3D graphics animation is increasingly used in movies and virtual reality computer games to produce realistic visual simulations of physical and natural phenomena. The animation of diffuse liquids such as gases is an indispensable component in such special effects. The present system and methods utilize physically-based and more intuitive procedurally-based simulation techniques to simulate and render natural phenomena in computer graphics. The present invention facilitates user interaction in order to generate a variety of gas effects, for example, waves within water, plumes within hot gas, and flames within fire. Improved user interaction is achieved by improving rendering performance and introducing a new method of high-level control for Eulerian simulations.