[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.

[FMDenaro]

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

[Hooman]

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.

[FMDenaro]

Numerical solution of PDE, Morton & Mayers is the book wherein you can find infos for that