# Boundary Layer Equations

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 November 2, 2006, 14:37 Boundary Layer Equations #1 ROUND Guest   Posts: n/a 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.

 November 3, 2006, 07:28 Re: Boundary Layer Equations #2 Tom Guest   Posts: n/a I'd use the Keller Box method - it's implicit + 2nd order accurate in space and time.

 November 3, 2006, 16:02 Re: Boundary Layer Equations #3 ROUND Guest   Posts: n/a 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.

 November 6, 2006, 04:36 Re: Boundary Layer Equations #4 Tom Guest   Posts: n/a 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.

 November 6, 2006, 12:34 Re: Boundary Layer Equations #5 ROUND Guest   Posts: n/a Tom, Thanks a lot.

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