A volume of fluid method based on multidimensional advection and spline interface reconstruction

López, J.; Hernández, J.; Gómez, Pablo; Faura, F.

doi:10.1016/j.jcp.2003.10.030

Cited by 155 publications

(175 citation statements)

References 40 publications

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“…It should be mentioned that, for the steady and uniform flow considered in this test, the contribution of the advection step to the error is negligible; therefore, the error E is only due to reconstruction. On the other hand, as in a similar test carried out by Harvie and Fletcher [23] and López et al [9] for 2D, the reconstruction error tends to reach a minimum value as the Courant number approaches unity and tends to reach a bounded value as the Courant number approaches zero. As discussed by Harvie and Fletcher [23], this asymptotic behavior is important for the viability of the method when small time steps are required.…”

Section: Simple Translation Testsupporting

confidence: 50%

A new volume of fluid method in three dimensions—Part II: Piecewise‐planar interface reconstruction with cubic‐Bézier fit

López

Zanzi

Gómez

et al. 2008

Numerical Methods in Fluids

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SUMMARYA new interface reconstruction method in 3D is presented. The method involves a conservative levelcontour reconstruction coupled to a cubic-Bézier interpolation. The use of the proposed piecewise linear interface calculation (PLIC) reconstruction scheme coupled to a multidimensional time integration provides solutions of second-order spatial and temporal accuracy. The accuracy and efficiency of the proposed reconstruction algorithm are demonstrated through several tests, whose results are compared with those obtained with other recently proposed methods. An overall improvement in accuracy with respect to other recent methods has been achieved, along with a substantial reduction in the central processing unit time required.

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Section: Simple Translation Testsupporting

confidence: 50%

A new volume of fluid method in three dimensions—Part II: Piecewise‐planar interface reconstruction with cubic‐Bézier fit

López

Zanzi

Gómez

et al. 2008

Numerical Methods in Fluids

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“…Many numerical methods are based on this principle, for example SPH methods push around chunks of mass, momentum and energy assigned to particles, and have been used to solve both compressible and incompressible flows, including flows with shock waves, see for example [9,35,20,19,53,4,2,28,32,41,10]. In fact, the idea of pushing around conserved quantities is the basis for volume of fluid methods, which attempt to conserve volume (see for example [40,42,27,14,29,56]). In addition, ALE methods also push material around using a moving grid, and some of those methods use a background grid along with a two-step procedure where the material is first advected forward on a moving grid, and then remapped or redistributed to the background mesh in a conservative fashion, see for example [15,37,33,34,1].…”

Section: Introductionmentioning

confidence: 99%

An unconditionally stable fully conservative semi-Lagrangian method

Lentine

Gretarsson

Fedkiw

2011

Journal of Computational Physics

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Semi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had.

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“…The SLIC method was furthermore improved by Ashgriz and Poo [4] who introduced in 1991 the Flux Line-segment model of Advection and Interface Reconstruction (FLAIR). More recently, Pillod and Tuckett [71] introduced a least-squares procedure while Lopez et al [57] proposed reconstructions based on splines. The main drawback of all these methods is that they are clearly limited to structured grids composed of rectangular or parallelepipedic control volumes.…”

Section: Introductionmentioning

confidence: 99%

Free-Surface Viscous Flow Solution Methods for Ship Hydrodynamics

Wackers

Koren²,

Raven³

et al. 2011

Arch Computat Methods Eng

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The simulation of viscous free-surface water flow is a subject that has reached a certain maturity and is nowadays used in industrial applications, like the simulation of the flow around ships. While almost all methods used are based on the Navier-Stokes equations, the discretisation methods for the water surface differ widely. Many of these highly different methods are being used with success.We review three of these methods, by describing in detail their implementation in one particular code that is being used in industrial practice. The descriptions concern the principle of the method, numerical details, and the method's strengths and limitations. For each code, examples are given of its use. Finally, the methods are compared to determine the best field of application for each.The following surface descretisation methods are reviewed. First, surface fitting/mesh deformation in PARNAS-SOS, developed by MARIN; the description focuses on the efficient steady-state solution method of this code. Then surface capturing with Volume-of-Fluid in ISIS-CFD, developed by CNRS/Ecole Centrale de Nantes; the main topic of this review are the compressive flux discretisation schemes for the volume fraction that are used in this code. And finally, the Level Set method in SURF, developed by NMRI;

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A volume of fluid method based on multidimensional advection and spline interface reconstruction

Cited by 155 publications

References 40 publications

A new volume of fluid method in three dimensions—Part II: Piecewise‐planar interface reconstruction with cubic‐Bézier fit

A new volume of fluid method in three dimensions—Part II: Piecewise‐planar interface reconstruction with cubic‐Bézier fit

An unconditionally stable fully conservative semi-Lagrangian method

Free-Surface Viscous Flow Solution Methods for Ship Hydrodynamics

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