Galerkin Method of Regularized Stokeslets for Procedural Fluid Flow with Control Curves

TL;DR

This paper introduces a novel fluid flow authoring tool that uses a Galerkin discretization of the Regularized Stokeslets method, enabling precise control of volumetric flow along specified curves with minimal computational complexity.

Contribution

The paper presents a new approach combining the Regularized Stokeslets with Galerkin discretization for procedural fluid flow design, improving stability and control compared to previous methods.

Findings

Method is less sensitive to vertex sampling rate.

Requires only small linear system solves.

Enables control of angular velocity along curves.

Abstract

We present a new procedural incompressible velocity field authoring tool, which lets users design a volumetric flow by directly specifying velocity along control curves. Our method combines the Method of Regularized Stokeslets with Galerkin discretization. Based on the highly viscous Stokes flow assumption, we find the force along a given set of curves that satisfies the velocity constraints along them. We can then evaluate the velocity anywhere inside the surrounding infinite 2D or 3D domain. We also show the extension of our method to control the angular velocity along control curves. Compared to a collocation discretization, our method is not very sensitive to the vertex sampling rate along control curves and only requires a small linear system solve.