Hi, I would like to begin working on AMR method with incompressible flow. Since there has been done little work in this area I would appreciate it if someone could help me find papers or people who have implemented such a method with incompressible flow. There are some papers written by Martine, Collela, Berger and Quirk but those are all about implementing AMR for compressible flow. I would also like to discuss it with everyone else who is interested in this area or has any idea and would like to develop it.

Maybe a silly question but, What does AMR mean? What is it about?

Thank you.

AMR = Adaptive Mesh Refinement.

Methods for moving the points of an existing grid or inserting new cells into a grid to better resolve flow features of interest. There are a whole host of methods for structured and unstructured grids.

I think I should have added this before, I am specifically looking for AMR methods which are used in structured grids and also refine the grids locally or local adaptive multigird method. That means where the solution needs more accuracy the method places finer grids in these areas by the means of inserting subgrids over the coarse grid covering the domain. It is possible that the fine subgrids will contain even finer subgrids within their boundaries.

I'm not as familiar with structured grid methods, but the keywords you're looking for in your literature search are "embedded grid" techniques or "non-conforming" cell refinement methods.

From what I understand you need to store the match the cell faces or indices between each subgrid in order to compute the fluxes across each level.

As far as suitability for incompressible vs. compressible applications/solvers, that's separate from the actual grid adaptation procedure. That issue comes down to what you use as a solution error measurement (gradients of velocity or pressure, or another suitable quantity).

You may look at this site.

http://seesar.lbl.gov/ccse/Software/index.html

See: http://www.camk.edu.pl/~tomek/AMRA/amr.html

This is a cool site, You'll find some papers related to AMR, not only for compressible flow, and people working on AMR.

Sorry for my bad English.

Look for the Gerris fluid solver under sourceforge...

Peter