Flip solver update

for the past few days I've been working on this solver.

I imported the ghost sph sampler and anisotropic kernel part for surface reconstruction. This time everything was done with tbb(Thread Building Blocks), parallelizing all the particles. The performance is really satisfying: for 150K particles, the mesh reconstruction took less than 2 seconds per frame, including neighbor search, iterative matrix decomposition and color field gathering.

Compare to my previous implementation of this part, due to everything is done on the fly, the memory deallocation cost reduced drastically, and that is one of the major reason for boosting the performance.


However, I discovered a huge problem for this solver.
It is COMPRESSIBLE!
The error is introduced by particle advection. Within each single frame, the projection is ensured to be incompressible, however, after particles being advected, the number for fluid cells would change, and that is the reason why it is compressible.

With the 150k particle configuration, using 50*50*50 grid would lead to volume increasing, while 100*100*100 would shrink volume into a thin sheet.


In fact, setting the divergence to be free would not be sufficient for FLIP solver. Because the density(or mass) is carried with the particles, while for the grid solving part, there's no way in ensuring the density of each cell to be constant.

This problem could be alleviated with a certain grid size for a certain particle distribution. Yet only alleviation is possible, cause the particle and grid are kind of coupled in terms of density.

Right now I had an idea which might be useful for decoupling the two, but I need to take a further look into the physics and math.

I'll discuss with the author of FLIP paper, and hopefully I can find a better way for it soon.