I am not a CFD expert and my knowledge of CFD is a bit sketchy but I am currently involved in a research focused on accelerating convergence of CFD codes using AI techniques. In brief, there is an intelligent software agent on top of CFD solver, which (the agent) constantly monitors the simulation output (mainly residual errors) and adjusts the crucial control parameters (relaxation and time step size). The agent is quite sophisticated, as it can perform automatic divergence recovery and also occasionally experiments by trying out different relaxation parameters/time step sizes in order to speed up the solution. The initial results are very encouraging but there is still a lot of work to turn it into a usable piece of code.

Does anyone know of anyone doing similar research? Do you know if there are other codes that use automated dynamic control (any kind)? I know that Phoenics has EXPERT module in their software that dynamically adjusts the relaxation but I could not find any details how it works (well, I did not expect to find any . Any help appreciated.

(1). How do you know that it will converge to the right solution? and will not run into a closed loop? (2). Actually, if one just take the density-based, explicit approach, one can march in time without worrying about the convergence issue, right? Now you have an initial value problem.

Firstly, the agent only works for transient cases, i.e. when the time accuracy is important and we are interested in finding correct solutions to several consecutive time steps. It is assumed (this is the requirement) that the simulation is correct if all the time steps converged. (1). You never know for sure whether you got the right solution, do you? The agent is concerned with convergence assurance and performance, not solution validation. I guess it is OK to assume that if the solver converged then the solution is likely to be correct. On the other hand, if 80% of time steps did not converge (which often happens) then the solution is at least inaccurate. Closed loop is detected and if the agent fails to recover from it then human interaction is necessary. (2) Does the first part fo my message answer that? What exactly do you mean by initial value problem? The technique I am using is a completely different to other convergence acceleration methods like preconditioning.

Despite the expressed reservations, this idea has some merit.

After training on Fluent, then on CFX-4 (and at least one more product), I observed that the one common feature for using these products was/is the call to the support line for help in guiding the iterations to convergence. Typically the help staff (gurus) drew on their experience (which varied wildly!) to suggest changes in technique (multi-grid, over-relaxation, relaxation by lines, etc), relaxation factors, etc.

One problem with this technique was that the advice given would often vary depending on who answered the phone and his/her mood for the day. Another was the occasional delay in getting any answer. One advisor (name and company surpressed to protect the guilty) had been taught somewhere that his efficiency could be enhanced if he answered his phone messages early in the morning, just after lunch, or late in the afternoon!

But the advice given by the support staff could surely be captured by an AI agent as you have done. Feedback to the user would be immediate, and the support staff could give more concentrated attention to the problems that the agent could not solve.

The unique useful responsibility of support staff is/was their help in setting up problems, drawing on a large experience base obtained by helping many customers. If a similar problem has been solved and the staff knows about it, you gain a head start by drawing on that experience.

Of course any solution obtained should be given very careful scrutiny by the end user. As always, it's buyer beware!

(1). Well, there is a big difference between "commercial cfd codes" and "reliable engineering solutions". (2). If the reader is interested in "reliable engineering solutions" then gothroughing through "commercial cfd codes" and "software support" plus "user's skill in using the codes" is one possibility, but not a very good one. (3). The existence of "commercial cfd codes" is business issue, it is not linked to the user's ability to solve his problem using the codes. (4). As you have mentioned, even the software support is a function of time (which is consistent with the no-warranty policy of software business.) (5). Commercial cfd codes are somethings for the experts, who knows how to use it properly.(understand the limitations)

Something similar has been done at University of Waterloo, Mechanical Engineering, (www.uwaterloo.ca) regarding multigrid methods. They decided on how to coarsen the mesh at every timestep by using a (very simple) dynamic method that I guess could be called AI.

I would like to point out Prof. Deborah Kaminski's work at RPI. There are some interesting applications of "fuzzy logic" in accelerating code convergence.

Within the CFX commercial software, we use the "Algebraic Multigrid Method", with or without variable coupling. This work originated at the University of Waterloo. The method does indeed use coarsening strategies (ie how the virtual coarse meshes are created) that vary from timestep to timestep with the intent to maximize the solution rate of the LINEARIZED equations - ie it does not directly accelerate the convergence of the outer loop. Of course if you don't solve the linear system, the outer loop will not converge either! The software to do this is "simple" in the sense of not taking a lot of source code, but "powerful" in the sense of speed and robustness. Finally, I don't think it would be justified in calling the coarsening algorithm "AI". It is a subroutine that looks at varies scales in the matrix and follows some heuristics - there is no learning, or pattern recognition, etc., that characterizes real AI. For details see paper AIAA 96-0297.