Model Reduction Based Fast Fluid Simulation Technology

Fluid Animation has been a hard problem in computer graphics for a long time. Ever since the computing fluid dynamics was introduced into animation simulation in computer graphics, researchers are always seeking for fast fluid simulation methods. The main reason of why fluid animation efficiency is slow is that the physical model is complex in nature. Because there’s no analytical solution, only interpolation or matching method can be used to get approximate solution. To achieve this, it is needed to construct discrete grid, which makes the computing complexity proportional to the scale of grid. So it is very important to introduce grid scale independent fast simulation method.The main achievement of this essay includes those contents:(1) This essay firstly tried to introduce the Balanced Truncation model reduction method into the simulation part of fluid animation. This essay also combined Balanced Truncation method with the Proper Orthogonal Decomposition method to get a more efficiency Balanced Truncation method.(2) This essay figured out the flexibility drawback of model reduction method, and introduced model reduction based up-sample method. It combined the output of model reduction pre-computing and output of low-dimension simulation to get the up-sample correction method. This essay also introduced energy correction method to make the energy remain unchanged during up-sampling.(3) In order to further improve the efficiency of the whole simulation process, a fast particle-based liquid surface reconstruction method is introduced. As the complexity of particle advection is proportional to the number of particles which is independent of simulation grids, it is possible to adjust the particle sample as adjust simulation efficiency. This method accelerates the anisotropic kernel method in parallel, which is a famous method for particle surface reconstruction.