CFD Online Logo CFD Online URL
Home > Forums > Main CFD Forum

stability of scheme due to skewness/aspect ratio

Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Display Modes
Old   May 14, 2006, 11:50
Default stability of scheme due to skewness/aspect ratio
Posts: n/a

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?

  Reply With Quote

Old   May 14, 2006, 13:05
Default Re: stability of scheme due to skewness/aspect rat
Posts: n/a
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



  Reply With Quote

Old   May 14, 2006, 16:03
Default Re: stability of scheme due to skewness/aspect rat
Posts: n/a
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.
  Reply With Quote

Old   May 14, 2006, 21:23
Default Re: stability of scheme due to skewness/aspect rat
Posts: n/a
oh thanks for all your enlightenment!
  Reply With Quote


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
Stability problem due to turbulent dispersion force in a subcooled boiling model Edy OpenFOAM 7 August 10, 2011 12:00
pressure eq. "converges" after few time steps maddalena OpenFOAM Running, Solving & CFD 69 July 21, 2011 07:42
Numerical viscosity due to the MUSCL and HLL coulpled scheme sonsiest Main CFD Forum 0 May 23, 2011 15:37
numerical stability due to cross derivatives wen long Main CFD Forum 2 September 12, 2005 02:10
Stability for Nonlinear Numerical Scheme Guo Main CFD Forum 3 February 12, 2001 13:21

All times are GMT -4. The time now is 03:09.