# Stabiltiy Analysis Of Explicit Euler

 Register Blogs Members List Search Today's Posts Mark Forums Read

 February 7, 2012, 11:11 Stabiltiy Analysis Of Explicit Euler #1 Member   Join Date: Jun 2010 Posts: 98 Rep Power: 7 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, 15:43
#2
Senior Member

Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,603
Rep Power: 23
Quote:
 Originally Posted by Hooman 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.

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, 12:06 #3 Member   Join Date: Jun 2010 Posts: 98 Rep Power: 7 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, 13:26 #4 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 1,603 Rep Power: 23 Numerical solution of PDE, Morton & Mayers is the book wherein you can find infos for that

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post Irshad22 FLUENT 0 December 17, 2009 05:33 gricci OpenFOAM Running, Solving & CFD 1 October 1, 2009 06:54 anybody Main CFD Forum 2 May 8, 2006 02:12 Dean S. Schrage Main CFD Forum 11 September 27, 2000 17:46 John C. Chien Main CFD Forum 36 October 5, 1999 12:58

All times are GMT -4. The time now is 14:04.