流体模拟的压缩感知上采样方法研究

Compressed-sensing Based Up-sampling Method for Fluid Simulation

在计算机流体动画模拟中,欧拉网格方法是一种比较成熟和常用的模拟方法,但其关键瓶颈在于数据采样环节,受限于传统的Nyquist采样理论,难以缩减流场中的海量数据采样和计算。针对这一问题,基于压缩感知理论,探究流体动画中突破传统数据采样的局限性的方法。通过研究流体速度场数据的稀疏性和可压缩性特征,选取了适合于流体模拟的采样基、压缩基和重构算法,建立流体模拟的压缩感知上采样方法的框架。多种场景下的模拟结果显示,流体模拟的压缩感知上采样方法可以一定程度上恢复得到流场的细节,验证了压缩感知理论在流体动画上应用的可行性。

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.