### Industrial Light + Magic

"... Figure 1: Many fluid phenomena consist of thin films and filaments. (Far Left) Film Catenoid: a membrane suspended between two rings contracts due to surface tension. (Middle Left) Fishbone: two colliding jets form a thin sheet, filaments, and droplets. This phenomena is named for its resemblance to ..."

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Figure 1: Many fluid phenomena consist of thin films and filaments. (Far Left) Film Catenoid: a membrane suspended between two rings contracts due to surface tension. (Middle Left) Fishbone: two colliding jets form a thin sheet, filaments, and droplets. This phenomena is named for its resemblance to a fish skeleton. (Middle Right) Waterbell: a jet of water striking an impactor results in a closed circular water sheet that resembles a bell. (Far Right) Paint Splash: a splash caused by a rock falling into a tank filled with layers of colored paint. Many visually interesting natural phenomena are characterized by thin liquid sheets, long filaments, and droplets. We present a new Lagrangian-based numerical method to simulate these codimen-sional surface tension driven phenomena using non-manifold sim-plicial complexes. Tetrahedra, triangles, segments, and points are used to model the fluid volume, thin films, filaments, and droplets, respectively. We present a new method for enforcing fluid incom-pressibility on simplicial complexes along with a physically-guided meshing algorithm to provide temporally consistent information for interparticle forces. Our method naturally allows for transitions be-tween codimensions, either from tetrahedra to triangles to segments to points or vice versa, regardless of the simulation resolution. We demonstrate the efficacy of this method by simulating various natu-ral phenomena that are characterized by thin fluid sheets, filaments, and surface tension effects.

### Swansea University

"... This paper presents a versatile and robust SPH simulation approach for multiple-fluid flows. The spatial distribution of different phases or com-ponents is modeled using the volume fraction representation, the dynam-ics of multiple-fluid flows is captured by using an improved mixture mod-el, and a s ..."

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This paper presents a versatile and robust SPH simulation approach for multiple-fluid flows. The spatial distribution of different phases or com-ponents is modeled using the volume fraction representation, the dynam-ics of multiple-fluid flows is captured by using an improved mixture mod-el, and a stable and accurate SPH formulation is rigorously derived to re-solve the complex transport and transformation processes encountered in multiple-fluid flows. The new approach can capture a wide range of real-world multiple-fluid phenomena, including mixing/unmixing of miscible and immiscible fluids, diffusion effect and chemical reaction etc. Moreover,

### A NONLINEAR VERTEX-BASED MODEL FOR ANIMATION OF TWO-DIMENSIONAL DRY FOAM

"... Abstract: Foam is the natural phenomenon of bubbles that arise due to nucleation of gas in liquids. The current state of art in Computer Graphics rarely includes foam effects on large scales. In this paper we introduce a vertex-based, quasi-static equilibrium model from the field of Computational Ph ..."

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Abstract: Foam is the natural phenomenon of bubbles that arise due to nucleation of gas in liquids. The current state of art in Computer Graphics rarely includes foam effects on large scales. In this paper we introduce a vertex-based, quasi-static equilibrium model from the field of Computational Physics as a new paradigm for foam effects. Dynamic processes like gas diffusion and bubble collapse are added prior equilibration. Animation-wise the numerical model is well behaved and stable and can converge even if the foam is locally ill-defined. A novel contribution is the Ghost-Bubble method that allows foam simulations with free dynamic boundary conditions. The presented model is interesting and well suited for 2D graphics applications like video games and procedural or animated textures.

### Multiphase Flow of Incompressible Fluids Employing Regional Level Set and Volume Control

"... Fig. 1. Resulting simulations of at least two different interacting fluids. Abstract—In this work, the regional level set is employed to track interfaces in multiphase fluid simulations, while considering the behavior of the film between distinct phases. Also, properties of each phase are tracked as ..."

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Fig. 1. Resulting simulations of at least two different interacting fluids. Abstract—In this work, the regional level set is employed to track interfaces in multiphase fluid simulations, while considering the behavior of the film between distinct phases. Also, properties of each phase are tracked as they merge or split, and an algorithm to apply these operations is proposed. Furthermore, it is introduced a method to handle undesired volume changes that tries to minimize the total volume error by making local corrections trough an additional advection step. Moreover, it is put forward an accurate volume calculation technique that takes advantage of the phase distribution determined by the chosen interpolation method. Finally, particles are employed to avoid volumes losses due to discretization’s problems. Keywords-multiphase simulation; volume control; level set; I.

### Eurographics / ACM SIGGRAPH Symposium on Computer Animation (2012) P. Kry and J. Lee (Editors) Simulating Free Surface Flow with Very Large Time Steps

"... We provide a novel simulation method for incompressible free surface flows that allows for large time steps on the order of 10-40 times bigger than the typical explicit time step restriction would allow. Although semi-Lagrangian advection allows for this from the standpoint of stability, large time ..."

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We provide a novel simulation method for incompressible free surface flows that allows for large time steps on the order of 10-40 times bigger than the typical explicit time step restriction would allow. Although semi-Lagrangian advection allows for this from the standpoint of stability, large time steps typically produce significant visual errors. This was addressed in previous work for smoke simulation using a mass and momentum conserving version of semi-Lagrangian advection, and while its extension to water for momentum conservation for small time steps was addressed, pronounced issues remain when taking large time steps. The main difference between smoke and water is that smoke has a globally defined velocity field whereas water needs to move in a manner uninfluenced by the surrounding air flow, and this poses real issues in determining an appropriate extrapolated velocity field. We alleviate problems with the extrapolated velocity field by not using it when it is incorrect, which we determine via conservative advection of a color function which adds forwardly advected semi-Lagrangian rays to maintain conservation when mass is lost. We note that one might also use a more traditional volume-of-fluid method which is more explicitly focused on the geometry of the interface but can be less visually appealing – it is also unclear how to extend volume-of-fluid methods to have larger time steps. Finally, we prefer the visual smoothness of a particle level set method coupled to a traditional backward tracing semi-Lagrangian advection where possible, only using our forward traced color function solution in areas of the flow where the particle level set method fails due to the extremely large time steps. 1.

### ORIGINAL ARTICLE Realistic simulation of mixing fluids

, 2010

"... Abstract Recently, simulation of mixing fluids, for which wide applications can be found in multimedia, computer games, special effects, virtual reality, etc., is attracting more and more attention. Most previous methods focus separately on binary immiscible mixing fluids or binary miscible mixing f ..."

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Abstract Recently, simulation of mixing fluids, for which wide applications can be found in multimedia, computer games, special effects, virtual reality, etc., is attracting more and more attention. Most previous methods focus separately on binary immiscible mixing fluids or binary miscible mixing fluids. Until now, little attention has been paid to realistic simulation of multiple mixing fluids. In this paper, based on the solution principles in physics, we present a unified framework for realistic simulation of liquid–liquid mixing with different solubility, which is called LLSPH. In our method, the mixing process of miscible fluids is modeled by a heat-conduction-based Smooth Particle Hydrodynamics method. A special self-diffusion coefficient is designed to simulate the interactions between miscible fluids. For immiscible fluids, marching-cube-based method is adopted to trace the interfaces between different types of fluids efficiently. Then, an optimized spatial hashing method is adopted for simulation of boundary-free mixing fluids such as the marine oil spill. Finally, various realistic scenes of mixing fluids are rendered using our method. Electronic supplementary material The online version of this article (doi:10.1007/s00371-010-0531-1) contains supplementary material, which is available to authorized users.

### Noname manuscript No. (will be inserted by the editor) A Distributed Spatial Index for Error-Prone Wireless Data Broadcast

"... Abstract Information is valuable to users when it is available not only at the right time but also at the right place. To support efficient location-based data access in wireless data broadcast systems, a distributed spatial index (called DSI) is presented in this paper. DSI is highly efficient beca ..."

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Abstract Information is valuable to users when it is available not only at the right time but also at the right place. To support efficient location-based data access in wireless data broadcast systems, a distributed spatial index (called DSI) is presented in this paper. DSI is highly efficient because it has a linear yet fully distributed structure that naturally shares links in different search paths. DSI is very resilient to the error-prone wireless communication environment because interrupted search operations based on DSI can be resumed easily. It supports search algorithms for classical locationbased queries such as window queries and kNN queries in both of the snapshot and continuous query modes. In-depth analysis and simulation-based evaluation have been conducted. The results show that DSI significantly out-performs a variant of R-trees tailored for wireless data broadcast environments.

### unknown title

, 2010

"... In this paper, we focus on the geometry and dynamics to distinguish our work from the research that focuses on optical effects and the interference colors phenomenon. The paper is organized as follows. Section 2 describes the related work both on simulation of bubbles and fluid simulation in compute ..."

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In this paper, we focus on the geometry and dynamics to distinguish our work from the research that focuses on optical effects and the interference colors phenomenon. The paper is organized as follows. Section 2 describes the related work both on simulation of bubbles and fluid simulation in computer graphics. Section 3 gives an overview of the fluid simulator our work is based on. Section 4 proposes a new interface tracking method, Regional Level Set method, which allows multi-manifold surfaces, to represent our approximated bubble structure. Section 5 proposes a new semi-implicit surface tension model which is much more stable. Section 6 presents a simple control scheme of bubble’s lifecycle. Several animation results produced by our method are explained in Section 7, while Section 8 offers a brief survey and discussion of recent papers

### in

, 2011

"... Physically-based liquid animations often ignore the influence of air, giving up interesting behaviour. We present a new method which treats both air and liquid as incompressible, more accurately reproducing the reality observed at scales relevant to computer animation. The Fluid Implicit Particle (F ..."

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Physically-based liquid animations often ignore the influence of air, giving up interesting behaviour. We present a new method which treats both air and liquid as incompressible, more accurately reproducing the reality observed at scales relevant to computer animation. The Fluid Implicit Particle (FLIP) method, already shown to effectively simulate incompressible fluids with low numerical dissipation, is extended to two-phase flow by associating a phase bit with each particle. The liquid surface is reproduced at each time step from the particle positions, which are adjusted to prevent mixing near the surface and to allow for accurate surface tension. The liquid surface is adjusted around small-scale features so they are represented in the grid-based pressure projection, while separate, loosely coupled velocity fields reduce unwanted influence between the phases. The resulting scheme is easy to implement, requires little parameter tuning and is shown to reproduce lively two-phase fluid phenomena. ii Preface The entirety of this thesis has been submitted as a paper entitled “MultiFLIP for Energetic Two-Phase Fluid Simulation ” to the journal, ACM Transactions on Graphics. The authors listed on the paper are, in order, Landon Boyd and Robert Bridson. The paper was written by Landon Boyd with minor revisions from Robert Bridson. The research was conducted by Landon Boyd, exploring and extending key ideas proposed by Robert Bridson: two velocity fields, particle bumping and level set adjustment for escaped particles. The MultiFLIP implementation was written by Landon Boyd as an extension to a single-phase fluid solver by Robert Bridson. The formula to estimate 3-D face fractions described in section 3.2.1 was contributed by Robert Bridson.

### Curvature-based Offset Distance: Implementations and Applications

"... We address three related problems. The first problem is to change the volume of a solid by a prescribed amount, while minimizing Hausdorff error. This is important for compensating volume change due to smoothing, subdivision, or advection. The second problem is to preserve the individual areas of in ..."

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We address three related problems. The first problem is to change the volume of a solid by a prescribed amount, while minimizing Hausdorff error. This is important for compensating volume change due to smoothing, subdivision, or advection. The second problem is to preserve the individual areas of infinitely small chunks of a planar shape, as the shape is deformed to follow the gentle bending of a smooth spine (backbone) curve. This is important for bending or animating textured regions. The third problem is to generate consecutive offsets, where each unit element of the boundary sweeps the same region. This is important for constant material-removal rate during numerically controlled (NC) machining. For all three problems, we advocate a solution based on normal offsetting, where the offset distance is a function of local or global curvature measures. We discuss accuracy and smoothness of these solutions for models represented by triangle or quad meshes or, in 2D, by spine-aligned planar quads. We also explore the combination of local distance offsetting with a new selective smoothing process that reduces discontinuities and preserves curvature sign. 1.