FD and Linear Stability Analysis
 

I have coded for Linear stability analysis. The result seems unacceptable by my code. I would like you to give me some comments and suggestions on the question below before I modify this code:

The basic state is 2D, I solve basic state with FVM, and result is consistent with result in literature. Because the linearizied equations can not be expressed as conserved form, I have to adopt Finite Difference Methods (FDM) in this part. In my previous code, the cental difference is used for internal nodes and forward and backward differences are adopted for nodes near boundary condition. i would like to know

(1) if it is better to discretize the convective term with upwind scheme rather than my previous central difference scheme?

(2) if it is better to choose high-order upwind scheme rather that a simple upwind scheme?

(3)if it is better to choose high-order forward and backward differences scheme for nodes near boundary condition?

(4) Is there any potential problems if I choose different schemes with different order for internal nodes and nodes near boundary?

(5) Could you please suggest me a good reference for high-order upwind scheme to discretize convective term?

Any suggestion are highly appreciated.

Zeng

Re: FD and Linear Stability Analysis
 

Zeng, I have some experience with some of your problems.

(1) Upwind schemes should be used when coding the convective terms. Theese schemes are based on the analytical solution to the Riemann problem. Central difference approximations may introduce instabilities.

(5) A good reference may be (book): Computational methods for astrophysical fluid flow, by Randal J. Leveque et. al. (out in 1997, I think).