[FMDenaro]

Originally Posted by hunt_mat

Then I think we're talking about different things. Could you give me a link regarding the stability you're talking about?

Link? This topic is illustrated in any texbook of numerical analysis and CFD!

[hunt_mat]

It is, but not in the way you have presented it. The way that it's presented seems to get rid of the trigonometric terms, and that's done analytically.

I've simplified the problem by setting the temperature equal to a constant, and I can simply solve for the velocity equation and then insert into the density to get the density.

[FMDenaro]

Originally Posted by hunt_mat

It is, but not in the way you have presented it. The way that it's presented seems to get rid of the trigonometric terms, and that's done analytically.

I've simplified the problem by setting the temperature equal to a constant, and I can simply solve for the velocity equation and then insert into the density to get the density.

In simple cases, that is when you study the stability of pure advection or pure diffusion, you can get an analytical constraint.
But since from the 1d convection-diffusion equation the stability region is defined by a function cfl(Re_h).
In your case start with the linear equation with convection-diffusion-production terms and evaluate your 2d function cfl(Re_h, gamma).

[FMDenaro]

Have a look to Sec.8.2.2 in:

Charles Hirsch - Numerical Computation of Internal and External Flows