Abstract: In computer fluid animation, the grid-based Euler method is a well-matured and effective way of simulating fluids, but a key bottleneck of Euler method is that it is limited to the traditional Nyquist-Shannon sampling theorem in sampling step. So it cannot effectively reduce the massive data and computing of the large-scale flow fields. In order to solve this problem, compressed sensing theory was used to probe a way to break through the limitation of the sampling theorem in fluid simulation. The sparsity and compressibility of fluid data were explored, then applicable sampling function, compressive basis and reconstruction algorithm for fluid data are selected. A compressed-sensing based up-sampling method and framework for fluid simulation was constructed based on researches and experiments. Several scenes of smoke animation were presented, the results show that compressed-sensing based up-sampling method can recover the details of the flow field to a certain extent, and prove the compressed sensing theory can apply to fluid simulation.

Key words: fluid simulation, compressed sensing, up-sampling, sparse representation, reconstruction algorithm