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60
Fast viscoelastic behavior with thin features
 ACM Trans. Graph
, 2008
"... We introduce a method for efficiently animating a wide range of deformable materials. We combine a high resolution surface mesh with a tetrahedral finite element simulator that makes use of frequent remeshing. This combination allows for fast and detailed simulations of complex elastic and plastic ..."
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Cited by 44 (6 self)
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We introduce a method for efficiently animating a wide range of deformable materials. We combine a high resolution surface mesh with a tetrahedral finite element simulator that makes use of frequent remeshing. This combination allows for fast and detailed simulations of complex elastic and plastic behavior. We significantly expand the range of physical parameters that can be simulated with a single technique, and the results are free from common artifacts such as volumeloss, smoothing, popping, and the absence of thin features like strands and sheets. Our decision to couple a high resolution surface with lowresolution physics leads to efficient simulation and detailed surface features, and our approach to creating the tetrahedral mesh leads to an orderofmagnitude speedup over previous techniques in the time spent remeshing. We compute masses, collisions, and surface tension forces on the scale of the fine mesh, which helps avoid visual artifacts due to the differing mesh resolutions. The result is a method that can simulate a large array of different material behaviors with high resolution features in a short amount of time.
Matching Fluid Simulation Elements to Surface Geometry and Topology
"... Figure 1: Sphere Splash. Coupling an explicit surface tracker to a Voronoi simulation mesh built from pressure points sampled in a geometryaware fashion lets us capture very fine details in this sphere splash animation that uses only 314K tetrahedra. We introduce an Eulerian liquid simulation frame ..."
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Cited by 35 (7 self)
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Figure 1: Sphere Splash. Coupling an explicit surface tracker to a Voronoi simulation mesh built from pressure points sampled in a geometryaware fashion lets us capture very fine details in this sphere splash animation that uses only 314K tetrahedra. We introduce an Eulerian liquid simulation framework based on the Voronoi diagram of a potentially unorganized collection of pressure samples. Constructing the simulation mesh in this way allows us to place samples anywhere in the computational domain; we exploit this by choosing samples that accurately capture the geometry and topology of the liquid surface. When combined with highresolution explicit surface tracking this allows us to simulate nearly arbitrarily thin features, while eliminating noise and other artifacts that arise when there is a resolution mismatch between the simulation and the surface—and allowing a precise inclusion of surface tension based directly on and at the same resolution as the surface mesh. In addition, we present a simplified Voronoi/Delaunay mesh velocity interpolation scheme, and a direct extension of embedded free surfaces and solid boundaries to Voronoi meshes.
Deforming Meshes that Split and Merge
"... Figure 1: Dropping viscoelastic balls in an Eulerian fluid simulation. Invisible geometry is quickly deleted, while the visible surfaces retain their details even after translating through the air and splashing on the ground. We present a method for accurately tracking the moving surface of deformab ..."
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Cited by 31 (5 self)
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Figure 1: Dropping viscoelastic balls in an Eulerian fluid simulation. Invisible geometry is quickly deleted, while the visible surfaces retain their details even after translating through the air and splashing on the ground. We present a method for accurately tracking the moving surface of deformable materials in a manner that gracefully handles topological changes. We employ a Lagrangian surface tracking method, and we use a triangle mesh for our surface representation so that fine features can be retained. We make topological changes to the mesh by first identifying merging or splitting events at a particular grid resolution, and then locally creating new pieces of the mesh in the affected cells using a standard isosurface creation method. We stitch the new, topologically simplified portion of the mesh to the rest of the mesh at the cell boundaries. Our method detects and treats topological events with an emphasis on the preservation of detailed features, while simultaneously simplifying those portions of the material that are not visible. Our surface tracker is not tied to a particular method for simulating deformable materials. In particular, we show results from two significantly different simulators: a Lagrangian FEM simulator with tetrahedral elements, and an Eulerian gridbased fluid simulator. Although our surface tracking method is generic, it is particularly wellsuited for simulations that exhibit fine surface details and numerous topological events. Highlights of our results include merging of viscoplastic materials with complex geometry, a taffypulling animation with many fold and merge events, and stretching and slicing of stiff plastic material.
Simulation of Bubbles in Foam With The Volume Control Method
"... Figure 1: When the level set is advected by the BFECC [Dupont and Liu 2003] method, the simulation of a rising bubble produces volume loss (top). When the proposed volume control method is used, the volume of bubble is preserved regardless of the length of the simulation (bottom). From left to right ..."
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Cited by 25 (0 self)
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Figure 1: When the level set is advected by the BFECC [Dupont and Liu 2003] method, the simulation of a rising bubble produces volume loss (top). When the proposed volume control method is used, the volume of bubble is preserved regardless of the length of the simulation (bottom). From left to right, each column shows the bubble at t = 0, 0.0625, 0.125, 0.25, 0.5, and 10.0 second. The image on the far right shows a foam structure obtained after raising more than 400 bubbles. Liquid and gas interactions often produce bubbles that stay for a long time without bursting on the surface, making a dry foam structure. Such long lasting bubbles simulated by the level set method can suffer from a small but steady volume error that accumulates to a visible amount of volume change. We propose to address this problem by using the volume control method. We track the volume change of each connected region, and apply a carefully computed divergence that compensates undesired volume changes. To compute the divergence, we construct a mathematical model of the volume change, choose control strategies that regulate the modeled volume error, and establish methods to compute the control gains that provide robust and fast reduction of the volume error, and (if desired) the control of how the volume changes over time. 1
Textured liquids based on the marker level set
 Computer Graphics Forum
, 2007
"... In this work we propose a new Eulerian method for handling the dynamics of a liquid and its surface attributes (for example its color). Our approach is based on a new method for interface advection that we term the Marker Level Set (MLS). The MLS method uses surface markers and a level set for track ..."
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Cited by 13 (3 self)
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In this work we propose a new Eulerian method for handling the dynamics of a liquid and its surface attributes (for example its color). Our approach is based on a new method for interface advection that we term the Marker Level Set (MLS). The MLS method uses surface markers and a level set for tracking the surface of the liquid, yielding more efficient and accurate results than popular methods like the Particle Level Set method (PLS). Another novelty is that the surface markers allow the MLS to handle nondiffusively surface texture advection, a rare capability in the realm of Eulerian simulation of liquids. We present several simulations of the dynamical evolution of liquids and their surface textures.
A Pointbased Method for Animating Elastoplastic Solids
 EUROGRAPHICS / ACM SIGGRAPH SYMPOSIUM ON COMPUTER ANIMATION (2009) E. GRINSPUN AND J. HODGINS (EDITORS)
, 2009
"... In this paper we describe a pointbased approach for animating elastoplastic materials. Our primary contribution is a simple method for computing the deformation gradient for each particle in the simulation. The deformation gradient is computed for each particle by finding the affine transformatio ..."
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Cited by 11 (1 self)
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In this paper we describe a pointbased approach for animating elastoplastic materials. Our primary contribution is a simple method for computing the deformation gradient for each particle in the simulation. The deformation gradient is computed for each particle by finding the affine transformation that best approximates the motion of neighboring particles over a single timestep. These transformations are then composed to compute the total deformation gradient that describes the deformation around a particle over the course of the simulation. Given the deformation gradient we can apply arbitrary constitutive models and compute the resulting elastic forces. Our method has two primary advantages: we do not store or compare to an initial rest configuration and we work directly with the deformation gradient. The first advantage avoids poor numerical conditioning and the second naturally leads to a multiplicative model of deformation appropriate for finite deformations. We demonstrate our approach on a number of examples that exhibit a wide range of material behaviors.
MultiFLIP for Energetic TwoPhase Fluid Simulation
"... Fig. 1: The “glugging ” effect of water pouring through a spout cannot be reproduced with singlephase liquid simulation. Physicallybased liquid animations often ignore the influence of air, giving up interesting behaviour. We present a new method which treats both ..."
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Cited by 7 (0 self)
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Fig. 1: The “glugging ” effect of water pouring through a spout cannot be reproduced with singlephase liquid simulation. Physicallybased liquid animations often ignore the influence of air, giving up interesting behaviour. We present a new method which treats both
On boundary condition capturing for multiphase interfaces
 J. Sci. Comput
, 2007
"... This paper begins with an overview of the boundary condition capturing approach to solving problems with interfaces. Although, the authors ’ original motivation was to extend the ghost fluid method from compressible to incompressible flow, the elliptic nature of incompressible flow quickly quenched ..."
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Cited by 7 (2 self)
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This paper begins with an overview of the boundary condition capturing approach to solving problems with interfaces. Although, the authors ’ original motivation was to extend the ghost fluid method from compressible to incompressible flow, the elliptic nature of incompressible flow quickly quenched the idea that ghost cells could be defined and used in the usual manner. Instead the boundary conditions had to be implicitly captured by the matrix formulation itself, leading to the novel approach. We first review the work on the variable coefficient Poisson equation, noting that the simplicity of the method allowed for an elegant convergence proof. Simplicity and robustness also allowed for a quick extension to threedimensional twophase incompressible flows including the effects of viscosity and surface tension, which is discussed subsequently. The method has enjoyed popularity in both computational physics and computer graphics, and we show some comparisons with the traditional delta function approach for the visual simulation of bubbles. Finally, we discuss extensions to problems where the velocity is discontinuous as well, as is the case for premixed flames, and show an example of multiple interacting liquids that includes all of the aforementioned phenomena. 1
A Hybrid LagrangianEulerian Formulation for Bubble Generation and Dynamics
"... Figure 1: (Left) a faucet generating bubbles through air entrainment, (Center) a source seeding tiny bubbles which merge and grow as they rise, as well as interact with a moving armadillo illustrating complex object interaction, (Right) a cavitating propeller generates the characteristic helical pat ..."
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Cited by 3 (0 self)
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Figure 1: (Left) a faucet generating bubbles through air entrainment, (Center) a source seeding tiny bubbles which merge and grow as they rise, as well as interact with a moving armadillo illustrating complex object interaction, (Right) a cavitating propeller generates the characteristic helical pattern in its wake. We present a hybrid LagrangianEulerian framework for simulating both small and large scale bubble dynamics, where the bubbles can grow or shrink in volume as dictated by pressure forces in the surrounding fluid. Small underresolved bubbles are evolved using Lagrangian particles that are monolithically twoway coupled to the surrounding flow in a manner that closely approximates the analytic bubble oscillation frequency while converging to the analytic volume as predicted by the wellknown RayleighPlesset equation. We present a novel scheme for interconverting between these underresolved Lagrangian bubbles and larger wellresolved bubbles that are modeled with a traditional Eulerian level set approach. We also present a novel seeding mechanism to realistically generate bubbles when simulating fluid structure interaction with complex objects such as ship propellers. Moreover, our framework for bubble generation is general enough to be incorporated into all gridbased as well as particlebased fluid simulation methods.