The algorithm was first prototyped is Octave (Matlab) and found to slow. Then I coded a native C version with SDL graphics and OpenMP to speed up some of the calculations, it worked pretty well. The code is available at my GitHub. A video showing the live rendering is embedded below.
As the video shows the liquid is extremely pressure driven and thus does not represent incompressible liquids, like water. The physical correctness of this simulation as a whole has to be taken with a grain of salt because of the extremely simple implementation. But it serves as a very visual way of communicating how the method works and what strengths/weaknesses it has.
One nice property is that the method conserves mass.