Compensating the vorticity loss during advection with an adaptive vorticity confinement force

Abstract

The advection step in grid-based fluid simulation is prone to numerical dissipation, which results in loss of detail. How to improve the advection accuracy to preserve more fluid details is still challenging. On the other hand, a common way to enhance smoke details is to use vorticity confinement. However, most of the previous methods simply used a fine-tuned scale factor ε to adjust the strength of the confinement force, which can only amplify existing vortex details and is easy to cause instability when ε is large. In this article, we proposed an adaptive vorticity confinement method, which does not suffer from the above problems, to compensate the vorticity loss during advection with little extra cost. The main idea is to first calculate a scale factor whose value depends on the vorticity loss during advection, and then use it to adaptively control the vorticity confinement force for vorticity compensation with high stability. The experiment results show the effectiveness and efficiency of our method.

Learning frequency‐aware convolutional neural network for spatio‐temporal super‐resolution water surface waves

“…To overcome CFL condition or the Nyquist limit, Jeschke et al 14 applied Gabor transformation to establish a novel 4D wave discretization across Cartesian and polar coordinate grids. For achieving higher numerical accuracy, an adaptive vorticity confinement factor is employed in Reference 15. The performance of their method greatly benefits from precomputed profile buffer and GPU parallelization.…”