Efficient Liquid Animation: New Discretizations for Spatially Adaptive Liquid Viscosity and Reduced-Model Two-Phase Bubbles and Inviscid Liquids

The work presented in this thesis focuses on improving the computational efficiency when simulating viscous liquids and air bubbles immersed in liquids by designing new discretizations to focus computational effort in regions that meaningfully contribute to creating realistic motion. For example, when simulating air bubbles rising through a liquid, the entire bubble volume is traditionally simulated despite the bubble’s interior being visually unimportant. We propose our constraint bubbles model to avoid simulating the interior of the bubble volume by reformulating the usual incompressibility constraint throughout a bubble volume as a constraint over only the bubble’s surface. Our constraint method achieves qualitatively similar results compared to a two-phase simulation ground-truth for bubbles with low densities (e.g., air bubbles in water). For bubbles with higher densities, we propose our novel affine regions to model the bubble’s entire velocity field with a single affine vector field. We demonstrate that affine regions can correctly achieve hydrostatic equilibrium for bubble densities that match the surrounding liquid and correctly sink for higher densities. Finally, we introduce a tiled approach to subdivide large-scale affine regions into smaller subregions. Using this strategy, we are able to accelerate single-phase free surface flow simulations, offering a novel approach to adaptively enforce incompressibility in free surface liquids without complex data structures. While pressure forces are often the bottleneck for inviscid fluid simulations, viscosity can impose orders of magnitude greater computational costs. We observed that viscous liquids require high simulation resolution at the surface to capture detailed viscous buckling and rotational motion but, because viscosity dampens relative motion, do not require the same resolution in the liquid’s interior. We therefore propose a novel adaptive method to solve free surface viscosity equations by discretizing the variational finite difference approach of Batty and Bridson (2008) on an octree grid. Our key insight is that the variational method guarantees a symmetric positive definite linear system by construction, allowing the use of fast numerical solvers like the Conjugate Gradients method. By coarsening simulation grid cells inside the liquid volume, we rapidly reduce the degrees-of-freedom in the viscosity linear system up to a factor of 7.7x and achieve performance improvements for the linear solve between 3.8x and 9.4x compared to a regular grid equivalent. The results of our adaptive method closely match an equivalent regular grid for common scenarios such as: rotation and bending, buckling and folding, and solid-liquid interactions

Constraint bubbles and affine regions: reduced fluid models for efficient immersed bubbles and flexible spatial coarsening

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]. © 2020 Copyright held by the owner/author(s). Publication rights licensed to ACM. 0730-0301/2020/7-ART43 $15.00 https://doi.org/10.1145/3386569.3392455We propose to enhance the capability of standard free-surface flow simulators with efficient support for immersed bubbles through two new models: constraint-based bubbles and affine fluid regions. Unlike its predecessors, our constraint-based model entirely dispenses with the need for advection or projection inside zero-density bubbles, with extremely modest additional computational overhead that is proportional to the surface area of all bubbles. This surface-only approach is easy to implement, realistically captures many familiar bubble behaviors, and even allows two or more distinct liquid bodies to correctly interact across completely unsimulated air. We augment this model with a per-bubble volume-tracking and correction framework to minimize the cumulative effects of gradual volume drift. To support bubbles with non-zero densities, we propose a novel reduced model for an irregular fluid region with a single pointwise incompressible affine vector field. This model requires only 11 interior velocity degrees of freedom per affine fluid region in 3D, and correctly reproduces buoyant, stationary, and sinking behaviors of a secondary fluid phase with non-zero density immersed in water. Since the pressure projection step in both the above schemes is a slightly modified Poisson-style system, we propose novel Multigrid-based preconditioners for Conjugate Gradients for fast numerical solutions of our new discretizations. Furthermore, we observe that by enforcing an incompressible affine vector field over a coalesced set of grid cells, our reduced model is effectively an irregular coarse super-cell. This offers a convenient and flexible adaptive coarsening strategy that integrates readily with the standard staggered grid approach for fluid simulation, yet supports coarsened regions that are arbitrary voxelized shapes, and provides an analytically divergence-free interior. We demonstrate its effectiveness with a new adaptive liquid simulator whose interior regions are coarsened into a mix of tiles with regular and irregular shapes.This work was supported in part by the Natural Sciences and En- gineering Research Council of Canada (RGPIN-04360-2014), the Rutgers University start-up grant, and the Ralph E. Powe Junior Fac- ulty Enhancement Award. We would like to thank Cristin Barghiel and SideFX for their generous software donation and Ryoichi Ando for his insightful discussion on comparing our constraint method with stream functions

An adaptive variational finite difference framework for efficient symmetric octree viscosity

While pressure forces are often the bottleneck in (near-)inviscid fluid simulations, viscosity can impose orders of magnitude greater computational costs at lower Reynolds numbers. We propose an implicit octree finite difference discretization that significantly accelerates the solution of the free surface viscosity equations using adaptive staggered grids, while supporting viscous buckling and rotation effects, variable viscosity, and interaction with scripted moving solids. In experimental comparisons against regular grids, our method reduced the number of active velocity degrees of freedom by as much as a factor of 7.7 and reduced linear system solution times by factors between 3.8 and 9.4. We achieve this by developing a novel adaptive variational finite difference methodology for octrees and applying it to the optimization form of the viscosity problem. This yields a linear system that is symmetric positive definite by construction, unlike naive finite difference/volume methods, and much sparser than a hypothetical finite element alternative. Grid refinement studies show spatial convergence at first order in L∞ and second order in L1, while the significantly smaller size of the octree linear systems allows for the solution of viscous forces at higher effective resolutions than with regular grids. We demonstrate the practical benefits of our adaptive scheme by replacing the regular grid viscosity step of a commercial liquid simulator (Houdini) to yield large speed-ups, and by incorporating it into an existing inviscid octree simulator to add support for viscous flows. Animations of viscous liquids pouring, bending, stirring, buckling, and melting illustrate that our octree method offers significant computational gains and excellent visual consistency with its regular grid counterpart.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (RGPIN-04360-2014, CRDPJ-499952-2016) and the Rutgers University start-up grant

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)

Towards real-time sea-floor surface reconstruction and classification using 3-D side-scan sonar

This thesis presents a computer algorithm to solve two major hurdles for generating real-time automated sea-floor maps with composition classification using 3-D side-scan sonar data. The algorithm consists of two distinct parts: sea-floor profiling and sea-flooring classification with computation acceleration from a graphics processing unit (GPU). The sea-floor profiling algorithm is an automated method that identifies bathymetry data corresponding to the sea-floor while ignoring bathymetry corresponding to water column objects and multi-path returns. The algorithm improves upon a fuzzy curve tracing method to handle discontinuities in the point-cloud data along the sea-floor and to discriminate between the sea-floor and other data. With an average error of 2.6% and a computation time of 7.40ms, the sea-floor profiling algorithm is extremely accurate and efficient. Classification of the sea-floor regions consists of applying image texture methods and machine learning classifiers to side-scan sonar images. In this thesis, a feature space for each side-scan sonar image pixel is created using image texture analysis algorithms, and classified with an artificial neural network. The accuracy and performance of the algorithm is tested with side-scan sonar images from the Underwater Research Lab\u27s Pam Rocks sonar survey. Real-time classification was achieved by the use of GPU computing. Porting the algorithm onto the GPU using OpenCL reduced the per-ping computation time to an average of 100ms, with an average error of 3.4%, making it a viable real-time solution in a sonar system

Emergency Vehicle Traffic Light Control System

BC RoadSense for Drivers states that “Emergency vehicles displaying flashing lights and sirens always have the right of way”. However, emergency vehicles are often forced to sit in traffic or weave through causing delays to their response times to crime scenes or medical emergencies. Enlightenment Solutions Corporation (ESC) proposes a solution which is to provide traffic light preemption to emergency vehicles in order to reduce emergency vehicle accidents and delay in responses. By installing Emergency Vehicle Traffic Lighting Control (EVTLC) system, the emergency vehicle will be able to control the operation of traffic light.&nbsp

Zinc Phosphide-coated Cabbage for Managing Belding’s Ground Squirrels (Abstract)

Belding’s ground squirrels (Urocitellus beldingi) cause extensive damage in alfalfa and other hay crops throughout substantial portions of the Intermountain West. Recent management efforts have largely focused on shooting, burrow fumigation, and occasionally grain baits. However, these tools are often either too costly to implement or ineffective. In 2015, the California Department of Pesticide Regulation approved a Special Local Needs permit to use zinc phosphide-coated cabbage for managing Belding’s ground squirrels in Siskiyou, Modoc, and Lassen Counties. This baiting strategy could provide a cost effective and efficacious management approach, although efficacy data were lacking. Therefore, we established a study to assess the importance of spatial variability of location sites, prebaiting, and ground squirrel density on efficacy of zinc phosphide-coated cabbage for Belding’s ground squirrel management across impacted hay-growing regions in northeastern CA. We also assessed potential differences in bait mixing strategies (in a tub via hand mixing vs. the use of a commercial-style cement mixer) on targeted zinc phosphide concentrations, as well as the degradation rate of zinc phosphide and moisture content of cabbage under environmental conditions. We did not detect a significant difference between hand and mechanical mixing. However, mechanical mixing was closer to the target level (mean = 101% vs. 115% for mechanical and hand mixing, respectively), was more precise, and allowed for the mixing of larger batches. As such, mechanical mixing was the strategy we used for field application. Furthermore, both moisture content (0.29% loss per hour) and zinc phosphide concentration (31% loss in 48 hours) steadily declined during a three-day observation period, indicating a fairly minimal window of exposure for nontarget species. See Baldwin et al. (2018) for additional details on lab testing of mixing methods and residual zinc phosphide levels associated with cabbage bait. During field trials, we found that prebaiting increased overall efficacy by approximately 18%, with efficacy 23% greater in the western (eastern Siskiyou and western Modoc Counties) vs. eastern portions (south-central Modoc County) of the study area. The tested bait was also substantially more efficacious when initial ground squirrel populations were larger, presumably due to a greater need for forage at high densities. Ground squirrel activity was relatively consistent throughout the day, although peaks were noted from 09:00 to 11:00 and from 13:00 to 15:00. Consumption of cabbage bait diminished throughout the day after initial application. Consumption was again high the following morning, but again diminished throughout the remainder of the day. Ideal times for bait application were likely before 09:00 and again before 13:00, although ground squirrels continued to feed on bait throughout the day. Zinc phosphide-coated cabbage bait appears to be an effective management option when prebaiting is used in Siskiyou County and in western portions of Modoc County. Additional research is needed to determine methods to increase efficacy in central and eastern Modoc County. See Baldwin et al. (2019) for additional details on this study

Zinc Phosphide-coated Cabbage for Managing Belding’s Ground Squirrels (Abstract)

Belding’s ground squirrels (Urocitellus beldingi) cause extensive damage in alfalfa and other hay crops throughout substantial portions of the Intermountain West. Recent management efforts have largely focused on shooting, burrow fumigation, and occasionally grain baits. However, these tools are often either too costly to implement or ineffective. In 2015, the California Department of Pesticide Regulation approved a Special Local Needs permit to use zinc phosphide-coated cabbage for managing Belding’s ground squirrels in Siskiyou, Modoc, and Lassen Counties. This baiting strategy could provide a cost effective and efficacious management approach, although efficacy data were lacking. Therefore, we established a study to assess the importance of spatial variability of location sites, prebaiting, and ground squirrel density on efficacy of zinc phosphide-coated cabbage for Belding’s ground squirrel management across impacted hay-growing regions in northeastern CA. We also assessed potential differences in bait mixing strategies (in a tub via hand mixing vs. the use of a commercial-style cement mixer) on targeted zinc phosphide concentrations, as well as the degradation rate of zinc phosphide and moisture content of cabbage under environmental conditions. We did not detect a significant difference between hand and mechanical mixing. However, mechanical mixing was closer to the target level (mean = 101% vs. 115% for mechanical and hand mixing, respectively), was more precise, and allowed for the mixing of larger batches. As such, mechanical mixing was the strategy we used for field application. Furthermore, both moisture content (0.29% loss per hour) and zinc phosphide concentration (31% loss in 48 hours) steadily declined during a three-day observation period, indicating a fairly minimal window of exposure for nontarget species. See Baldwin et al. (2018) for additional details on lab testing of mixing methods and residual zinc phosphide levels associated with cabbage bait. During field trials, we found that prebaiting increased overall efficacy by approximately 18%, with efficacy 23% greater in the western (eastern Siskiyou and western Modoc Counties) vs. eastern portions (south-central Modoc County) of the study area. The tested bait was also substantially more efficacious when initial ground squirrel populations were larger, presumably due to a greater need for forage at high densities. Ground squirrel activity was relatively consistent throughout the day, although peaks were noted from 09:00 to 11:00 and from 13:00 to 15:00. Consumption of cabbage bait diminished throughout the day after initial application. Consumption was again high the following morning, but again diminished throughout the remainder of the day. Ideal times for bait application were likely before 09:00 and again before 13:00, although ground squirrels continued to feed on bait throughout the day. Zinc phosphide-coated cabbage bait appears to be an effective management option when prebaiting is used in Siskiyou County and in western portions of Modoc County. Additional research is needed to determine methods to increase efficacy in central and eastern Modoc County. See Baldwin et al. (2019) for additional details on this study