A good paper on SPH
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As known ‘Fluid Simulation for Computer Graphics’ only emphasizes Eulerian view (fixed grid) and almost no attention is paid on Lagrangian method.
For beginners who are more interested in the latter, I recommend one paper on SPH:
Particle-Based Fluid Simulation for Interactive Applications (Ref. Count 349)
by Muller & Charypar & Gross from Federal Institute of Technology Zurich
The authors possess wonderful skills on English manipulation – their words are concise, accurate and comprehensive. The derivatives of SPH and comparison between SPH and Eulerian method are well stated, clearly and easy to understand. What’s more, a whole solution for SPH, including physical model, acceleration and rendering method, is elaborated.
From this paper we can know that SPH is basically a Newtonian model. The special part is how to handle the interactions among the particles, like pressure(repelling forces), viscosity(attraction forces). Both are modeled by considering a certain range of the neighboring particles around one particle - not all of the particles - obviously that is only a theoretical situation. This leads to another numerical issue - how to select the Kernel Functions? We need take care of several potential numerical problems here. Pressure gradient will approach to Zero in the center of the kernel while it is totally opposite in real world - so we need a spiky kernel for pressures; Laplacian of the smoothed velocity affected by viscosity may be negative that will actually increase the current velocity, so we need the kernel that make Laplacian value positive everywhere.
It is noticeable that Surface Tension should also be taken care of. By using the expression of surface curvature, we can put 'tension forces' onto the particles on/near the fluid surfaces.
The rendering is not in detail in this paper. Only two solutions of 'point splatting' and 'marching cubes' are introduced briefly. They are quite popular, but a much elegant/realistic/beautiful solution exists already - Level Set Method. I am not quite sure whether it is suitable for real-time applications yet. On-going...
The authors claim that their solution in this paper suits for real-time application - I think they don't involve the transparency of the water - so ray-casting like techniques are not included. I think this is one of the important reasons that it can be in real-time.
BTW, I noticed that [Stam 99] is the paper that almost each paper on fluid simulation will mention. I will come to it at a later time.
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