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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.
A second order accurate level set method on nongraded adaptive Cartesian grids
 J. Comput. Phys
"... We present a level set method on nongraded adaptive Cartesian grids, i.e. grids for which the ratio between adjacent cells is not constrained. We use quadtree and octree data structures to represent the grid and a simple algorithm to generate a mesh with the finest resolution at the interface. In p ..."
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Cited by 30 (3 self)
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We present a level set method on nongraded adaptive Cartesian grids, i.e. grids for which the ratio between adjacent cells is not constrained. We use quadtree and octree data structures to represent the grid and a simple algorithm to generate a mesh with the finest resolution at the interface. In particular, we present (1) a locally third order accurate reinitialization scheme that transforms an arbitrary level set function into a signed distance function, (2) a second order accurate semiLagrangian methods to evolve the linear level set advection equation under an externally generated velocity field, (3) a second order accurate upwind method to evolve the nonlinear level set equation under a normal velocity as well as to extrapolate scalar quantities across an interface in the normal direction, and (4) a semiimplicit scheme to evolve the interface under mean curvature. Combined, we obtain a level set method on adaptive Cartesian grids with a negligible amount of mass loss. We propose numerical examples in two and three spatial dimensions to demonstrate the accuracy of the method. 1
Computation of solid–liquid phase fronts in the sharp interface limit on fixed grids
 J. Comput. Phys
, 1999
"... A finitedifference formulation is applied to track solid–liquid boundaries on a fixed underlying grid. The interface is not of finite thickness but is treated as a discontinuity and is explicitly tracked. The imposition of boundary conditions exactly on a sharp interface that passes through the Ca ..."
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Cited by 29 (2 self)
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A finitedifference formulation is applied to track solid–liquid boundaries on a fixed underlying grid. The interface is not of finite thickness but is treated as a discontinuity and is explicitly tracked. The imposition of boundary conditions exactly on a sharp interface that passes through the Cartesian grid is performed using simple stencil readjustments in the vicinity of the interface. Attention is paid to formulating difference schemes that are globally secondorder accurate in x and t. Error analysis and grid refinement studies are performed for test problems involving the diffusion and convection–diffusion equations, and for stable solidification problems. Issues concerned with stability and change of phase of grid points in the evolution of solid–liquid phase fronts are also addressed. It is demonstrated that the field calculation is secondorder accurate while the position of the phase front is calculated to firstorder accuracy. Furthermore, the accuracy estimates hold for the cases where there is a property jump across the interface. Unstable solidification phenomena are simulated and an attempt is made to compare results with previously published work. The results indicate the need to begin an effort to benchmark computations of instability phenomena. c ° 1999 Academic Press
Delaunay Deformable Models: Topologyadaptive Meshes Based on the Restricted Delaunay triangulation
, 2006
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The lattice Boltzmann equation method: Theoretical interpretation, numerics and implications
 Int. Multiphase Flow, J
, 2003
"... During the last ten years the Lattice Boltzmann Equation (LBE) method has been developed as an alternative numerical approach in computational fluid dynamics (CFD). Originated from the discrete kinetic theory, the LBE method has emerged with the promise to become a superior modeling platform, both c ..."
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Cited by 27 (1 self)
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During the last ten years the Lattice Boltzmann Equation (LBE) method has been developed as an alternative numerical approach in computational fluid dynamics (CFD). Originated from the discrete kinetic theory, the LBE method has emerged with the promise to become a superior modeling platform, both computationally and conceptually, compared to the existing arsenal of the continuumbased CFD methods. The LBE method has been applied for simulation of various kinds of fluid flows under different conditions. The number of papers on the LBE method and its applications continues to grow rapidly, especially in the direction of complex and multiphase media. The purpose of the present paper is to provide a comprehensive, selfcontained and consistent tutorial on the LBE method, aiming to clarify misunderstandings and eliminate some confusion that seems to persist in the LBErelated CFD literature. The focus is placed on the fundamental principles of the LBE approach. An excursion into the history, physical background and details of the theory and numerical implementation is made. Special attention is paid to advantages and limitations of the method, and its perspectives to be a useful framework for description of complex flows and interfacial (and multiphase) phenomena. The computational performance of the LBE method is examined, comparing it to other CFD methods, which directly solve for the transport equations of the macroscopic variables.
G.: Reconstructing surfaces of particlebased fluids using anisotropic kernels
 In Proc. of the 2010 ACM SIGGRAPH/Eurographics Symp. on Comput. Anim
, 2010
"... In this paper we present a novel surface reconstruction method for particlebased fluid simulators such as Smoothed Particle Hydrodynamics. In particlebased simulations, fluid surfaces are usually defined as a level set of an implicit function. We formulate the implicit function as a sum of anisotr ..."
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Cited by 24 (3 self)
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In this paper we present a novel surface reconstruction method for particlebased fluid simulators such as Smoothed Particle Hydrodynamics. In particlebased simulations, fluid surfaces are usually defined as a level set of an implicit function. We formulate the implicit function as a sum of anisotropic smoothing kernels, and the direction of anisotropy at a particle is determined by performing Principal Component Analysis (PCA) over the neighboring particles. In addition, we perform a smoothing step that repositions the centers of these smoothing kernels. Since these anisotropic smoothing kernels capture the local particle distributions more accurately, our method has advantages over existing methods in representing smooth surfaces, thin streams and sharp features of fluids. Our method is fast, easy to implement, and our results demonstrate a significant improvement in the quality of reconstructed surfaces as compared to existing methods.
A LagrangianEulerian shellfluid coupling algorithm based on level sets
, 2005
"... We propose arobuq compuyx;qII] method for thecouS/; simu;]#yx of a compressible highspeed flow interacting with a highlyflexible thinshell strushell A standard Eundard finite voluy formu#I##y on a fixed Cartesian mesh isuyq for thefluyB and a Lagrangian formugiany based onsu[T[;yx;S finite element ..."
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Cited by 24 (14 self)
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We propose arobuq compuyx;qII] method for thecouS/; simu;]#yx of a compressible highspeed flow interacting with a highlyflexible thinshell strushell A standard Eundard finite voluy formu#I##y on a fixed Cartesian mesh isuyq for thefluyB and a Lagrangian formugiany based onsu[T[;yx;S finite elements on anu;BIqTyx;Sq mesh isuyq for the shell. The fluTBB[yx; interface on the Cartesian mesh is tracked with level sets. The conservation laws at the interface are enforced byapplying proper interfaceboufaceyS;]T[yx;T to the fluy and shell solvers at the beginning of each time step. The basic approach furoachy a general algorithm for explicit loosecouey;I of Lagrangian shell solvers with Cartesian gridbasedEuidba flui solvers. The e#ciencyandrobuncyan of the proposed approach is demonstrated with an airbag deployment simuymenty # 2004 Elsevier Ltd. Allrl rl Keywords: Shell; Flu;y Shellfluy interaction; Finite elements; FinitevolueyS Level sets 1. I442x14 A large class of flu#I[]yx# interaction problems requ yS a combined Lagrangian/Eu#/qIT description of the governing dynamics. It is well known that Lagrangian formu[yx#;S are inadequyx for describing highspeed flows with significant vorticityand/or with large boueyS/[I/yx#S#[]yu since thecompu[Syx##T mesh inevitablyincuT deformationinduyu distortions, which breaks thenu#TBT]y method. This problem can be alleviated byrecoued tocontinux[ adaptive remeshing [23],bu notcuy# in general, especiallyin three dimensions.Eumensi approaches with the field equy tionsformuTTq# in terms of spatial variables and fixed meshes are better suter for most flut flows. By contrast, large deformations of shells are moreadequ#[By described in a Lagrangian framework. The principal advantage of the Lagrangian approach for shells lies in its a...
Numerical Methods for FluidStructure Interaction  A Review
, 2012
"... The interactions between incompressible fluid flows and immersed structures are nonlinear multiphysics phenomena that have applications to a wide range of scientific and engineering disciplines. In this article, we review representative numerical methods based on conforming and nonconforming me ..."
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Cited by 22 (0 self)
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The interactions between incompressible fluid flows and immersed structures are nonlinear multiphysics phenomena that have applications to a wide range of scientific and engineering disciplines. In this article, we review representative numerical methods based on conforming and nonconforming meshes that are currently available for computing fluidstructure interaction problems, with an emphasis on some of the recent developments in the field. A goal is to categorize the selected methods and assess their accuracy and efficiency. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study in fluidstructure interactions.
Volume Tracking of Interfaces Having Surface Tension in Two and Three Dimensions
, 1996
"... . Solution algorithms are presented for tracking interfaces with piecewise linear (PLIC) volumeoffluid (VOF) methods on Eulerian grids (structured and unstructured) in two and three dimensions. We review the theory of volume tracking methods, derive appropriate volume evolution equations, identify ..."
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Cited by 20 (3 self)
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. Solution algorithms are presented for tracking interfaces with piecewise linear (PLIC) volumeoffluid (VOF) methods on Eulerian grids (structured and unstructured) in two and three dimensions. We review the theory of volume tracking methods, derive appropriate volume evolution equations, identify and present solutions to the basic geometric functions needed for interface reconstruction and volume fluxing, and provide algorithm templates for modern 2D and 3D PLIC VOF interface tracking methods. We discuss some key issues for PLIC VOF methods, namely the method used for time integration of fluid volumes (operator splitting, unsplit, RungeKutta, etc.) and the estimation of interface normals. We also present our latest developments in the continuum surface force (CSF) model for surface tension, namely extension to 3D and variable surface tension effects. We identify and focus on CSF model issues that become especially critical on fine meshes with high density ratio interfacial flows...
Dye Advection without the Blur: A LevelSet Approach for Texture
 PROC. EUROGRAPHICS 2004
, 2004
"... Dye advection is an intuitive and versatile technique to visualize both steady and unsteady flow. Dye can be easily combined with noisebased dense vector field representations and is an important element in usercentric visual exploration processes. However, fast texturebased implementations of dy ..."
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Cited by 17 (5 self)
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Dye advection is an intuitive and versatile technique to visualize both steady and unsteady flow. Dye can be easily combined with noisebased dense vector field representations and is an important element in usercentric visual exploration processes. However, fast texturebased implementations of dye advection rely on linear interpolation operations that lead to severe diffusion artifacts. In this paper, a novel approach for dye advection is proposed to avoid this blurring and to achieve long and clearly defined streaklines or extended streaklike patterns. The interface between dye and background is modeled as a levelset within a signed distance field. The levelset evolution is governed by the underlying flow field and is computed by a semiLagrangian method. A reinitialization technique is used to counteract the distortions introduced by the levelset evolution and to maintain a levelset function that represents a local distance field. This approach works for 2D and 3D flow fields alike. It is demonstrated how the texturebased levelset representation lends itself to an efficient GPU implementation and therefore facilitates interactive visualization.