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stability of scheme due to skewness/aspect ratio

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Old   May 14, 2006, 11:50
Default stability of scheme due to skewness/aspect ratio
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i would like to know how the skewness or aspect ratio of a structured grid can affect the stability of a FVM scheme.

For instance, near the boundary, the cells are usually "elongated" rectangles ie they've high aspect ratio. will this affect the stability if their ratio are too high?

So is the best type of cells almost squarish ie non skew and aspect ratio of 1?

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Old   May 14, 2006, 13:05
Default Re: stability of scheme due to skewness/aspect rat
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Dear Zonexo,

The effect of skewness or aspect ratio is definitely an issue in FVM, especially in viscous flow problems. The skewed cells near the boundary, are from a physical consideration, viz. the variations in the normal direction are more important than the streamwise direction in case of boundary layers. However, standard viscous discretisation procedures suffer from stability problems on such grids. This stability loss is directly related to the loss in positivity of the viscous flux discretisation. It can be shown for instance that the quadratic reconstruction is less robust on finer meshes. It is true from this perspective of stability that a non-skew cell with unit AR is better, bu this would end up in lot more cells than actually desire and more computational effort. The trick is not to bypass the numerical issue, but tackle it, as the skewed cells are a direct consequence of the boundary layer theory. The need is to construct a robust, consistent viscous flux discretisation procedure, which behaves reasonably on stretched meshes. However, to expect a procedure to work on any mesh is not possible, even such procedures may fail on highly random and skewed grids.

Hope this helps



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Old   May 14, 2006, 16:03
Default Re: stability of scheme due to skewness/aspect rat
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You can overcome the stability issue by treating the viscous terms in an implicit manner, e.g. Crank-Nicholson sheme (you should be able to find papers on this). As a result, the viscous time-stepping criterion (Von-Neumann) can be side-stepped.
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Old   May 14, 2006, 21:23
Default Re: stability of scheme due to skewness/aspect rat
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oh thanks for all your enlightenment!
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