# Residual averaging/smoothing on unstructured grids

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 April 11, 2001, 18:06 Residual averaging/smoothing on unstructured grids #1 clifford bradford Guest   Posts: n/a Does anyone have a list of references for residual averaging on unstructured meshes?

 April 13, 2001, 12:56 Re: Residual averaging/smoothing on unstructured g #2 John C. Chien Guest   Posts: n/a (1). What is residual averaging?

 April 14, 2001, 09:24 Re: Residual averaging/smoothing on unstructured g #3 clifford bradford Guest   Posts: n/a As you are probably aware Jameson implemented several convergence acceleration techniques for the NS/Euler equation. Residual averaging is a tehnique by which after calculating the residual (ie the space dependent terms in the equations) a smoothing operator similar to the laplacian is applied. the smooothed residual is then used for time stepping. This technique is useful in accelerating convergence for explicit schemes. I was interested to know if there are any special approaches required for unstructured meshes.

 April 14, 2001, 11:30 Re: Residual averaging/smoothing on unstructured g #4 John C. Chien Guest   Posts: n/a (1). Sorry, I am not using Jameson's method. (2)."a smoothing operator similar to the laplacian is applied", how was this operator derived and how does it look like? I heard that he had developed many special techniques. (3).Was this technique originally developed for structured or unstructured meshes?

 April 17, 2001, 13:49 Re: Residual averaging/smoothing on unstructured g #5 frank Guest   Posts: n/a In some early papers of Mavriplis, this approach is described, which I implemented once too ...some time ago. It is not very difficult..just some jacobi iteration. Should be a paper by Mavriplis/Jameson if I remember it correctly. Residual smoothing is ok, but at the end I did not go for it since I use fully implicit schemes. If you do not have multigrid, explicit will be too slow anyhow and a factor of 2 or so, which you may push up the CFL number is not too exciting. Of course, if one can this factor by just a few additional smoothing operations, it is probably nice to implement. My experience is too low on it to evaluate it adequately ! If one implements boundary conditions by some kind of residual modification, one has to be somewhat careful when averaging the residuals and be sure that boundary conditions are still implemented correctly after smoothing. That is what I felt, when I did this. I will look for the Mavriplis paper tomorrow or so and post it again. Anyway, I would have a look at all the Mavriplis papers at ICASE, where he often describes this technique in context of multigrid agglomeration. Frank

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