Compressed-sensing Based Up-sampling Method And Framework For Fluid Simulation

Computer fluid simulation is an important research branch of computer animation. Recent years, as the increase of related demands and applications, fluid simulation has attracted attention of many researchers. Grid-based Euler method is a mature and effective way of simulating fluids, but more realistic simulation results need higher grids resolution and more sampling points, which leads to more temporal and spatial costs. The key bottleneck is that sampling step is limited by the traditional Nyquist-Shannon sampling theorem, so it cannot effectively reduce the massive data and computing of the large-scale fluid fields.In order to solve this problem, this paper introduces compressed sensing theory into fluid simulation, and probes a way to break through the limitation of the sampling theorem in Euler method. Compressed sensing can hold almost all of the information of the data with only a few sampling points, and then recover a good approximation of the original data from these sampling points through reconstruction algorithm.Based on compressed sensing theory, this paper uses uniform sampling matrix as sampling basis according to the characteristic of Euler grids, wavelet transform matrix as compressive basis according to compressibility of velocity field, and SPG algorithm as reconstruction algorithm according to scale of data and sampling points. A compressed-sensing based up-sampling method is proposed, and combined to Euler fluid simulation framework to construct the compressed-sensing based up-sampling simulation framework. In this framework, the projection step, which is the most time-consuming step in simulation process, is solved on low-resolution grids, and then up-sampled to high-resolution fluid field using compressed sensing method.Several scenes of smoke animation are presented. The experiments show that compressed-sensing based up-sampling method can recover fluid details of the low-resolution results to a certain extent, and get more details than bicubic interpolation, which proves the feasibility of compressed sensing theory in fluid animation applications. To improve the efficiency of the reconstruction algorithm, this paper tries to replace matrix multiplications using equivalent functions and loose the convergence precision of the algorithm, aimed at optimizing the simulation performance while ensuring the reconstruction result. Besides, some other problems about boundary, divergence, energy and shape during up-sampling and down-sampling are also explored in the framework.