SPGrid

Abstract

Figure 1: Smoke flow past sphere with 135M active voxels, 1K×1K×2K maximum resolution. Adaptive grid shown on the right. AbstractWe introduce a new method for fluid simulation on high-resolution adaptive grids which rivals the throughput and parallelism potential of methods based on uniform grids. Our enabling contribution is SPGrid, a new data structure for compact storage and efficient stream processing of sparsely populated uniform Cartesian grids. SPGrid leverages the extensive hardware acceleration mechanisms inherent in the x86 Virtual Memory Management system to deliver sequential and stencil access bandwidth comparable to dense uniform grids. Second, we eschew tree-based adaptive data structures in favor of storing simulation variables in a pyramid of sparsely populated uniform grids, thus avoiding the cost of indirect memory access associated with pointer-based representations. We show how the costliest algorithmic kernels of fluid simulation can be implemented as a composition of two kernel types: (a) stencil operations on a single sparse uniform grid, and (b) structured data transfers between adjacent levels of resolution, even when modeling non-graded octrees. Finally, we demonstrate an adaptive multigridpreconditioned Conjugate Gradient solver that achieves resolutionindependent convergence rates while admitting a lightweight implementation with a modest memory footprint. Our method is complemented by a new interpolation scheme that reduces dissipative effects and simplifies dynamic grid adaptation. We demonstrate the efficacy of our method in end-to-end simulations of smoke flow.

Asynchronous Eulerian Liquid Simulation

“…Time steps with CFL numbers smaller than one would be ideal in this respect, but unfortunately, they introduce significant numerical diffusion. A similar issue is also reported by Setaluri et al [SABS14] in their supplemental video. Empirically, we find that time steps around CFL = 2 are the sweet spot which provides qualitatively satisfactory results in practical scenarios when the semi-Lagrangian method is used for advection.…”

A moving least square reproducing kernel particle method for unified multiphase continuum simulation

“…Pure particle-based methods can easily obtain unbounded region adaptivity and as the particles only have information transfer within neighborhood particles, the program structure is simply two nested loops with a cached neighborhood list (Algorithm 1). To simulate unbounded domain, MPM usually requires the algorithm to be tightly coupled with sophisticated sparse grid structures like OpenVDB [Museth 2013] or SPGrid [Setaluri et al 2014]. Implementing P2G and G2P transfer for MPM is not an easy job, especially when spatial data structure is used.…”

An extended cut-cell method for sub-grid liquids tracking with surface tension

“…Poor volumetric scaling of 3D grids for tracking 2D liquid surfaces motivated researchers to develop adaptive simulation algorithms. Octrees can provide efficient spatial refinement, and were thus used to represent liquids [Losasso et al 2004], smoke [Shi and Yu 2004], surface tension [Hong and Kim 2005], bubbles [Kim et al 2007], viscous liquids [Goldade et al 2019] and were tailored for efficiency [Aanjaneya et al 2017;Setaluri et al 2014]. While these methods concentrate variables near the free surfaces, they break the grid's regularity, and the discretization accuracy has to be sacrificed for maintaining positive-definite systems.…”