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603
Computation of solid–liquid phase fronts in the sharp interface limit on fixed grids
- J. Comput. Phys
, 1999
"... A finite-difference 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 dis-continuity 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 32 (2 self)
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A finite-difference 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 dis-continuity 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 formu-lating difference schemes that are globally second-order 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 calcu-lation is second-order accurate while the position of the phase front is calculated to first-order 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
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 grid-based fluid simulator. Although our surface tracking method is generic, it is particularly well-suited for simulations that exhibit fine surface details and numerous topological events. Highlights of our results include merging of viscoplastic materials with complex geometry, a taffy-pulling animation with many fold and merge events, and stretching and slicing of stiff plastic material.
A second order accurate level set method on non-graded adaptive cartesian grids
, 2007
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Delaunay Deformable Models: Topology-adaptive 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 28 (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 continuum-based 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, self-contained and consistent tutorial on the LBE method, aiming to clarify misunderstandings and eliminate some confusion that seems to persist in the LBE-related 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.
A Lagrangian-Eulerian shell-fluid coupling algorithm based on level sets
, 2005
"... We propose arobuq compuyx;qII] method for thecouS/; simu;]#yx of a compressible high-speed flow interacting with a highlyflexible thin-shell 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 high-speed flow interacting with a highlyflexible thin-shell 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 grid-basedEuid-ba 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 Shell--fluy interaction; Finite elements; FinitevolueyS Level sets 1. I442x-14 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 deformation-induyu 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...
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 particle-based fluid simulators such as Smoothed Particle Hydrodynamics. In particle-based 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 particle-based fluid simulators such as Smoothed Particle Hydrodynamics. In particle-based 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 re-positions 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.
Volume Tracking of Interfaces Having Surface Tension in Two and Three Dimensions
, 1996
"... . Solution algorithms are presented for tracking interfaces with piecewise linear (PLIC) volume-of-fluid (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 23 (3 self)
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. Solution algorithms are presented for tracking interfaces with piecewise linear (PLIC) volume-of-fluid (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 2-D and 3-D 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, Runge-Kutta, 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 3-D 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...
Numerical Methods for Fluid-Structure Interaction -- A Review
, 2012
"... The interactions between incompressible fluid flows and immersed struc-tures are nonlinear multi-physics 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 non-conforming me ..."
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Cited by 21 (0 self)
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The interactions between incompressible fluid flows and immersed struc-tures are nonlinear multi-physics 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 non-conforming meshes that are currently avail-able for computing fluid-structure 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 fluid-structure interactions.
Design Automation for Microfluidics-Based Biochips
, 2006
"... Advances in microfluidics technology offer exciting possibilities in the realm of enzymatic analysis, DNA analysis, proteomic analysis involving proteins and peptides, immunoassays, implantable drug delivery devices, and environmental toxicity monitoring. Microfluidics-based biochips are therefore g ..."
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Cited by 20 (5 self)
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Advances in microfluidics technology offer exciting possibilities in the realm of enzymatic analysis, DNA analysis, proteomic analysis involving proteins and peptides, immunoassays, implantable drug delivery devices, and environmental toxicity monitoring. Microfluidics-based biochips are therefore gaining popularity for clinical diagnostics and other laboratory procedures involving molecular biology. As more bioassays are executed concurrently on a biochip, system integration and design complexity are expected to increase dramatically. This paper presents different actuation mechanisms for microfluidics-based biochips, as well as associated design automation trends and challenges. The underlying physical principles of eletrokinetics, electrohydrodynamics, and thermocapillarity are discussed. Next, the paper presents an overview of an integrated system-level design methodology that attempts to address key issues in the modeling, simulation, synthesis, testing and reconfiguration of digital microfluidics-based biochips. The top-down design automation will facilitate the integration of fluidic components with microelectronic component in next-generation
