However, it's far from enough. It could be a good solution for the inner particles. while for the boundary particles(either in contact with air or solid), the pressure gathering is incorrect, which will lead to an artifact.
Ghost sph(http://www.cs.ubc.ca/~rbridson/docs/schechter-siggraph2012-ghostsph.pdf) to me is the best solution for improving the quality of SPH. But the problem is ghost sph is kind of expensive. The number of sample particles for the solids is usually much more than the fluid particles. And re-sampling ghost particles is not trivial task.
In order to solve the compressibility problem and maintain the details that particles bring about, I decided to turn to FLIP(http://www.cs.ubc.ca/~rbridson/docs/zhu-siggraph05-sandfluid.pdf) for help.
FLIP is a combination of Lagrangian method and Eulerian method. Particles are used for advection, which eliminates the numerical dissipation caused by Eulerian methods, and MACGrid is used for solving the Poisson equation, which solve the pressure distribution problem perfectly.
For the past few days I've been reading lots of papers related to Eulerian fluid simulation, including Robert Bridson's book: Fluid Simulation for Computer Graphics. And finally I got a good understanding of each steps that is necessary for FLIP solver.
I'll list my understanding of the core steps in FLIP solver here:
1. transfer velocity from particles to grid. The grid is only used for solving the pressure distribution, so only the velocity field is needed. The way used for transferring is splatting each particle's velocity onto the grid using tri-linear weighting.
2. generate a level set from the particles. The level set is necessary for later use.
3. extend the velocity field to the whole grid. Before this step, only the grid cells that intersect the particles have a non-zero velocity. In order to get the correct velocity distribution, we have to extrapolate the velocity to the whole grid based on one simple principal: the dot product of the gradient of velocity and the gradient of level set should be zero. Which means the extrapolated velocity should not change in the normal direction of fluid surface.
4. solve for Poisson equation. I haven't start coding with this part. Yet from the previous smoke simulation project, this should be similar. The key is setting boundary condition, using ghost pressure and apply pre-conditioner.
5. extend the velocity again. In the previous step, only the velocity field of the fluid cells have been updated, so in order to get a correct value in interpolating back to particles, we need to update the rest part of the grid.
6. transfer back to the particles. Update particles' velocity based on the new velocity field.
That's basically my understanding for the FLIP solver from reading during the past few days. I'm starting to write this solver part and integrate that for my fluid simulation project.
No comments:
Post a Comment