Galerkin Method of Regularized Stokesletsfor Procedural Fluid Flow with Control Curves

Supplementary video for our ACM SIGGRAPH Asia 2024 Technical Communications Paper, "Galerkin Method of Regularized Stokesletsfor Procedural Fluid Flow with Control Curves," by Ryusuke Sugimoto, Jeff Lait, Christopher Batty, and Toshiya Hachisuka.
Project Website:
rsugimoto.net/...
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.