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131
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.
A Fast and Accurate SemiLagrangian Particle Level Set Method
 COMPUTERS AND STRUCTURES
, 2004
"... In this paper, we present an efficient semiLagrangian based particle level set method for the accurate capturing of interfaces. This method retains the robust topological properties of the level set method without the adverse effects of numerical dissipation. Both the level set method and the p ..."
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Cited by 83 (11 self)
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In this paper, we present an efficient semiLagrangian based particle level set method for the accurate capturing of interfaces. This method retains the robust topological properties of the level set method without the adverse effects of numerical dissipation. Both the level set method and the particle level set method typically use high order accurate numerical discretizations in time and space, e.g. TVD RungeKutta and HJWENO schemes. We demonstrate that these computationally expensive schemes are not required. Instead, fast, low order accurate numerical schemes suffice. That is, the addition of particles to the level set method not only removes the difficulties associated with numerical diffusion, but also alleviates the need for computationally expensive high order accurate schemes. We use an efficient, first order accurate semiLagrangian advection scheme coupled with a first order accurate fast marching method to evolve the level set function. To accurately track the underlying flow characteristics, the particles are evolved with a second order accurate method. Since we avoid complex high order accurate numerical methods, extending the algorithm to arbitrary data structures becomes more feasible, and we show preliminary results obtained with an octreebased adaptive mesh.
An accurate adaptive solver for surfacetensiondriven interfacial flows
 Journal of Computational Physics
, 2009
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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.
Robust topological operations for dynamic explicit surfaces
 SIAM Journal on Scientific Computing
"... Abstract. We present a solution to the mesh tangling problem in surface tracking. Using an explicit triangle mesh to track the location of a surface as it moves in three dimensions has many potential advantages for accuracy and efficiency, compared to implicit capturing methods such as level sets. H ..."
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Cited by 36 (6 self)
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Abstract. We present a solution to the mesh tangling problem in surface tracking. Using an explicit triangle mesh to track the location of a surface as it moves in three dimensions has many potential advantages for accuracy and efficiency, compared to implicit capturing methods such as level sets. However, particularly when “mesh surgery ” is required for topological changes, this approach is prone to tangling: The mesh may selfintersect or otherwise no longer represent a physical interface. Our new approach uses robust collision testing to determine when a mesh operation—such as motion, adaptive refinement, coarsening, or topological change—will lead to an invalid state; we then either roll back noncritical operations or apply robust collision response algorithms, minimally perturbing the mesh to guarantee validity. We present numerical examples demonstrating the robustness and accuracy of the method.
2005 Runup and rundown generated by threedimensional sliding masses
 J. Fluid Mech
"... To study the waves and runup/rundown generated by a sliding mass, a numerical simulation model, based on the largeeddysimulation (LES) approach, was developed. The Smagorinsky subgrid scale model was employed to provide turbulence dissipation and the volume of fluid (VOF) method was used to track ..."
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Cited by 30 (1 self)
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To study the waves and runup/rundown generated by a sliding mass, a numerical simulation model, based on the largeeddysimulation (LES) approach, was developed. The Smagorinsky subgrid scale model was employed to provide turbulence dissipation and the volume of fluid (VOF) method was used to track the free surface and shoreline movements. A numerical algorithm for describing the motion of the sliding mass was also implemented. To validate the numerical model, we conducted a set of largescale experiments in a wave tank of 104m long, 3.7m wide and 4.6m deep with a plane slope (1:2) located at one end of the tank. A freely sliding wedge with two orientations and a hemisphere were used to represent landslides. Their initial positions ranged from totally aerial to fully submerged, and the slide mass was also varied over a wide range. The slides were instrumented to provide position and velocity time histories. The timehistories of water surface and the runup at a number of locations were measured. Comparisons between the numerical results and experimental data are presented only for wedge shape slides. Very good agreement is shown for the time histories of runup and generated waves. The detailed threedimensional complex flow patterns, free surface and shoreline deformations are further illustrated by the numerical results. The maximum runup heights are presented as a function of the initial elevation and the specific weight of the slide. The effects of the wave tank width on the maximum runup are also discussed. 1.
A Coupled Level Set and Volume of Fluid Method for computing 3d and axisymmetric Incompressible twophase flows
, 1998
"... We present a coupled level set and volume of fluid method (CLS) for computing 3d and axisymmetric incompressible twophase flows. The (CLS) method combines some of the advantages of the level set approach (LS) with that of the volume of fluid approach (VOF). We do direct comparisons with computation ..."
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Cited by 26 (12 self)
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We present a coupled level set and volume of fluid method (CLS) for computing 3d and axisymmetric incompressible twophase flows. The (CLS) method combines some of the advantages of the level set approach (LS) with that of the volume of fluid approach (VOF). We do direct comparisons with computations using the level set method, volume of fluid method, and the boundary integral method. We also compare our computations to experimental results for a rising gas bubble in liquid. Our comparisons focus on ows in which surface tension forces and changes in topology are present in the flow.
Interface Reconstruction with LeastSquare Fit and Split EulerianLagrangian Advection
 Int. J. Numer. Meth. Fluids
, 2002
"... Two new VOF reconstruction algorithms, which are based on a leastsquare fit technique, are presented. Their performance is tested for several standard shapes and is compared to a few other VOF/PLIC reconstruction techniques, showing in general a better convergence rate. The geometric nature of Lagr ..."
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Cited by 25 (3 self)
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Two new VOF reconstruction algorithms, which are based on a leastsquare fit technique, are presented. Their performance is tested for several standard shapes and is compared to a few other VOF/PLIC reconstruction techniques, showing in general a better convergence rate. The geometric nature of Lagrangian and Eulerian split advection algorithms is investigated in detail and a new mixed split Eulerian ImplicitLagrangian Explicit (EILE) scheme is presented. This method conserves the mass to machine error, performs better than split Eulerian and Lagrangian algorithms, and it is only slightly worse than unsplit schemes. However, the combination of the interface reconstruction with the leastsquare fit and its advection with the EILE scheme appears superior to other existing approaches.
Momentoffluid interface reconstruction
 Los Alamos National Laboratory, Oct 2005. Available online athttp://math.lanl.gov/˜vdyadechko/doc/2005mof.pdf
, 2005
"... We designed a new volumeconservative interface reconstruction method. An input data set for the interface reconstruction algorithm consists of volumes and centroids of the cell fractions occupied by different materials. Compared to pure volume fractions, traditionally used by volumeoffluid (VoF) ..."
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Cited by 23 (6 self)
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We designed a new volumeconservative interface reconstruction method. An input data set for the interface reconstruction algorithm consists of volumes and centroids of the cell fractions occupied by different materials. Compared to pure volume fractions, traditionally used by volumeoffluid (VoF) methods, this choice of the input data allows to define a linear interface approximation per mixed cell (i.e. offers PiecewiseLinear Interface Calculation or Construction (PLIC)) even without exchanging information between neighboring elements. The location of linear interface in each mixed cell is chosen to preserve the volumes and provide the best approximation to the centroids of the cell fractions. The technique proposed yields a second order accurate approximation to interfaces given by simple C 2 curves and is shown to be more accurate than known VoFPLIC methods. 1