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42
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 49 (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.
Constructing material interfaces from data sets with volumefraction information
 In Proceedings Visualization 2000
"... We present a new algorithm for material boundary interface reconstruction from data sets containing volume fractions. We transform the reconstruction problem to a problem that analyzes the dual data set, where each vertex in the dual mesh has an associated barycentric coordinate tuple that represent ..."
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Cited by 22 (10 self)
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We present a new algorithm for material boundary interface reconstruction from data sets containing volume fractions. We transform the reconstruction problem to a problem that analyzes the dual data set, where each vertex in the dual mesh has an associated barycentric coordinate tuple that represents the fraction of each material present. After constructing the dual tetrahedral mesh from the original mesh, we construct material boundaries by mapping a tetrahedron into barycentric space and calculating the intersections with Voronoi cells in barycentric space. These intersections are mapped back to the original physical space and triangulated to form the boundary surface approximation. This algorithm can be applied to any grid structure and can treat any number of materials per element/vertex.
Numerical simulation of bubble and droplet deformation by a level set approach with surface tension
, 2009
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NUMERICAL SIMULATION OF DROPLETDEFORMATION BY A LEVEL SET APPROACH WITH SURFACE TENSION
"... Abstract. In this paper we present a threedimensional Navier–Stokes solver for incompressible twophase flow problems with surface tension and apply the proposed scheme to the simulation of dropletdeformation. Our approach employs a standard finite difference/finite volume discretization on unifor ..."
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Cited by 8 (2 self)
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Abstract. In this paper we present a threedimensional Navier–Stokes solver for incompressible twophase flow problems with surface tension and apply the proposed scheme to the simulation of dropletdeformation. Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin’s projection approach. The free surface between the two fluid phases is tracked with a level set technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and third order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the level set function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface which leads to a first order convergence in the smoothing region. We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature and the application of our solver to the simulation of dropletdeformation due to a shear flow in three space dimensions.
A meshdependent model for applying dynamic contact angles to VOF simulations
 JOURNAL OF COMPUTATIONAL PHYSICS
, 2009
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LARGE DROPLET IMPACT ON WATER LAYERS
"... The impact of large droplets onto an otherwise undisturbed layer of water is considered. The work, which is motivated primarily with regard to aircraft icing, is to try and help understand the role of splashing on the formation of ice on a wing, in particular for large droplets where splash appears ..."
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Cited by 4 (4 self)
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The impact of large droplets onto an otherwise undisturbed layer of water is considered. The work, which is motivated primarily with regard to aircraft icing, is to try and help understand the role of splashing on the formation of ice on a wing, in particular for large droplets where splash appears to have a significant effect. Analytical and numerical approaches are used to investigate a single droplet impact onto a water layer. The flow for small times after impact is determined analytically, for both direct and oblique impacts. The impact is also examined numerically using the volume of fluid (VOF) method. At small times there are promising comparisons between the numerical results, the analytical solution and experimental work capturing the ejector sheet. At larger times there is qualitative agreement with experiments and related simulations. Various cases are considered, varying the droplet size to layer depth ratio, including surface roughness, droplet distortion and air effects. The amount of fluid splashed by such an impact is examined and is found to increase with droplet size and to be significantly influenced by surface roughness. The makeup of the splash is also considered, tracking the incoming fluid, and the splash is found to consist mostly of fluid originating in the layer.
A Monolithic Mass Tracking Formulation for Bubbles in Incompressible Flow
"... We devise a novel method for treating bubbles in incompressible flow that relies on the conservative advection of bubble mass and an associated equation of state in order to determine pressure boundary conditions inside each bubble. We show that executing this algorithm in a traditional manner leads ..."
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Cited by 4 (3 self)
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We devise a novel method for treating bubbles in incompressible flow that relies on the conservative advection of bubble mass and an associated equation of state in order to determine pressure boundary conditions inside each bubble. We show that executing this algorithm in a traditional manner leads to stability issues similar to those seen for partitioned methods for solidfluid coupling. Therefore, we reformulate the problem monolithically. This is accomplished by first proposing a new fully monolithic approach to coupling incompressible flow to fully nonlinear compressible flow including the effects of shocks and rarefactions, and then subsequently making a number of simplifying assumptions on the air flow removing not only the nonlinearities but also the spatial variations of both the density and the pressure. The resulting algorithm is quite robust, has been shown to converge to known solutions for test problems, and has been shown to be quite effective on more realistic problems including those with multiple bubbles, merging and pinching, etc. Notably, this approach departs from a standard twophase incompressible flow model where the air flow preserves its volume despite potentially large forces and pressure differentials in the surrounding incompressible fluid that should change its volume. Our bubbles readily change volume according to an isothermal equation of state. 1.
A Mass Tracking Formulation for Bubbles in Incompressible Flow
"... We devise a novel method for treating bubbles in incompressible flow that relies on the conservative advection of bubble mass and an associated equation of state in order to determine pressure boundary conditions inside each bubble. We show that executing this algorithm in a traditional manner leads ..."
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Cited by 2 (0 self)
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We devise a novel method for treating bubbles in incompressible flow that relies on the conservative advection of bubble mass and an associated equation of state in order to determine pressure boundary conditions inside each bubble. We show that executing this algorithm in a traditional manner leads to stability issues similar to those seen for partitioned methods for solidfluid coupling. Therefore, we reformulate the problem monolithically. This is accomplished by first proposing a new fully monolithic approach to coupling incompressible flow to fully nonlinear compressible flow including the effects of shocks and rarefactions, and then subsequently making a number of simplifying assumptions on the air flow removing not only the nonlinearities but also the spatial variations of both the density and the pressure. The resulting algorithm is quite robust, has been shown to converge to known solutions for test problems, and has been shown to be quite effective on more realistic problems including those with multiple bubbles, merging and pinching, etc. Notably, this approach departs from a standard twophase incompressible flow model where the air flow preserves its volume despite potentially large forces and pressure differentials in the surrounding incompressible fluid that should change its volume. Our bubbles readily change volume according to an isothermal equation of state. 1.
A MassConserving LevelSet (MCLS) Method for Modeling of MultiPhase Flows
, 2003
"... The MassConserving LevelSet (MCLS) method is proposed to model multiphase ows. The aim is to model high densityratio
ows with complex interface topologies, such as mixtures of bubbles and droplets. Aspects which are taken into account are: a sharp front (density changes rapidly), arbitrary sh ..."
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Cited by 2 (0 self)
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The MassConserving LevelSet (MCLS) method is proposed to model multiphase ows. The aim is to model high densityratio
ows with complex interface topologies, such as mixtures of bubbles and droplets. Aspects which are taken into account are: a sharp front (density changes rapidly), arbitrary shaped interfaces, surface tension, buoyancy and coalescence of drops/bubbles. Attention is paid to massconservation and integrity of the interface. A survey of available computational methods is performed in [1]. The proposed computational method is a combination of LevelSet and VolumeofFluid methods. The
ow is computed with a pressure correction method with a MarkerandCell layout. Interface conditions are satised by means of the continuous surface force/stress (CSF/CSS) methodology and the GhostFluid method for incompressible
ows. The LevelSet method is an elegant method. The major disadvantage is that it is not rigorously massconserving. This means that additional eort is necessary to conserve mass. The MCLS method introduces a VolumeofFluid function, which is advected without the necessity to reconstruct the interface. There is a strong relationship between the VolumeofFluid function and the LevelSet function. In the spirit of the LevelSet methodology, the advection of the VOFfunction is, unlike other VOF methods, purely implicit at every time. This makes the method straightforward to apply to arbitrarily shaped interfaces, which may collide and break up. 1
Shear cell rupture of nematic liquid crystal droplets in viscous fluids
 J. NonNewt. Fluid Mech
"... Abstract. We model the hydrodynamics of a shear cell experiment with an immiscible nematic liquid crystal droplet in a viscous fluid using an energetic variational approach and phasefield methods [86]. The model includes the coupled system for the flow field for each phase, a phasefield function f ..."
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Abstract. We model the hydrodynamics of a shear cell experiment with an immiscible nematic liquid crystal droplet in a viscous fluid using an energetic variational approach and phasefield methods [86]. The model includes the coupled system for the flow field for each phase, a phasefield function for the diffuse interface and the orientational director field of the liquid crystal phase. An efficient numerical scheme is implemented for the twodimensional evolution of the shear cell experiment for this initial data. The same model reduces to an immiscible viscous droplet in a viscous fluid, which we simulate first to compare with other numerical and experimental behavior. Then we simulate drop deformation by varying capillary number (independent of liquid crystal physics), liquid crystal interfacial anchoring energy and OseenFrank distortional elastic energy. We show the number of eventual droplets (one to several) and “beads on a string ” behavior are tunable with these three physical parameters. All stable droplets possess signature quadrupolar shear and normal stress distributions. The liquid crystal droplets always possess a global surface defect structure, called a boojum, when tangential surface anchoring is imposed. Boojums [79, 32] consist of degree +1/2 and −1/2 surface defects within a bipolar global orientational structure. 1.