Synthetic fluid details for the vorticity loss in advection

Abstract

In this paper, a novel method with good numerical stability is proposed from the perspective of energy preserving to alleviate the numerical dissipations in the advection step of Eulerian fluid simulation. The main idea is to measure the vorticity loss during advection, calculate the lost angular kinetic energy with a proposed scheme, and then synthesize a high-frequency incompressible details field to compensate the lost energy in a way that is consistent with Kolmogorov's theory, which prevents the synthetic details from interfering with the existing fluid flow. The method works independently of the advection scheme and can be easily combined with other advection schemes to enhance the effect. It adds only 5% to 10% of the computational overhead while producing convincing fluid details without changing the overall behavior of the original flow.

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

“…Zhang et al 9 took their difference , that is, , as the vorticity loss, and recovered a velocity field from it by solving a Poisson equation. Zhu et al 10 used to compute the angular kinetic energy loss in advection, and recovered the lost energy by synthesizing a turbulent high‐frequency velocity field. Instead, we only use in the next step to decide whether to assign the default value or a new value to the loss factor , and the new value is calculated by using the length ratio of to and the angle between them.…”

“…As shown in Figure 6, even though a large value of is used, the enhancement F I G U R E 7 3D smoke column. From left to right: Zhang et al, 9 Zhu et al, 10 's method is still not significant in many areas. However, our loss factor is able to better adjust the confinement force to produce more details, no matter the speed is large or small.…”

“…We also compared the ability to restore the vorticity loss during advection with other two methods by Zhang et al 9 and Zhu et al. 10 was set to 1.8 in our method, while in the other methods no vorticity confinement was implemented. As shown in Figure 7, Zhang et al's method has the best restoring effect, since they tried to fully recover the vorticity loss by solving a Poisson equation.…”

“…However, the method involves the solution of Poisson equation, which inevitably brings high computational overhead. By calculating angular momentum loss, Zhu et al 10 transformed vorticity loss into artificially synthesized turbulence details, thus recovering high‐frequency energy loss caused by numerical dissipation. In addition, the idea of vorticity‐based detail enhancement was also applied in SPH fluid simulation methods 29‐31 .…”

“…However, the above advection methods disregard the divergence‐free constraint of the velocity field, and can cause a violation of conservation of angular momentum, thereby some researchers used the scheme of simultaneous advection with velocity and vorticity to improve the advection accuracy. For instance, both Zhang et al 9 and Zhu et al 10 tried to synthesize high‐frequency velocity field for compensating the vorticity loss during advection. These methods reduced the numerical dissipation of advection, but the velocity synthesis process made the algorithms too complicated.…”