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Old   November 2, 2006, 14:37
Default Boundary Layer Equations
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ROUND
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Hello! Does anyone has idea on solving unsteady boundary layer equations. I have two methods on hand: Fully implicit method and Box method. Which one is better to solve a 2-D compressible unsteady boundary layer equation? Thanks for your advice.
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Old   November 3, 2006, 07:28
Default Re: Boundary Layer Equations
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Tom
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I'd use the Keller Box method - it's implicit + 2nd order accurate in space and time.
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Old   November 3, 2006, 16:02
Default Re: Boundary Layer Equations
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Thank you, Tom.

I have some more questions.

1.Will box method become tedious when governing equations reach four or five ( there might has 7 by 7 matrix inversion and linearization become tedious )?

2. Is variable transformation necessary for compressible flow?

3. How you advice to do the matrix inversion(implicitly? )?

My email is: JakyL6@hotmail.com. I would appreciate any advice.
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Old   November 6, 2006, 04:36
Default Re: Boundary Layer Equations
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Tom
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1. It's only redious if you try to do it by hand.

2. It depends on your problem. Most boundary layer calculations are initiated from a similarity solution which can involve a change of transverse coordinate. If a vertical cordinate transformation is required at the initial station then it's a good idea to solve the equations everywhere in this new coordinate.

3. The way I would perform the inversion is through a block LU factorization. Assuming you've rearanged the equations (as you're Q1 suggests you have) so that the only nonzero entries lie on in a band around the diagonal then you can rewrite your matrix as a triagonal system whose entries are 3x3 matrices. The LU factorization will also be of this form and so it is relatively easy to invert; i.e. follow the methodology for a tridiagonal system with the scalars replaced by 3x3 matrices.

Alternatively you could use a general matrix solver such as BiCG - Although it will be a lot slower.
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Old   November 6, 2006, 12:34
Default Re: Boundary Layer Equations
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Tom, Thanks a lot.
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