Smoothed-Particle Hydrodynamics (SPH) is a method of simulating fluid flow. It is based on representing a fluid by a large number of discreet (individual) particles. Each particle has properties like position, pressure, density, mass, etc. The particles are fed through a bunch of equations that make them move in a fluid like flow.
If you are a maths nerd then one of the better and recommended papers for SPH fluids is Particle-based Viscoelastic Fluid Simulation.
Multiphase SPH is when you have 2 or more fluids with different densities etc (think oil and water) that flow around each other and clump together.
I have always had a fascination with simulating fluids. Over the years I have tried to understand SPH and have had many failed attempts at writing programs to do it (the basic formulas seem relatively simple, but getting the code to run stable without explosions and crashes is far from simple). Then I found this blog post by Tom Madams that had sample source code. With that I was finally able to get SPH working. It can still be fiddly to find a nice set of parameters to make a nice looking movie, but Tom’s code seems to be a great start. Thanks Tom!!
Multiphase SPH is now available in Visions Of Chaos.
A future release will include 3D support.