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Old   February 1, 2006, 04:24
Default One-sided extrapolation
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I am trying to find a formulation for the gradient at the wall in a cell-centered FVM scheme.

It is well-known that at an orthogonal wall boundary, a one-sided 2-point or 3-point finite difference method can be used to calculate for the boundary values.

What should be the equivalent formulation for the above one-sided extrapolation if the grid at the wall boundary is not orthogonal?

Or is there any method of formulating dphi/dn, which is n.del(phi) at the wall?

Thank you so much for your help.

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Old   February 8, 2006, 19:01
Default Re: One-sided extrapolation
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The apporach described by Hasselbacher in his recent AIAA conference papers (Reno 2005 and Reno 2006) works pretty well. His approach is based upon a constrained least squares fit with the assumption of a quadratic reconstruction of the field. The constraints are the values at the wall. This will give you dqdx,dqdy and dqdx which you could then transform into dqdn using the normal vector at the wall. The idea can be extended to higher order reconstructions provided you have sufficient support in the stencil.
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Old   February 8, 2006, 21:24
Default Re: One-sided extrapolation
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Hi AnotherCFDUser....

Thank you for your suggestion. I am currently using the least squares fit, but with linear recontruction.

As for the AIAA conference paper by Hasselbacher, do you have the full title of that paper? Or if you have it, do you mind sending me a copy?

Thank you again. Coolblizz
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