Signal-processing And Multigrid Based Highly Efficient Fluid Simulation

Physically based fluid simulation is an important and challengingresearch topic in the area of computer animation. The movement of fluidsystem is so complex that techniques nowadays are often hard to beapplied to real-time systems. Grid-based fluid simulation is one of themost widely used techniques. However, solution of Poisson equation in―projection step‖is quite time consuming on large grids, which have tobe used to produce a fluid animation full of small-scale details.In this paper, we present a novel projection framework whichintegrates techniques in Signal Processing and theoretical ideas inmultigrid method. Frequency-domain techniques are used to analyze thesolution of Poisson equation, which represents the pressure field of fluid.We found that high-frequency components of the solution greatlyinfluence the visual details in the final animation, while low-frequencycomponents influence the overall shape. Moreover, our eyes are quiteinterested in fluid details and the numerical accuracy is very important indetail-generation. On the other hand, our eyes are not captious to theoverall shape of fluid and the numerical accuracy is relatively lessimportant here. As a result, we split projection into two steps, which areDetail Capture and Shape Correction.In Detail Capture step, an efficient DST (Discrete SineTransformation) Poisson Solver is used to solve the Poisson equation.Although the solver can’t deal with complex solid-fluid boundarycondition, the solution can represent the high-frequency componentsquite well. An additional boundary sweeping step can then be used tomake this solution better in areas near solid-fluid boundaries.In Shape Correction step, a correcting Poisson equation isconstructed and then solved on a coarse grid. After that, the coarse solution is mapped back to fine grid to correct the final velocity field.This step is similar to techniques in multigrid method, and the ideabehind is that coarse grid can approximate low-frequency componentmore efficiently.Our novel projection method is quite fast and easy to be implemented.Experiments show that our projection is about10-30times faster than thetraditional projection with PCG (Preconditioned Conjugate Gradient),while convincingly preserves both the flow details and the overall shapeof fluid animation.