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

IST Austria Thesis

Computer graphics is an extremely exciting field for two reasons. On the one hand, there is a healthy injection of pragmatism coming from the visual effects industry that want robust algorithms that work so they can produce results at an increasingly frantic pace. On the other hand, they must always try to push the envelope and achieve the impossible to wow their audiences in the next blockbuster, which means that the industry has not succumb to conservatism, and there is plenty of room to try out new and crazy ideas if there is a chance that it will pan into something useful. Water simulation has been in visual effects for decades, however it still remains extremely challenging because of its high computational cost and difficult artdirectability. The work in this thesis tries to address some of these difficulties. Specifically, we make the following three novel contributions to the state-of-the-art in water simulation for visual effects. First, we develop the first algorithm that can convert any sequence of closed surfaces in time into a moving triangle mesh. State-of-the-art methods at the time could only handle surfaces with fixed connectivity, but we are the first to be able to handle surfaces that merge and split apart. This is important for water simulation practitioners, because it allows them to convert splashy water surfaces extracted from particles or simulated using grid-based level sets into triangle meshes that can be either textured and enhanced with extra surface dynamics as a post-process. We also apply our algorithm to other phenomena that merge and split apart, such as morphs and noisy reconstructions of human performances. Second, we formulate a surface-based energy that measures the deviation of a water surface froma physically valid state. Such discrepancies arise when there is a mismatch in the degrees of freedom between the water surface and the underlying physics solver. This commonly happens when practitioners use a moving triangle mesh with a grid-based physics solver, or when high-resolution grid-based surfaces are combined with low-resolution physics. Following the direction of steepest descent on our surface-based energy, we can either smooth these artifacts or turn them into high-resolution waves by interpreting the energy as a physical potential. Third, we extend state-of-the-art techniques in non-reflecting boundaries to handle spatially and time-varying background flows. This allows a novel new workflow where practitioners can re-simulate part of an existing simulation, such as removing a solid obstacle, adding a new splash or locally changing the resolution. Such changes can easily lead to new waves in the re-simulated region that would reflect off of the new simulation boundary, effectively ruining the illusion of a seamless simulation boundary between the existing and new simulations. Our non-reflecting boundaries makes sure that such waves are absorbed

Liquid simulation with mesh-based surface tracking

Animating detailed liquid surfaces has always been a challenge for computer graphics researchers and visual effects artists. Over the past few years, researchers in this field have focused on mesh-based surface tracking to synthesize extremely detailed liquid surfaces as efficiently as possible. This course provides a solid understanding of the steps required to create a fluid simulator with a mesh-based liquid surface. The course begins with an overview of several existing liquid-surface-tracking techniques and the pros and cons of each method. Then it explains how to embed a triangle mesh into a finite-difference-based fluid simulator and describes several methods for allowing the liquid surface to merge together or break apart. The final section showcases the benefits and further applications of a mesh-based liquid surface, highlighting state-of-the-art methods for tracking colors and textures, maintaining liquid volume, preserving small surface features, and simulating realistic surface-tension waves

A Practical Method for High-Resolution Embedded Liquid Surfaces

This is the peer reviewed version of the following article: Goldade, R., Batty, C., & Wojtan, C. (2016). A Practical Method for High-Resolution Embedded Liquid Surfaces. Computer Graphics Forum, 35(2), 233–242, which has been published in final form at https://doi.org/10.1111/cgf.12826. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.Combining high-resolution level set surface tracking with lower resolution physics is an inexpensive method for achieving highly detailed liquid animations. Unfortunately, the inherent resolution mismatch introduces several types of disturbing visual artifacts. We identify the primary sources of these artifacts and present simple, efficient, and practical solutions to address them. First, we propose an unconditionally stable filtering method that selectively removes sub-grid surface artifacts not seen by the fluid physics, while preserving fine detail in dynamic splashing regions. It provides comparable results to recent error-correction techniques at lower cost, without substepping, and with better scaling behavior. Second, we show how a modified narrow-band scheme can ensure accurate free surface boundary conditions in the presence of large resolution mismatches. Our scheme preserves the efficiency of the narrow-band methodology, while eliminating objectionable stairstep artifacts observed in prior work. Third, we demonstrate that the use of linear interpolation of velocity during advection of the high-resolution level set surface is responsible for visible grid-aligned kinks; we therefore advocate higher-order velocity interpolation, and show that it dramatically reduces this artifact. While these three contributions are orthogonal, our results demonstrate that taken together they efficiently address the dominant sources of visual artifacts arising with high-resolution embedded liquid surfaces; the proposed approach offers improved visual quality, a straightforward implementation, and substantially greater scalability than competing methods.This research was supported by NSERC (RGPIN-04360-2014), ERC (638176), and IST Austri

Surface-Only Simulation of Fluids

Surface-only simulation methods for fluid dynamics are those that perform computation only on a surface representation, without relying on any volumetric discretization. Such methods have superior asymptotic complexity in time and memory than the traditional volumetric discretization approaches, and thus are more tractable for simulation of complex fluid phenomena. Although for most computer graphics applications and many engineering applications, the interior flow inside the fluid phases is typically not of interest, the vast majority of existing numerical techniques still rely on discretization of the volumetric domain. My research first tackles the mesh-based surface tracking problem in the multimaterial setting, and then proposes surface-only simulation solutions for two scenarios: the soap-films and bubbles, and the general 3D liquids. Throughout these simulation approaches, all computation takes place on the surface, and volumetric discretization is entirely eliminated

Novel Paradigms in Physics-Based Animation: Pointwise Divergence-Free Fluid Advection and Mixed-Dimensional Elastic Object Simulation

This thesis explores important but so far less studied aspects of physics-based animation: a simulation method for mixed-dimensional and/or non-manifold elastic objects, and a pointwise divergence-free velocity interpolation method applied to fluid simulation. Considering the popularity of single-type models e.g., hair, cloths, soft bodies, etc., in deformable body simulations, more complicated coupled models have gained less attention in graphics research, despite their relative ubiquity in daily life. This thesis presents a unified method to simulate such models: elastic bodies consisting of mixed-dimensional components represented with potentially non-manifold simplicial meshes. Building on well-known simplicial rod, shell, and solid models, this thesis categorizes and defines a comprehensive palette expressing all possible constraints and elastic energies for stiff and flexible connections between the 1D, 2D, and 3D components of a single conforming simplicial mesh. For fluid animation, this thesis proposes a novel methodology to enhance grid-based fluid animation with pointwise divergence-free velocity interpolation. Unlike previous methods which interpolate discrete velocity values directly for advection, this thesis proposes using intermediate steps involving vector potentials: first build a discrete vector potential field, interpolate these values to form a pointwise potential, and apply the continuous curl to recover a pointwise divergence-free flow field. Particles under these pointwise divergence-free flows exhibit significantly better particle distributions than divergent flows over time. To accelerate the use of vector potentials, this thesis proposes an efficient method that provides boundary-satisfying and smooth discrete potential fields on uniform and cut-cell grids. This thesis also introduces an improved ramping strategy for the “Curl-Noise” method of Bridson et al. (2007), which enforces exact no-normal-flow on the exterior domain boundaries and solid surfaces. The ramping method in the thesis effectively reduces the incidence of particles colliding with obstacles or creating erroneous gaps around the obstacles, while significantly alleviating the artifacts the original ramping strategy produces

Heat Transfer Mechanism In Particle-Laden Turbulent Shearless Flows

Particle-laden turbulent flows are one of the complex flow regimes involved in a wide range of environmental, industrial, biomedical and aeronautical applications. Recently the interest has included also the interaction between scalars and particles, and the complex scenario which arises from the interaction of particle finite inertia, temperature transport, and momentum and heat feedback of particles on the flow leads to a multi-scale and multi-physics phenomenon which is not yet fully understood. The present work aims to investigate the fluid-particle thermal interaction in turbulent mixing under one-way and two-way coupling regimes. A recent novel numerical framework has been used to investigate the impact of suspended sub-Kolmogorov inertial particles on heat transfer within the mixing layer which develops at the interface of two regions with different temperature in an isotropic turbulent flow. Temperature has been considered a passive scalar, advected by the solenoidal velocity field, and subject to the particle thermal feedback in the two-way regime. A self-similar stage always develops where all single-point statistics of the carrier fluid and the suspended particles collapse when properly re-scaled. We quantify the effect of particle inertial, parametrized through the Stokes and thermal Stokes numbers, on the heat transfer through the Nusselt number, defined as the ratio of the heat transfer to the thermal diffusion. A scale analysis will be presented. We show how the modulation of fluid temperature gradients due to the statistical alignments of the particle velocity and the local carrier flow temperature gradient field, impacts the overall heat transfer in the two-way coupling regime

Mandoline: robust cut-cell generation for arbitrary triangle meshes

Although geometry arising "in the wild" most often comes in the form of a surface representation, a plethora of geometrical and physical applications require the construction of volumetric embeddings either of the geometry itself or the domain surrounding it. Cartesian cut-cell-based mesh generation provides an attractive solution in which volumetric elements are constructed from the intersection of the input surface geometry with a uniform or adaptive hexahedral grid. This choice, especially common in computational fluid dynamics, has the potential to efficiently generate accurate, surface-conforming cells; unfortunately, current solutions are often slow, fragile, or cannot handle many common topological situations. We therefore propose a novel, robust cut-cell construction technique for triangle surface meshes that explicitly computes the precise geometry of the intersection cells, even on meshes that are open or non-manifold. Its fundamental geometric primitive is the intersection of an arbitrary segment with an axis-aligned plane. Beginning from the set of intersection points between triangle mesh edges and grid planes, our bottom-up approach robustly determines cut-edges, cut-faces, and finally cut-cells, in a manner designed to guarantee topological correctness. We demonstrate its effectiveness and speed on a wide range of input meshes and grid resolutions, and make the code available as open source.This work is graciously supported by NSERC Discovery Grants (RGPIN-04360-2014 & RGPIN-2017-05524), NSERC Accelerator Grant (RGPAS-2017-507909), Connaught Fund (503114), and the Canada Research Chairs Program

Physics of environmental flows interacting with obstacles

2017 Fall.Includes bibliographical references.The effects of natural and man-made obstacles on their surrounding environmental flows such as rivers, lakes, estuaries, oceans and the atmosphere has been the subject of numerous studies for many decades. The flow-obstacle interaction can lead to the generation of turbulence which determines local flow dynamics and even large-scale circulations. The characteristic chaotic and enhanced mixing properties of turbulence in conjunction with other environmental conditions such as the clustering of multiple obstacles and density variations raise a number of interesting problems pertaining to both fundamental fluid dynamics and practical engineering applications. Insights into these processes is of fundamental importance for many applications, such as determining the fate of deep water-masses formed in the abyssal ocean, optimizing the productivity and environmental impact of marine farms, predicting the amount of power that a group of turbines can generate, estimating carbon dioxide exchange between the forests and the atmosphere or modeling flood routing in vegetated rivers. The main aim of this dissertation is to use high-resolution numerical simulations to study environmental flows of different forcing mechanisms interacting with obstacles of different geometries. The objectives are multi-fold: (i) To gain insights into the three-dimensional hydrodynamics of constant-density flows interacting with a finite canopy; (ii) To develop an unambiguous geometrical framework for characterizing canopy planar geometry; (iii) To explore the fundamental differences in the flow dynamics between porous canopies and their solid counterpart; and (iv) To investigate the effect of ambient density stratification on flow-obstacle interactions. The first part of this dissertation focuses on the mean three-dimensional hydrodynamics in the vicinity of a suspended cylindrical canopy patch with a bulk diameter of D. The patch was made of Nc constituent solid circular cylinders with h in height and d in diameter, and was suspended in deep water (H/h ≫ 1 where H is the total flow depth). After the validation against published experimental data, large eddy simulations (LES) were conducted to study the effects of patch density (0.16 ≤ φ = Nc(d/D)2 ≤ 1, by varying Nc) and patch aspect ratio (0.25 ≤ AR = h/D ≤ 1, by varying h) on the near-field flow properties. It was observed qualitatively and quantitatively that an increase in either φ or AR decreases bleeding velocity along the streamwise direction but increases bleeding velocities along the lateral and vertical directions, respectively. A close examination at the flow inside the patch reveals that despite the similar dependence of vertical bleeding on φ and AR, the underlying physics are different. However, in contrast to the bleeding velocity, a flow-rate budget shows that the proportion of the vertical bleeding flow leaving the patch with respect to the total flow entering the patch (i.e. relative vertical bleeding) decreases with increasing AR. Finally, the interlinks between patch geometry, flow bleeding and flow diversion are identified: the patch influences the flow diversion not only directly by its real geometrical dimensions, but also indirectly by modifying flow bleeding which enlarges the size of the near-wake. While loss of flow penetrating the patch increases monotonically with increasing φ, its partition into flow diversion around and beneath the patch shows a non-monotonic dependence, highlighting the fundamental differences in the flow dynamics between porous patches and their solid counterpart. Next, the propagation of full-depth lock-exchange bottom gravity currents over a submerged array of circular cylinders is investigated using laboratory experiments and LES. Firstly, to investigate the front velocity of gravity currents across the whole range of array density φ, the array is densified from a flat-bed (φ = 0) towards a solid-slab (φ = 1) under a particular submergence ratio H/h, where H is the flow depth and h is the array height. The time-averaged front velocity in the slumping phase of the gravity current is found to first decrease and then increase with increasing φ. Next, a new geometrical framework consisting of a streamwise array density μx = d/sx and a spanwise array density μy = d/sy is proposed to account for organized but nonequidistant arrays (μx 6 ≠ μy), where sx and sy are the streamwise and spanwise cylinder spacings, respectively, and d is the cylinder diameter. It is argued that this two-dimensional parameter space can provide a more quantitative and unambiguous description of the current-array interaction compared with the array density given by φ = (π/4) μxμy. Both in-line and staggered arrays are investigated. Four dynamically different flow regimes are identified: (i) through-flow propagating in the array interior subject to individual cylinder wakes (μx: small for in-line array and arbitrary for staggered array; μy: small); (ii) over-flow propagating on the top of the array subject to vertical convective instability (μx: large; μy: large); (iii) plunging-flow climbing sparse close-to-impermeable rows of cylinders with minor streamwise intrusion (μx: small; μy: large); and (iv) skimming-flow channelized by an in-line array into several sub-currents with strong wake sheltering (μx: large; μy: small).Finally, the flow dynamics of intrusive gravity currents past a bottom-mounted obstacle in a continuously stratified ambient was numerically investigated, highlighting the effect of ambient stratification which is not considered in the previous sections. The propagation dynamics of a classic intrusive gravity current was first simulated in order to validate the numerical model with previous laboratory experiments. A bottom-mounted obstacle with a varying non-dimensional height of ˜D = D/H, where D is the obstacle height and H is the total flow depth, was then added to the problem in order to study the downstream flow pattern of the intrusive gravity current. For short obstacles, the intrusion re-established itself downstream without much distortion. However, for tall obstacles, the downstream flow was found to be a joint effect of horizontal advection, overshoot-spring back phenomenon, and associated Kelvin-Helmholtz instabilities. Analysis of the numerical results show that the relationship between the downstream propagation speed and the obstacle height can be subdivided into three regimes: a retarding regime (˜D ≈ 0 ∼ 0.3), an impounding regime (˜D ≈ 0.3 ∼ 0.6), and a choking regime (˜D ≈ 0.6 ∼ 1.0).Overall, at a fundamental level, this dissertation aims to contribute to an improved understanding of the physics associated with environmental flows interacting with obstacles. Moreover, the results from this research are expected to facilitate better parameterizations of this important class of flows