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An Adaptive Level Set Approach For Incompressible TwoPhase Flows
 J. Comput. Phys
, 1998
"... In Sussman, Smereka and Osher (1994), a numerical method using the level set approach was formulated for solving incompressible twophase flow with surface tension. In the level set approach, the interface is represented as the zero level set of a smooth function; this has the effect of replacing th ..."
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Cited by 135 (13 self)
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In Sussman, Smereka and Osher (1994), a numerical method using the level set approach was formulated for solving incompressible twophase flow with surface tension. In the level set approach, the interface is represented as the zero level set of a smooth function; this has the effect of replacing the advection of density, which has steep gradients at the interface, with the advection of the level set function, which is smooth. In addition, the interface can merge or break up with no special treatment. We maintain the level set function as the signed distance from the interface in order to robustly compute flows with high density ratios and stiff surface tension effects. In this work, we couple the level set scheme to an adaptive projection method for the incompressible NavierStokes equations, in order to achieve higher resolution of the interface with a minimum of additional expense. We present twodimensional axisymmetric and fully threedimensional results of air bubble and water dr...
A coupled level set and volumeoffluid method for computing 3D and axisymmetric incompressible twophase flows
 Journal of Computational Physics
, 1006
"... We present a coupled level set/volumeoffluid (CLSVOF) method for computing 3D and axisymmetric incompressible twophase flows. This method combines some of the advantages of the volumeoffluid method with the level set method to obtain a method which is generally superior to either method alone. ..."
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Cited by 92 (2 self)
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We present a coupled level set/volumeoffluid (CLSVOF) method for computing 3D and axisymmetric incompressible twophase flows. This method combines some of the advantages of the volumeoffluid method with the level set method to obtain a method which is generally superior to either method alone. We present direct comparisons between computations made with the CLSVOF method and computations made with the level set method, the volumeoffluid method, and the boundary integral method. We also compare our computations to the exact solution for an oscillating ellipse due to Lamb and experimental results obtained for a rising gas bubble in liquid obtained by Hnat and Buckmaster. Our computational examples focus on flows in which surface tension forces and changes in topology are dominant features of the flow. c ° 2000 Academic Press Key Words: level set; volumeoffluid; curvature; incompressible.
An accurate adaptive solver for surfacetensiondriven interfacial flows
 Journal of Computational Physics
, 2009
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A sharp interface method for incompressible twophase flows
, 2007
"... We present a sharp interface method for computing incompressible immiscible twophase flows. It couples the levelset and volumeoffluid techniques and retains their advantages while overcoming their weaknesses. It is stable and robust even for large density and viscosity ratios on the order of 100 ..."
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Cited by 44 (8 self)
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We present a sharp interface method for computing incompressible immiscible twophase flows. It couples the levelset and volumeoffluid techniques and retains their advantages while overcoming their weaknesses. It is stable and robust even for large density and viscosity ratios on the order of 1000 to 1. The numerical method is an extension of the secondorder method presented by Sussman [M. Sussman, A second order coupled levelset and volume of fluid method for computing growth and collapse of vapor bubbles, Journal of Computational Physics 187 (2003) 110–136] in which the previous method treated the gas pressure as spatially constant and the present method treats the gas as a second incompressible fluid. The new method yields solutions in the zero gas density limit which are comparable in accuracy to the method in which the gas pressure was treated as spatially constant. This improvement in accuracy allows one to compute accurate solutions on relatively coarse grids, thereby providing a speedup over continuum or "ghostfluid" methods.
An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems Part I: The standard grid sequence
, 1996
"... : In this paper we try to achieve hindependent convergence with preconditioned GMRES ([13]) and BiCGSTAB ([18]) for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as a preconditioner. They are also used as solution methods in order to compare the performanc ..."
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Cited by 29 (7 self)
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: In this paper we try to achieve hindependent convergence with preconditioned GMRES ([13]) and BiCGSTAB ([18]) for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as a preconditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid methods differ only in the transfer operators. One uses standard matrixdependent prolongation operators from [3], [5]. The second uses "upwind" prolongation operators, developed in [24]. Both employ the Galerkin coarse grid approximation and an alternating zebra line GaussSeidel smoother. The third method is based on the block LU decomposition of a matrix and on an approximate Schur complement. This multigrid variant is presented in [11]. All three multigrid algorithms are algebraic methods. The eigenvalue spectra of the three multigrid iteration matrices are analyzed for the equations solved on a 33 2 grid, in order...
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.
Perspective on Eulerian Finite Volume Methods for Incompressible Interfacial Flows
 Kuhlmann and H Rath
, 1999
"... Incompressible interfacial flows here refer to those incompressible flows possessing multiple distinct, immiscible fluids separated by interfaces of arbitrarily complex topology. A prototypical example is free surface flows, where fluid properties across the interface vary by orders of magnitude. In ..."
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Cited by 10 (1 self)
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Incompressible interfacial flows here refer to those incompressible flows possessing multiple distinct, immiscible fluids separated by interfaces of arbitrarily complex topology. A prototypical example is free surface flows, where fluid properties across the interface vary by orders of magnitude. Interfaces present in these flows possess topologies that are not only irregular but also dynamic, undergoing gross changes such as merging, tearing, and filamenting as a result of the flow and interface physics such as surface tension and phase change. The interface topology requirements facing an algorithm tasked to model these flows inevitably leads to an underlying Eulerian methodology. The discussion herein is confined therefore to Eulerian schemes, with further emphasis on finite volume methods of discretization for the partial differential equations manifesting the physical model. Numerous algorithm choices confront users and developers of simulation tools designed to model the timeun...
An Improved Sharp Interface Method for Viscoelastic and Viscous TwoPhase Flows
 J SCI COMPUT
"... We introduce a robust method for computing viscous and viscoelastic twophase bubble and drop motions. Our method utilizes a coupled levelset and volumeoffluid technique for updating and representing the airwater interface. Our method introduces a novel approach for treating the viscous coupli ..."
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Cited by 8 (3 self)
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We introduce a robust method for computing viscous and viscoelastic twophase bubble and drop motions. Our method utilizes a coupled levelset and volumeoffluid technique for updating and representing the airwater interface. Our method introduces a novel approach for treating the viscous coupling terms at the airwater interface; these improvements result in improved stability for computing twophase bubble formation solutions. We also present an improved, “positivepreserving” discretization technique for updating the configuration tensor for viscoelastic flows, in the context of computing twophase bubble and drop motion.
A Computational Study of the Spreading of Oil Underneath a Sheet of Ice
, 1998
"... The spreading of oil underneath a sheet of ice is computed using an adaptive level set method for incompressible twofluid flow. Factors such as viscosity, surface tension, and wall adhesion are taken into account in the computations. The results of the computations agree well with previous experime ..."
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Cited by 7 (0 self)
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The spreading of oil underneath a sheet of ice is computed using an adaptive level set method for incompressible twofluid flow. Factors such as viscosity, surface tension, and wall adhesion are taken into account in the computations. The results of the computations agree well with previous experiments and theory. In this work, we also use a very efficient and accurate computational method for determining the final steady profile of a body of oil under ice in water. The computational models are used to make further observations regarding the dependency of the oil spreading radius on the surface energies between the oil, ice, and water. I. INTRODUCTION In recent years there has been increased oil excavation in ice covered waters 20;9 . As a result, chances are increased that an oil spill due to a tanker accident or the rupture of an oil pipeline will occur in ice covered waters. It is generally known that oil spreads over a much smaller area under the ice cover than in open waters ...
Efficient Implementation of the Multigrid Preconditioned Conjugate Gradient Method on Distributed Memory Machines
 in Proceedings of Supercomputing '94
, 1994
"... A multigrid preconditioned conjugate gradient (MGCG) method[15], which uses the multigrid method as a preconditioner for the CG method, has a good convergence rate even for the problems on which the standard multigrid method does not converge efficiently. This paper considers a parallelization of th ..."
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Cited by 7 (1 self)
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A multigrid preconditioned conjugate gradient (MGCG) method[15], which uses the multigrid method as a preconditioner for the CG method, has a good convergence rate even for the problems on which the standard multigrid method does not converge efficiently. This paper considers a parallelization of the MGCG method and proposes an efficient parallel MGCG method on distributed memory machines. For the good convergence rate of the MGCG method, several difficulties in parallelizing the multigrid method are successfully settled. Besides, the parallel MGCG method on Fujitsu multicomputer AP1000[8] has high performance and it is more than 10 times faster than the Scaled CG (SCG) method[6]. 1 Introduction Parallelization of the multigrid method has been studied and several parallel multigrid methods have been implemented. One natural parallelization approach is governed by the grid partitioning principles. Sbosny[13] analyzed and implemented parallel multigrid method using the domain decomposit...