A geometrical area-preserving Volume-of-Fluid advection method

Aulisa, Eugenio; Manservisi, Sandro; Scardovelli, Ruben; Zaleski, Stéphane

doi:10.1016/j.jcp.2003.07.003

Cited by 134 publications

(90 citation statements)

References 19 publications

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“…bounded between zero and one) volume fractions, it is necessary to reset any volume fraction violating this constraint before proceeding to the next direction sweep, which will lead to loss of exact mass conservation. In practice we have found that this scheme is simple to implement on quad/octrees with mass conservation usually not being an issue, however it would be interesting to investigate the extension to quad/octrees of flux-redistribution schemes [3,56] or exactly mass-preserving geometrical schemes [53,60].…”

Section: Interface Advection and Geometrical Flux Computationmentioning

confidence: 99%

An accurate adaptive solver for surface-tension-driven interfacial flows

Popinet

2009

Journal of Computational Physics

1,158

1,116

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A method combining an adaptive quad/octree spatial discretisation, geometrical Volume-OfFluid interface representation, balanced-force continuum-surface-force surface tension formulation and height-function curvature estimation is presented. The extension of these methods to the quad/octree discretisation allows adaptive variable resolution along the interface and is described in detail. The method is shown to recover exact equilibrium (to machine accuracy) between surfacetension and pressure gradient in the case of a stationary droplet, irrespective of viscosity and spatial resolution. Accurate solutions are obtained for the classical test case of capillary wave oscillations. An application to the capillary breakup of a jet of water in air further illustrates the accuracy and efficiency of the method. The source code of the implementation is freely available as part of the Gerris flow solver.1

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Section: Interface Advection and Geometrical Flux Computationmentioning

confidence: 99%

An accurate adaptive solver for surface-tension-driven interfacial flows

Popinet

2009

Journal of Computational Physics

1,158

1,116

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“…Volume of fluid methods also adopt an implicit formulation using the volume fraction of one phase in each computational cells (see e.g. [9,13,12,34,36,54,100,117,139,154,161,163] and the references therein). These methods have the advantage of conserving the total volume by construction.…”

Section: The Stefan Problemmentioning

confidence: 99%

“…I.e. we set u n+1 Γ = u Γ (x, t n+1 ) when building the linear system and set u n Γ = u Γ (x, t n ) when evaluating the right-hand-side of equation (9). Setting the boundary condition as u n+1 Γ = u Γ (x, t n ) in the linear system introduces a lagging in time (i.e.…”

Section: Importance Of Time Dependent Boundary Conditionsmentioning

confidence: 99%

“…As detailed in [46,45] and illustrated in figure 10, the interface may sweep some grid nodes from time t n to t n+1 , so the temperature at these nodes needs to be extrapolated to define a valid right-hand-side in the Crank-Nicholson formula (9). Also, as noted in [1,2], the interface's velocity, given by equation (5), is only valid exactly at the interface.…”

Section: Algorithm To Solve the Stefan Problemmentioning

confidence: 99%

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High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

2012

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We present a review of some of the state-of-the-art numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the level-set method for representing the (possibly moving) irregular domain's boundary, (ii) the ghost-fluid method for imposing the Dirichlet boundary condition at the irregular domain's boundary and (iii) a quadtree/octree nodebased adaptive mesh refinement for capturing small length scales while significantly reducing the memory and CPU footprint. In addition, we highlight common misconceptions and describe how to properly implement these methods. Numerical experiments illustrate quantitative and qualitative results.

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“…Surface capturing uses a continuum representation of the free surface and the actual position of the interface is obtained via post-processing. Examples include various forms of marker-in-cell or particle-in-cell simulations, solution of the Volume-ofFluid (VOF) [1,7,8], level-set [9,10,11,12] or similar [13,14]. …”

Section: Handling Of the Free Surfacementioning

confidence: 99%

CFD Analysis in Subsea and Marine Technology

Jasak

2017

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. Computational Fluid Dynamics (CFD) is established in design and analysis for a range of industries, but its use in Marine and Naval Hydrodynamics is behind the trend. This can be attributed to the complexity of modelling needs, including presence of free surface, irregular transient flows, fluid-structure coupling and presence of established modelling tools based on potential theory.In this paper, state-of-the-art of CFD in Naval Hydrodynamics, wave and offshore applications is given, with an update of recent advances, validation and computing requirements for typical simulation cases. IntroductionSince the beginning of the 21st century, Computational Fluid Dynamics (CFD) has become well established across the range of engineering applications. CFD results are well understood, expectations on accuracy in design studies can be satisfied. For example, automotive industry uses CFD to significantly reduce the use of experimental studies in aerodynamics, internal combustion engine design and exhaust gas after-treatment. Indeed, CFD studies are now regularly performed in applications which were never properly analysed experimentally, such as passenger compartment comfort, vehicle soiling and acoustics-related phenomena, where the design primarily relies on CFD results.Acceptance of CFD in marine engineering, naval hydrodynamics and evaluation of wave loads appears to be lagging behind the trend of other industries. This is partially due to the complexity of free surface flows, but mainly by the fact that the phenomena under consideration imply significantly higher computational requirements. For example, sea-keeping studies of ships in irregular waves or calculation of transfer functions for wave loading on floating structures still cannot be performed at acceptable speed. "Engineering time-scale" in product design requires turn-over time of 8-12 hours for simulations to be practically useful.An important factor in the acceptance of CFD is the presence of alternative simulation tools. Numerical models based on potential flow theory are widely accepted, fast and validated and have been in use for more than a decade. The potential flow assumption, whole adequate for a part of industrial needs, brings it own limitations, mainly due to the formulation, or failure to account for coupled/non-linear effects. The best example is the evaluation of added resistance in waves, which may provide adequate loading results on the hull, but cannot account for forward speed of the ship.The challenges for CFD modelling in naval hydrodynamics can be grouped as follows:

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A geometrical area-preserving Volume-of-Fluid advection method

Cited by 134 publications

References 19 publications

An accurate adaptive solver for surface-tension-driven interfacial flows

An accurate adaptive solver for surface-tension-driven interfacial flows

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

CFD Analysis in Subsea and Marine Technology

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