Real-Time Fluid Simulation on the Surface of a Sphere

Abstract

We present a novel approach for animating incompressible fluids with Eulerian advection-projection solvers on the surface of a sphere by extending the recent work by Hill and Henderson [2016] with a staggered spherical grid discretization. By doing so, we avoid the infamous checkerboard null modes. We additionally introduce new, straightforward polar singularity treatments that avoid the previous need for any spectral filtering of high-frequency noise at the poles. Lastly, we enforce incompressibility with a fast Fourier solution to Poisson's equation for pressure in spherical coordinates. Our high-performance GPU-based framework combines scalability, art-directability, and ease of implementation, and reaches real-time speeds for various practical scenarios.