Generalized Orr-Sommerfeld

Hector Carrasco Chamblas

¿pseudospectral code for thernal Orr-Sommerfelds?

I'm a Mathematical Engineer student, and I would like to ask you some questions concerning the matlab differentiation suite.

In one of my courses (numerical programming with matlab), I have a research project which deals with the numerical adaptation of your matlab differentiation suite for the problem of fluid mechanics analyzed in the article:

The linear stability of channel flow of fluid with temperature-dependent viscosity (Wall and Wilson) J. Fluid Mech., Vol. 323 pp. 107--132, 1996. In this paper, there is a coupling between the navier-stokes equations and the heat equation (with four different viscosity models). My Project consists in adapt the first viscosity model and to perform the resolution of this coupled problem by means of spectral techniques, specifically, by adapting the routines of your matlab suite.

I have try some tricks, (the modification of the Original Orr-Sommerfeld system of the example and the creation of the odd derivatives, but the eigenvalues are not correct). In addition, I have tried to view the system as a "vector-valued" values of an unknown, but there is surely something that I do in a wrong manner.

Any help will be grateful.

Thank you in advance

Hector Carrasco Chamblas Estudiante de Ingenieria Matematica Universidad de Concepcion