Question Regarding Stability of Nonlinear Terms
I am new to this forum and new to CFD. I am teaching myself the subject following the structure of "12 Steps to Navier Stokes" (link included) using the finite difference method. The problem with the "12 steps" program is that it omits very important topics such as stability of solutions, uses arbitrary boundary conditions and initial conditions that have no remote connection to the real world, fails to discuss what the actual equations represent. It also uses this garbage shorthand in python, where I am going to be using loops in MATLAB
Fortunately I graduated with a BS in Aeronautical Engineering and have some graduate school experience (had to leave for financial reasons sadly), so I have a sufficient fluids background. Regardless, I want to learn CFD and I think a good place to start is the finite difference method.
Now onto my question:
I am having trouble performing a stability analysis on the nonlinear unsteady convection equation in one and two dimensions (x,y,u,v as variables). I already know how to do a von Neumann stability analysis for 1-D linear systems. From my reading it appears that the VNA cannot be used for nonlinear equations and I have been unable to find a resource that clearly demonstrates a stability analysis procedure for the nonlinear terms.
If anyone can help me I would really appreciate it; I'll be able to resume my coding for these equations!
The 12 Steps I am following:
A non-linear stability analysis is quite more complex, if I remember well, the Hirsch book has some details
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