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Animation and Rendering of Complex Water Surfaces
, 2002
"... We present a new method for the animation and rendering of photorealistic water effects. Our method is designed to produce visually plausible three dimensional effects, for example the pouring of water into a glass (see figure 1) and the breaking of an ocean wave, in a manner which can be used in a ..."
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Cited by 274 (22 self)
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We present a new method for the animation and rendering of photorealistic water effects. Our method is designed to produce visually plausible three dimensional effects, for example the pouring of water into a glass (see figure 1) and the breaking of an ocean wave, in a manner which can be used in a computer animation environment. In order to better obtain photorealism in the behavior of the simulated water surface, we introduce a new "thickened" front tracking technique to accurately represent the water surface and a new velocity extrapolation method to move the surface in a smooth, waterlike manner. The velocity extrapolation method allows us to provide a degree of control to the surface motion, e.g. to generate a windblown look or to force the water to settle quickly. To ensure that the photorealism of the simulation carries over to the final images, we have integrated our method with an advanced physically based rendering system.
A Hybrid Particle Level Set Method for Improved Interface Capturing
 J. Comput. Phys
, 2002
"... In this paper, we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field. Our method uses Lagrangian marker particles to rebuild the level set in regions which are underresolved. This is ofte ..."
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Cited by 215 (25 self)
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In this paper, we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field. Our method uses Lagrangian marker particles to rebuild the level set in regions which are underresolved. This is often the case for flows undergoing stretching and tearing. The overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method. Our method compares favorably with volume of fluid methods in the conservation of mass and purely Lagrangian schemes for interface resolution. The method is presented in three spatial dimensions.
Reconstructing Volume Tracking
 J. Comput. Phys
, 1997
"... A new algorithm for the volume tracking of interfaces in two dimensions is presented. The algorithm is based upon a welldefined, secondorder geometric solution of a volume evolution equation. The method utilitizes local discrete material volume and velocity data to track interfaces of arbitrari ..."
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Cited by 131 (3 self)
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A new algorithm for the volume tracking of interfaces in two dimensions is presented. The algorithm is based upon a welldefined, secondorder geometric solution of a volume evolution equation. The method utilitizes local discrete material volume and velocity data to track interfaces of arbitrarily complex topology. A linearitypreserving, piecewise linear interface geometry approximation ensures that solutions generated retain secondorder spatial accuracy. Secondorder temporal accuracy is achieved by virtue of a multidimensional unsplit time integration scheme. We detail our geometricallybased solution method, in which material volume fluxes are computed systematically with a set of simple geometric tasks. We then interrogate the method by testing its ability to track interfaces through large (yet controlled) topology changes, whereby an initially simple interface configuration is subjected to vortical flows. Numerical results for these strenuous test problems provide evi...
TwoPhase Binary Fluids and Immiscible Fluids Described By an Order Parameter
, 1996
"... A unified framework for coupled NavierStokes/CahnHilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law. As a numerical application of the theory, we consider the kinetics ..."
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Cited by 83 (1 self)
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A unified framework for coupled NavierStokes/CahnHilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law. As a numerical application of the theory, we consider the kinetics of coarsening for a binary fluid in two spacedimensions. Typeset using REVT E X 1 I. INTRODUCTION The CahnHilliard equation [1] 1 ' . = m\Delta [f 0 (') \Gamma ff\Delta'] (1) is central to materials science, as it characterizes important qualitative features of twophase systems. This equation is based on a free energy /('; grad') = f(') + 1 2 ffjgrad'j 2 ; (2) with f(') a doublewell potential whose wells define the phases, and leads to an interfacial layer within which the density ' suffers large variations. The standard derivation of the CahnHilliard equation begins with the mass balance ' . = \Gammadiv h (3) and the constitutive equation 1 Notation. Tensors ar...
Evolution, implementation, and application of level set and fast marching methods for advancing fronts
 J. Comput. Phys
, 2001
"... A variety of numerical techniques are available for tracking moving interfaces. In this review, we concentrate on techniques that result from the link between the partial differential equations that describe moving interfaces and numerical schemes designed for approximating the solutions to hyperbol ..."
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Cited by 67 (2 self)
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A variety of numerical techniques are available for tracking moving interfaces. In this review, we concentrate on techniques that result from the link between the partial differential equations that describe moving interfaces and numerical schemes designed for approximating the solutions to hyperbolic conservation laws. This link gives rise to computational techniques for tracking moving interfaces in two and three space dimensions under complex speed laws. We discuss the evolution of these techniques, the fundamental numerical approximations, involved, implementation details, and applications. In particular, we review some work on three aspects of materials sciences: semiconductor process simulations, seismic processing, and optimal structural topology design. c ○ 2001 Academic Press 1.
A HighOrder Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows
, 1997
"... We present a numerical method for computing solutions of the incompressible Euler or NavierStokes equations when a principal feature of the flow is the presence of an interface between two fluids with different fluid properties. The method is based on a secondorder projection method for variable d ..."
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Cited by 54 (8 self)
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We present a numerical method for computing solutions of the incompressible Euler or NavierStokes equations when a principal feature of the flow is the presence of an interface between two fluids with different fluid properties. The method is based on a secondorder projection method for variable density flows using an "approximate projection" formulation. The boundary between the fluids is tracked with a secondorder, volumeoffluid interface tracking algorithm. We present results for viscous RayleighTaylor problems at early time with equal and unequal viscosities to demonstrate the convergence of the algorithm. We also present computational results for the RayleighTaylor instability in airhelium and for bubbles and drops in an airwater system without interfacial tension to demonstrate the behavior of the algorithm on problems with larger density and viscosity contrasts. 1. Introduction Fluid flows with free surfaces or material interfaces occur in a large number of natural and ...
Animation of bubbles in liquid
 Comput. Graph. Forum (Eurographics Proc
, 2003
"... We present a new fluid animation technique in which liquid and gas interact with each other, using the example of bubbles rising in water. In contrast to previous studies which only focused on one fluid, our system considers both the liquid and the gas simultaneously. In addition to the flowing moti ..."
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Cited by 48 (2 self)
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We present a new fluid animation technique in which liquid and gas interact with each other, using the example of bubbles rising in water. In contrast to previous studies which only focused on one fluid, our system considers both the liquid and the gas simultaneously. In addition to the flowing motion, the interactions between liquid and gas cause buoyancy, surface tension, deformation and movement of the bubbles. For the natural manipulation of topological changes and the removal of the numerical diffusion, we combine the volumeoffluid method and the fronttracking method developed in the field of computational fluid dynamics. Our minimumstress surface tension method enables this complementary combination. The interfaces are constructed using the marching cubes algorithm. Optical effects are rendered using vertex shader techniques.
VolumeofFluid Interface Tracking with Smoothed Surface Stress Methods for ThreeDimensional Flows
, 1997
"... This article is devoted to the description and assessment of a numerical procedure for the simulation of flows with interfaces between viscous Newtonian fluids. The interfaces are modeled as discontinuities with constant surface tension. This physical model is relevant for many applications. Of part ..."
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Cited by 45 (0 self)
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This article is devoted to the description and assessment of a numerical procedure for the simulation of flows with interfaces between viscous Newtonian fluids. The interfaces are modeled as discontinuities with constant surface tension. This physical model is relevant for many applications. Of particular interest to us are phenomena such as droplet formation and breakup where interface topology may change through the reconnection of the interface. The method may also be useful to study complex multiphase flows, when for instance the fluid particles undergo threedimensional perturbations.
A conservative threedimensional Eulerian method for coupled solidfluid shock capturing
 Copyright © by SIAM. Unauthorized reproduction of this article is prohibited
"... A new method is presented for the explicit Eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions. We solve separately for each phase the equations of fluid dynamics or solid mechanics, using as interface boundary conditions ..."
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Cited by 39 (9 self)
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A new method is presented for the explicit Eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions. We solve separately for each phase the equations of fluid dynamics or solid mechanics, using as interface boundary conditions artificially extended representations of the individual phases. For fluids we use a new 3D spatially unsplit implementation of the piecewise parabolic (PPM) method of Colella and Woodward. For solids we use the 3D spatially unsplit Eulerian solid mechanics method of Miller and Colella. Vacuum and perfectly incompressible obstacles may also be employed as phases. A separate problem is the time evolution of material interfaces, which are represented by planar segments constructed with a volumeoffluid method. The volume fractions are advanced in time using a secondorder 3D spatially unsplit advection routine with a velocity field determined by solution of interfacenormal twophase Riemann problems. From the Riemann problem solutions we also determine crossinterface momentum and energy fluxes.