A Positive-definite Cut-cell Method for Strong Two-way Coupling Between Fluids and Deformable Bodies

© ACM, 2017. 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 Zarifi, O., & Batty, C. (2017). A Positive-definite Cut-cell Method for Strong Two-way Coupling Between Fluids and Deformable Bodies. In Proceedings of the ACM SIGGRAPH / Eurographics Symposium on Computer Animation (p. 7:1–7:11). New York, NY, USA: ACM. https://doi.org/10.1145/3099564.3099572We present a new approach to simulation of two-way coupling between inviscid free surface fluids and deformable bodies that exhibits several notable advantages over previous techniques. By fully incorporating the dynamics of the solid into pressure projection, we simultaneously handle fluid incompressibility and solid elasticity and damping. Thanks to this strong coupling, our method does not suffer from instability, even in very taxing scenarios. Furthermore, use of a cut-cell discretization methodology allows us to accurately apply proper free-slip boundary conditions at the exact solid-fluid interface. Consequently, our method is capable of correctly simulating inviscid tangential flow, devoid of grid artefacts or artificial sticking. Lastly, we present an efficient algebraic transformation to convert the indefinite coupled pressure projection system into a positive-definite form. We demonstrate the efficacy of our proposed method by simulating several interesting scenarios, including a light bath toy colliding with a collapsing column of water, liquid being dropped onto a deformable platform, and a partially liquid-filled deformable elastic sphere bouncing.Natural Sciences and Engineering Research Council of Canad

An Efficient Geometric Multigrid Solver for Viscous Liquids

We present an efficient geometric Multigrid solver for simulating viscous liquids based on the variational approach of Batty and Bridson [2008]. Although the governing equations for viscosity are elliptic, the strong coupling between different velocity components in the discrete stencils mandates the use of more exotic smoothing techniques to achieve textbook Multigrid efficiency. Our key contribution is the design of a novel box smoother involving small and sparse systems (at most 9 x 9 in 2D and 15 x 15 in 3D), which yields excellent convergence rates and performance improvements of 3.5x - 13.8x over a naïve Multigrid approach. We employ a hybrid approach by using a direct solver only inside the box smoother and keeping the remaining pipeline assembly-free, allowing our solver to efficiently accommodate more than 194 million degrees of freedom, while occupying a memory footprint of less than 16 GB. To reduce the computational overhead of using the box smoother, we precompute the Cholesky factorization of the subdomain system matrix for all interior degrees of freedom. We describe how the variational formulation, which requires volume weights computed at the centers of cells, edges, and faces, can be naturally accommodated in the Multigrid hierarchy to properly enforce boundary conditions. Our proposed Multigrid solver serves as an excellent preconditioner for Conjugate Gradients, outperforming existing state-of-the-art alternatives. We demonstrate the efficacy of our method on several high resolution examples of viscous liquid motion including two-way coupled interactions with rigid bodies.This work was supported in part by the Rutgers University start-up grant, the Ralph E. Powe Junior Faculty Enhancement Award, and the Natural Sciences and Engineering Research Council of Canada (RGPIN-04360-2014, CRDPJ-499952-2016)

Preserving Geometry and Topology for Fluid Flows with Thin Obstacles and Narrow Gaps

© 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/10.1145/2897824.292591Fluid 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.Conselho Nacional de Desenvolvimento Científico e Tecnológico, Natural Sciences and Engineering Research Council of Canad

Animating Coupling between Inviscid Free-Surface Liquids and Elastic Deformable Bodies

Driven by demand for high-fidelity computer-generated imagery, physics-based animation has become an exciting frontier of research in computer science. Simulations of fluids and their interactions with other objects in the environment have particularly enjoyed much attention and investigation. Consequently, effective techniques have been developed to efficiently simulate two-way coupling between fluids and rigid bodies, allowing for convincing animation of, for instance, ships on the ocean. On the other hand, accurately capturing interactions between fluids and deformable solids has proven to be much more elusive. In particular, satisfaction of boundary conditions poses a significant difficulty, as the straightforward voxelized treatment suffers from visible grid artefacts, whereas use of a conforming mesh greatly increases the computational overhead of a simulation. This thesis investigates the problem of animating two-way coupling effects between free-surface liquids and linearly elastic solids. Aside from presenting simulation techniques for such liquids and solids separately, we introduce a new approach to simulating their interactions that exhibits several notable advantages over previous techniques. By fully incorporating the dynamics of the solid into pressure projection, we simultaneously handle fluid incompressibility and solid elasticity and damping. Thanks to this strong coupling, our method does not suffer from instability, even in very taxing scenarios. Furthermore, use of a cut-cell discretization methodology allows us to accurately apply proper free-slip boundary conditions at the exact solid-fluid interface. Consequently, our method is capable of correctly simulating inviscid tangential flow, devoid of grid artefacts or artificial sticking. Lastly, we present an efficient algebraic transformation to convert the indefinite coupled pressure projection system into positive-definite form. The thesis also contains an evaluation of our proposed method, including several animation scenarios, as well as comparisons to previous techniques

A Cut-Cell Geometric Multigrid Poisson Solver for Fluid Simulation

We present a novel multigrid scheme based on a cut-cell formulation on regular staggered grids which generates compatible systems of linear equations on all levels of the multigrid hierarchy. This geometrically motivated formulation is derived from a finite volume approach and exhibits an improved rate of convergence compared to previous methods. Existing fluid solvers with voxelized domains can directly benefit from this approach by only modifying the representation of the non-fluid domain. The necessary building blocks are fully parallelizable and can therefore benefit from multi- and many-core architectures