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I am using adaptive mesh refinement to solve one dimensional inviscid Burgers equation. However I am facing some difficulty to handle grid interfaces which are not uniform (coarse-fine grid interface). There has to be conservation of variable at the grid interfaces which I am not able to incorporate in my code.

If anyone has any idea about it or has done the similar work based preferably on finite difference schemes, it could be a great help to me.

Reference: http://epubs.siam.org/doi/abs/10.1137/0724063

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  • $\begingroup$ That paper seems to deal with arbitrary overlapping grids. Do you really need something that complex? The simplest AMR methods just cut grid size in half for each refinement and there is a well-defined relationship between the different grids. This case is much simpler. I think all you really need is interpolation methods (in time and space) of the appropriate order and to ensure your fluxes are consistent (assuming you're using finite volume). $\endgroup$ – Doug Lipinski May 28 '15 at 23:44
  • $\begingroup$ Hello, I am not using arbitrarily overlapping grids and instead I am using the cut cell grid just like you mentioned. However I am using FDM and not FVM. My PDE is in conservation form and all I want is to make sure that the fluxes are consistent at the interfaces. May you please give me references of those well defined relationship you are talking about? $\endgroup$ – Tanmay Agrawal May 29 '15 at 8:20
  • $\begingroup$ This presentation (PDF) has a high level overview, it's not really my area, but I think it should be similar for finite difference. $\endgroup$ – Doug Lipinski May 29 '15 at 11:20

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