h/p grid adaptation is usuall for this purpose. If you are interested i conduct you to seris of work in Heidelberg university due to R. Rannacher et. al. They publish a book that i found it as the best one in this field. 

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