[petsc-users] Using DM for a refined level-set grid

[Åsmund Ervik]

Dear users of PETSc,

We're talking about adding a refined level-set grid method (M. Herrmann, doi:10.1016/j.jcp.2007.11.002) to our code. Currently we solve two-phase Navier-Stokes (ghost fluid method) together with a standard level-set approach on a uniform Cartesian grid.

What we're thinking is the following: we will have 2 grids for the level-set function. One will be the same as for the flow field, this is the coarse grid. The other is a refined (still uniform Cartesian) grid used only for the level-set function. The coarse grid will have values that lets us know if we are close to an interface or not. If we are not close to an interface, we don't want to store (allocate) any value for the level-set function on the fine grid. I'm guessing "close" will mean roughly "when the absolute value of the level-set function is <5*dxCoarse".

Are there any DM tricks in PETSc we can use to achieve this "sparsely stored" refined grid? I realise this simplified version of Herrmann's method does not do load balancing etc., but level-set computations are cheap compared to the flow solver.

Best regards,
Åsmund


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