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To find the source of the instabilities, I pulled my code apart into more independent steps, that could individually be turned on or off. This did result in a speed hit, but allowed me to quickly trace the source of the problems to the advection routine. This is the part that moves the water along at its own speed.
Since no existing code fit my requirements, I started working on my own fluid simulator a few weeks ago. The idea was to try both a grid-based and a particle-based method, and see which worked better for my situation. I started with the grid-based version.
I looked around for existing code or libraries to do the fluid simulation for me. There are some, but most are either GPL-licensed or too expensive, so they are out of the question for a small-time independent developer like me. Some publications exist on the topic, most notably Jos Stam’s famous Real-Time Fluid Dynamics for Games from 2003. Mick West describes this algorithm in detail in his article Practical Fluid Dynamics. He provides a great overview of the basics, geared towards programmers. A somewhat more mathematical, but broader overview is in Michael Gourlay’s brilliant Gamasutra article Fluid Simulation for Video Games. He gives explanations of many techniques, their respective advantages and drawbacks. Many other interesting (academic) links are on the CFDtoy blog.
Today, I’m really getting started. I quit my job last Friday so that I can work on this project full-time. I have some financial reserves to keep me alive during the period of development.