High order compact finite difference
 

Hallo CFD people:)

I have some problem, may be someone who has expertise in high order compact finite differences (hcfd for short) can help me. Consider 1D stationary convection-diffusion eq. after applying hcfd to it, you get Ax=b, where A is 3x3 block matrix and x=(u'',u',u)'. Matrix A is generally ill-conditioned, but this is not the question of today:)

Now consider time-dependent 1D convection-diffusion eq. In all papers I've read (starting from Lele's paper) they all consider u (the function value ) to be known and at each step solve something like (for the first derivative) Au'=Bu, with A and B - nice tri (or penta) diagonal matrices. So the question is where they get u??? from previous time step or where????

Thanks a lot in advance to all who will answer:)

Re: High order compact finite difference
 

Yes u will be from previous time step

Re: High order compact finite difference
 

Hi

Look for Sanjiva Lele's paper in Journal of Computational Physics.

Hope it helps

Apurva

Re: High order compact finite difference
 

try Google Search

"compact higher order" + "finite difference"

It will help

Apurva Shukla