A follow-up to fluid simulation on non-uniform grids

In my last post, I discussed preliminary results for fluid simulation on non-uniform Cartesian grids.  In that post I showed some preliminary results, but there were some bugs that added disturbing artifacts.

I have fixed a number of bugs and now have a solver based on BFECC advection using min-max limited cubic interpolation for non-uniform and often highly anisotropic meshes for the velocity and pressure solve, with high-resolution uniform density fields for the density field.  The results are fairly impressive:

This image shows a volume rendering (in Paraview) of a simulation computed using the grid in the background.  Near the area of interest, the grid is uniform, but it grows very quickly (geometrically, with growth rate ~1.5) outside this region.  The velocity/pressure grid is 133x127x134, but covers nearly a 10x6x10 m cubic volume, with 2cm cells in the fine region.  The density field is 1x6x1 m with 1cm uniform resolution.

Being able to run different resolutions and gradings for the velocity and density fields is extremely helpful: fine fluid details distract from a poor velocity solution, and high-resolution densities help avoid diffusion in the physics.  The image above shows the density as resolved by the fluid grid. It is terrible.  However the density as resolved by the density grid is -way- better:

It's still not perfect, but given the cell size and anisotropy, I think it does extremely well.  Although there are definite artifacts, the payoff is in the memory usage and runtime. The whole simulation is 5 seconds in real time and takes approximately 22 seconds per output frame, meaning my 5 second simulation completes in under an hour.  These simulations used to take on the order of 4-5 hours.

The results look pretty good.  I think the grading is too steep to get really nice results, but it's an excellent proof-of-concept.