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

Viscous Liquid Animation with Spatially Adaptive Grids

Viscous fluid behaviors are among the most complex yet familiar physical phenomena we encounter in everyday life. Much attention and investigation has been paid to the creation of visually realistic results, especially some unique effects such as folding and buckling, in computer graphics. However, simulation of viscous fluids requires more computational resources than its inviscid counterpart, since the viscous solve typically has lower sparsity and more degrees of freedom than the Poisson problem used to compute pressure forces. One interesting feature of viscous fluids is that the most important visual details happen at free surfaces of the fluid, while the interior flow remains relatively smooth. Therefore, a spatially adaptive grid with higher density of cells for fluid surfaces and lower density for the interior can be very useful in reducing computational resources and maintaining high-fidelity imagery at the same time. The focus of this thesis is to provide a method for simulating a highly viscous liquid on an adaptive quadtree grid, and generating visually plausible results. Aside from reviewing the techniques for viscous fluid simulation in computer graphics, we propose a new finite difference scheme to accurately compute the results at junctions where different levels of the quadtree are adjacent to each other. In addition, we apply the variational approach originally proposed by Batty and Bridson [2008] to this scheme, and generate a symmetric positive definite system on which a preconditioned conjugate gradient solver works very well. Thanks to the variational formulation, our method enforces the boundary condition at viscous free surfaces without the need of extra efforts. Lastly, this thesis presents a new scheme transferring velocities between an adaptive grid and a regular grid, which makes it easy to embed our viscosity solver into any grid-based inviscid fluid solver. We experimentally demonstrate that our method is first order accurate and achieves visual results that are qualitatively consistent with those of dense uniform grids, while reducing the number of degrees of freedom by a factor between 2 and 6, depending on the scenario

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