Mehrstellenverfahren for different grid spacing along the three space directions

[kolmog]

Hi everybody,

I need to discretize a differential equation. The grid that I am considering has a different grid spacing along the three space directions. That is, h_x different than h_y and h_z. For that purpose, I would like to discretize the differential equation through the Mehrstellenverfahren scheme. The problem is that in all the references that I have found, the equation with the corresponding weights assumes that the grid spacing is the same along each of the three space directions (h_x=h_x=h_x=h). I show you the corresponding equation in the attached file.

I would like to use this scheme in my particular situation. Does someone know how this equation would look like?

Thank you very much in advance!

Miquel

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

 

[kolmog]

Hi,

As I see that maybe not many people use this scheme to discretize differential equations, I would reword this post. I have discretized a differential equation (generalized Poisson equation) in a real space grid. If you take a look to the attached file, this is the first equation. The left hand side of this equation can be rewritten like in the second equation. Then, I have used Fornberg weights to discretize first and second derivatives. Do you know if, a part from Bernt Fornbverg weights, there exist a better option?