I am coding a Linear Stability Analysis for fluid dynamic problem, and therefore a genernalized eigenvale problem A x=lamda B x must be solved. The dimension of A and B is (4xNJxNK)^2.(NJ and NK is number of grid in y and z direction). Due to the limitaion of memory, NJxNK can only be up to 30x30, but it seems too coarse for my calcutation.

My quesation is

(1) If a higher-order difference scheme (e.g. 4-order)is adopted in stead of my present 2-order scheme, the problem caused by coarse grid can be remedied?

(2) I remeber that a paper mentioned that a non-homgious grid would reduce the accurate of high-order scheme. I read it several years ago, and can not find it again now. What is your suggestion on a homgious or non-homgious grid?

(3) Could you suggests a good high order difference scheme to me with corresponding literature?

Your advises and suggestions on any above questions are highly appreciated.

Thanks in advance.

Zeng

Hi,

Check out the following publication:

http://landau.mae.missouri.edu/~vasi...high-order.pdf

Sincerely,

Frederic Felten

Hi,

It is a good idea to use a spectral type discretization if you are really limited by a coarse grid. This will give you much better results if your focus is to obtain very accurate eigenvalues.

With finite-difference you can use arbitrarily higher-order approximations which is obviously limited by the number of grid points you have. There is a paper in the SIAM Journal which gives an algorithm to generate coefficients for arbitrary order of accuracy finite-difference scheme. The author escapes my memory, I will look it up and repost.

chidu...

Thanks you all for your kind help.

Chidu mentioned paper seems very interesting, we wish you can find it.

zeng

Chidu & Zeng

You may look up Fornberg's paper "Generation of Finite-Difference Formulas on arbitrarily spaced grids", Math. Comp. V51, N0184, p699, 1988

Ravichandran

Exactly, Ravi. This is the paper. I was on vacation and did not have access to the info. Thanks.

regards, chidu...

please guide me for using higher order scheme for les