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 Faraz December 27, 1999 23:14

Grid Quality and the Solution

Has the solution accuracy and convergence been quantitatively or qualitatively been related to grid quality? I would include a measure of cell skewness (or minimum face angle) and grid smoothness (volume ratio of adjacent cells) as the criteria for grid quality. Has there been any attempts to solution adaptive mesh improvement (not refinement, but mere readjustment of nodes).

A related question: I have often heard from experience CFDers that they use a volume ratio of 1:2 max. But for unstructured grids this ratio may not be maintained after grid adaption (I am assuming the hanging node adaption). Assuming that the initial grid had a 1:2 volume ratio, a hanging node adaption would result in local volume ratios being in the range of 1:3 to 1:12. How does that affect the solution?

 Jin Wook LEE December 28, 1999 05:07

Re: Grid Quality and the Solution

Grid dependence on the solution accuracy is very hard to be explained. As many know, there are many factors which affect the solution accuracy. However, within my experience with structural grids, rapidly generated(so, maybe poor) grids always show difficult convergency trend. So, I am always spending much time to generate good grid net for my new simulation.

Jinwook

 Faraz January 4, 2000 02:17

Re: Grid Quality and the Solution

Thanks for your response. I am trying to understand the definition of a "good" grid. I think it varies from user to user. from solver to solver (or the persons who have actually coded the solver), and from problem to problem. But what do you pay attention to when generating good girds. Is it the orthogonality of cells, or is it the smoothness of mesh (no sudden jump in cell size). Again, is it by your experience for a class of problems that you judge a grid to be good or bad? Can there be any universal rules that can be followed. My guess is that it is still an art, that takes a lot of experience.

 John C. Chien January 4, 2000 03:57

Re: Grid Quality and the Solution

(1).It is very sad to hear such questions. But since you are not talking about a commercial code, I will make a short comment. (2). "Grid" is not CFD. So, it is nonsense to talk about the quality of a grid, or a good grid. (3). In CFD, it is necessary to use grids or cells to cover the computational domain in most cases (some approaches do not require volume meshes). So, the computational domain can be covered in infinite number of ways, using different grids or cells. There is also no limit in the total number of grid points or cells. (4). The only "requirement" is that the solution must become mesh independent as the mesh size or the cell size is reduced. This is necessary, because you don't want to have the solution changes as a function of the specific mesh used. So, there is no such thing as a good mesh, or a better mesh, because you are not after a beautiful girl. (5). So, as long as one can prove that his solution is mesh independent, the exact final mesh used is not the issue. It can be structured, or non-structured, it can have even number of grid points or odd number of cells. (6). As you can see, the mesh does not have to be uniform, and it can have non-uniform skewness distributions. (7). So, basically, a mesh is just part of the approach required to arrive at the final solution. There is no such thing as the "quality" of a grid. (8). As for the "orthogonality", "grid spacing ratio", and "grid skewness", these are related to the governing equations and the numerical formulation used in the processes. In short, if one develops a numerical formulation with arbitrary skewness grid, then he can use a grid with high or low skewness. On the other hand, if one develops a numerical formulation with only orthogonal grid, then he better looks for only orthogonal grid in the calculation. (9). So, it is nonsense to talk about the grid alone. If one can not get the mesh independent solution, it is not because of the quality of the mesh. It is because the numerical formulation is having trouble with the mesh. "Grid" is part of the numerical formulation, and the hair alone can not make a girl beautiful. (10). I hope that you are not going to ask a question like :" How can I make a non-structured mesh look more beautiful ?" GOOD GRIEF! no more Charlie Brown. Sorry for such a long "short comment".

 clifford bradford January 10, 2000 19:18

Re: Grid Quality and the Solution

it is always best for your grid triangles to be as close to equilateral as possible. however some grid skewness is to expected where the grid transitions from coarse to fine

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