Fluid Simulation Using Overcomplete Dictionaries Based On Sparse Coding

Smoke, water and other ?uids is an important part of the natural environment,and the computer simulation for ?uid behavior of real world can make the virtual world more real. In recent years, the ?elds of computer graphics have proposed a lot of stable,realistic, e?cient ?uid simulation methods, and have been widely used in movie and video game industry. However, when simulating large-scale ?uid scene, the projection step of Euler method which based on the computation of velocity ?eld will be very time-consuming, and it is the bottleneck of Euler method of ?uid simulation.Considering the bottleneck of Euler method of ?uid simulation, the paper proposed a method applies a couple of overcomplete dictionaries based on sparse coding into ?uid simulation. We use the local ?ne structure of high-resolution ?uid data to learn an overcomplete dictionary, which can match various complex local ?ne structures of high-resolution ?uid data and be used to recover these local ?ne structures by combining with the sparse representation. We calculate a low-resolution dictionary by multiplying the learned high-resolution dictionary with a down-sampling matrix. The down-sampling matrix will also be used to down-sample the high-resolution ?uid velocity data to its low-resolution version, thus in theory, this dictionary of low-resolution space can be used to decomposite the sparse representation of low-resolution velocity?eld.Meanwhile, in order to accelerate the simulation of ?uid animation by using overcomplete dictionaries, this paper also established a reconstruction and up-sampling framework for ?uid animation,Which compute the projection step on a low-resolution grid, and can accelerate the computation of ?uid simulation.The result of this method will be shown in the result section, and proves that our method can recover the highresolution details of ?uid to a certain extend. Using the appropriate parameters, even compared with a relatively fast ?uid simulator used in our experiment, our method can accelerate the computation speed to a certain extend.