|
[Sponsors] |
February 7, 2012, 10:11 |
Stabiltiy Analysis Of Explicit Euler
|
#1 |
Senior Member
Join Date: Jun 2010
Posts: 111
Rep Power: 15 |
Hi,
I'm trying to understand how Peric and Ferziger performed the stability analysis in their Computational methods for fluid dynamics book. The bit I don't understand is how they get equation 6.29, which is the eigenvectors in an exponential form. Thanks in advance. |
|
February 7, 2012, 14:43 |
|
#2 | |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,768
Rep Power: 71 |
Quote:
6.29 stands for a simple representation of a function in term of a generic Fourier components ... phi(xj,tn) = Ck(tn) * exp (i*k*xj) Supposing that the error behaves as the the numerical solution, you simply substitute the generic Fourier component of the error e(xj,tn) = Ek(tn) * exp (i*k*xj) into the numerical scheme ... The confusion in the book is (in my opinion) that the error is not introduced .... see par. 8.3 in the book of LeVeque on FV methods |
||
February 8, 2012, 11:06 |
|
#3 |
Senior Member
Join Date: Jun 2010
Posts: 111
Rep Power: 15 |
Thanks very much. I looked at the book but didn't see any mention of eigenvectors. Do you know how they get from eigenvectors to the Fourier components?
Thanks again. |
|
February 8, 2012, 12:26 |
|
#4 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,768
Rep Power: 71 |
Numerical solution of PDE, Morton & Mayers is the book wherein you can find infos for that
|
|
|
|
Similar Threads | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
3D analysis of Ahmed body | Irshad22 | FLUENT | 0 | December 17, 2009 04:33 |
Euler explicit for PISO | gricci | OpenFOAM Running, Solving & CFD | 1 | October 1, 2009 06:54 |
Euler (explicit or implicit) | anybody | Main CFD Forum | 2 | May 8, 2006 02:12 |
Short Course: Computational Thermal Analysis | Dean S. Schrage | Main CFD Forum | 11 | September 27, 2000 17:46 |
Is CFD Science or Art ? | John C. Chien | Main CFD Forum | 36 | October 5, 1999 12:58 |