Preserving Geometry and Topology for Fluid Flows with Thin Obstacles and Narrow Gaps
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Date
2016-07-01
Authors
Azevedo, Vinicius C.
Batty, Christopher
Oliveira, Manuel M.
Journal Title
Journal ISSN
Volume Title
Publisher
Association for Computing Machinery
Abstract
Fluid animation methods based on Eulerian grids have long struggled to resolve flows involving narrow gaps and thin solid features. Past approaches have artificially inflated or voxelized boundaries, although this sacrifices the correct geometry and topology of the fluid domain and prevents flow through narrow regions. We present a boundary-respecting fluid simulator that overcomes these challenges. Our solution is to intersect the solid boundary geometry with the cells of a background regular grid to generate a topologically correct, boundary-conforming cut-cell mesh. We extend both pressure projection and velocity advection to support this enhanced grid structure. For pressure projection, we introduce a general graph-based scheme that properly preserves discrete incompressibility even in thin and topologically complex flow regions, while nevertheless yielding symmetric positive definite linear systems. For advection, we exploit polyhedral interpolation to improve the degree to which the flow conforms to irregular and possibly non-convex cell boundaries, and propose a modified PIC/FLIP advection scheme to eliminate the need to inaccurately reinitialize invalid cells that are swept over by moving boundaries. The method naturally extends the standard Eulerian fluid simulation framework, and while we focus on thin boundaries, our contributions are beneficial for volumetric solids as well. Our results demonstrate successful one-way fluid-solid coupling in the presence of thin objects and narrow flow regions even on very coarse grids.
Description
© ACM, 2016. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Azevedo, V. C., Batty, C., & Oliveira, M. M. (2016). Preserving Geometry and Topology for Fluid Flows with Thin Obstacles and Narrow Gaps. Acm Transactions on Graphics, 35(4), 97. https://doi.org/10.1145/2897824.292591
Keywords
3 Dimensions, Boundaries, Coupling, Cut-Cell, Embedded Boundary Methods, Fluids, Interfaces, Irregular Domains, Meshes, Poissons-Equation, Shells, Simulation, Smoke, Thin Solids, Water