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.

I'd use the Keller Box method - it's implicit + 2nd order accurate in space and time.

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.

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.

Tom, Thanks a lot.