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

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

Coupling, Conservation, and Performance in Numerical Simulations

This thesis considers three aspects of the numerical simulations, which arecoupling, conservation, and performance. We conduct a project and addressone challenge from each of these aspects.We propose a novel penalty force to enforce contacts with accurate Coulombfriction. The force is compatible with fully-implicit time integration and theuse of optimization-based integration. In addition to processing collisionsbetween deformable objects, the force can be used to couple rigid bodies todeformable objects or the material point method. The force naturally leads tostable stacking without drift over time, even when solvers are not run toconvergence. The force leads to an asymmetrical system, and we provide apractical solution for handling these.Next we present a new technique for transferring momentum and velocity betweenparticles and MAC grids based on the Affine-Particle-In-Cell (APIC) frameworkpreviously developed for co-locatedgrids. We extend the original APIC paper and show thatthe proposed transfers preserve linear and angular momentum and also satisfyall of the original APIC properties.Early indications in the original APIC paper suggested that APIC might besuitable for simulating high Reynolds fluids due to favorable retention ofvortices, but these properties were not studied further. We use twodimensional Fourier analysis to investigate dissipation in the limit \dt=0.We investigate dissipation and vortex retention numerically to quantify theeffectiveness of APIC compared with other transfer algorithms.Finally we present an efficient solver for problems typically seen inmicrofluidic applications.Microfluidic ``lab on a chip'' devices are small devices that operate on smalllength scales on small volumes of fluid. Designs for microfluidic chips aregenerally composed of standardized and often repeated components connected bylong, thin, straight fluid channels. We propose a novel discretizationalgorithm for simulating the Stokes equations on geometry with these features,which produces sparse linear systems with many repeated matrix blocks. Thediscretization is formally third order accurate for velocity and second orderaccurate for pressure in the $L^\infty$ norm. We also propose a novel linearsystem solver based on cyclic reduction, reordered sparse Gaussian elimination,and operation caching that is designed to efficiently solve systems withrepeated matrix blocks

Monolith: a monolithic pressure-viscosity-contact solver for strong two-way rigid-rigid rigid-fluid coupling

We propose Monolith, a monolithic pressure-viscosity-contact solver for more accurately, robustly, and efficiently simulating non-trivial two-way interactions of rigid bodies with inviscid, viscous, or non-Newtonian liquids. Our solver simultaneously handles incompressibility and (optionally) implicit viscosity integration for liquids, contact resolution for rigid bodies, and mutual interactions between liquids and rigid bodies by carefully formulating these as a single unified minimization problem. This monolithic approach reduces or eliminates an array of problematic artifacts, including liquid volume loss, solid interpenetrations, simulation instabilities, artificial "melting" of viscous liquid, and incorrect slip at liquid-solid interfaces. In the absence of solid-solid friction, our minimization problem is a Quadratic Program (QP) with a symmetric positive definite (SPD) matrix and can be treated with a single Linear Complementarity Problem (LCP) solve. When friction is present, we decouple the unified minimization problem into two subproblems so that it can be effectively handled via staggered projections with alternating LCP solves. We also propose a complementary approach for non-Newtonian fluids which can be seamlessly integrated and addressed during the staggered projections. We demonstrate the critical importance of a contact-aware, unified treatment of fluid-solid coupling and the effectiveness of our proposed Monolith solver in a wide range of practical scenarios.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (Grant RGPIN-04360-2014)

A full Eulerian finite difference approach for solving fluid-structure coupling problems

A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and Nichols (1981, J. Comput. Phys., 39, 201)), which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney-Rivlin materials. In this paper, various verifications and validations of the present full Eulerian method, which solves the fluid and solid motions on a fixed grid, are demonstrated, and the numerical accuracy involved in the fluid-structure coupling problems is examined.Comment: 38 pages, 27 figures, accepted for publication in J. Comput. Phy

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

EFFICIENT PARTICLE-BASED VISCOUS FLUID SIMULATION WITH VIDEO-GUIDED REAL-TO-VIRTUAL PARAMETER TRANSFER

Viscous fluids, such as honey and molten chocolate, are common materials frequently seen in our daily life. These viscous fluids exhibit characteristic behaviors. Capturing and understanding such dynamics have been required for various applications. Although recent research made advances in simulating the viscous fluid dynamics, still many challenges are left to be addressed. In this dissertation, I present novel techniques to more efficiently and accurately simulate viscous fluid dynamics and propose a parameter identification framework to facilitate the tedious parameter tuning steps for viscous materials. In fluid simulation, enforcing the incompressibility robustly and efficiently is essential. One known challenge is how to set appropriate boundary conditions for free surfaces and solid boundaries. I propose a new boundary handling approach for an incompressible particle-based solver based on the connectivity analysis for simulation particles. Another challenge is that previously proposed techniques do not scale well. To address this, I propose a new multilevel particle-based solver which constructs the hierarchy of simulation particles. These techniques improve the robustness and efficiency achieving the nearly linear scaling unlike previous approaches. To simulate characteristic behaviors of viscous fluids, such as coiling and buckling phenomena and adhesion to other materials, it is necessary to develop a specialized solver. I propose a stable and efficient particle-based solver for simulating highly viscous fluids by using implicit integration with the full form of viscosity. To simulate more accurate interactions with solid objects, I propose a new two-way fluid-solid coupling method for viscous fluids via the unified minimization. These approaches also improve the robustness and efficiency while generating rotational and sticky behaviors of viscous fluids. One important challenge for the physically-based simulation is that it is not obvious how to choose appropriate material parameters to generate our desirable behaviors of simulated materials. I propose a parameter identification framework that helps to tune material parameters for viscous fluids with example video data captured from real world fluid phenomena. This framework identifies viscosity parameters for the real viscous fluids while estimating the hidden variables for the fluids, and enables the parameter transfer from the real world to virtual environment.Doctor of Philosoph

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

Signorini conditions for inviscid fluids

In this thesis, we present a new type of boundary condition for the simulation of inviscid fluids – the Signorini boundary condition. The new condition models the non-sticky contact of a fluid with other fluids or solids. Euler equations with Signorini boundary conditions are analyzed using variational inequalities. We derived the weak form of the PDEs, as well as an equivalent optimization based formulation. We proposed a finite element method to numerically solve the Signorini problems. Our method is based on a staggered grid and a level set representation of the fluid surfaces, which may be plugged into an existing fluid solver. We implemented our algorithm and tested it with some 2D fluid simulations. Our results show that the Signorini boundary cpndition successfully models some interesting contact behavior of fluids, such as the hydrophobic contact and the non-coalescence phenomenon