Primal-Dual Optimization for Fluids

TL;DR

This paper introduces a fast Primal-Dual optimization method applied to fluid simulations, enabling controllable fluid guiding and realistic boundary conditions with improved convergence and applicability.

Contribution

It presents a novel Primal-Dual optimization scheme tailored for fluid simulation problems, specifically for guiding and boundary condition enforcement, with demonstrated effectiveness and speed.

Findings

Achieves explicit control over fluid motion at multiple scales.

Effectively eliminates artifacts in boundary conditions.

Demonstrates fast convergence across various test cases.

Abstract

We apply a novel optimization scheme from the image processing and machine learning areas, a fast Primal-Dual method, to achieve controllable and realistic fluid simulations. While our method is generally applicable to many problems in fluid simulations, we focus on the two topics of fluid guiding and separating solid-wall boundary conditions. Each problem is posed as an optimization problem and solved using our method, which contains acceleration schemes tailored to each problem. In fluid guiding, we are interested in partially guiding fluid motion to exert control while preserving fluid characteristics. With our method, we achieve explicit control over both large-scale motions and small-scale details which is valuable for many applications, such as level-of-detail adjustment (after running the coarse simulation), spatially varying guiding strength, domain modification, and resimulation with different fluid parameters. For the separating solid-wall boundary conditions problem, our method effectively eliminates unrealistic artifacts of fluid crawling up solid walls and sticking to ceilings, requiring few changes to existing implementations. We demonstrate the fast convergence of our Primal-Dual method with a variety of test cases for both model problems.