Theoretical considerations on the free-surface role in the smoothed-particle-hydrodynamics model

Colagrossi, A.; Antuono, Matteo; Touzé, David Le

doi:10.1103/physreve.79.056701

Cited by 168 publications

(113 citation statements)

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“…Regarding more specifically the viscous free-surface flows at aim in the present work, a few papers address the consistency of SPH formulations of the viscous term; see, e.g., Español and Revenga [5] or Hu and Adams [6], but without the presence a.colagrossi@insean.it 'm.antuono@insean.it 'antonio.souto@upm.es ^david.letouze@ec-nantes.fr of a free surface. Conversely, Colagrossi et al [7] recently addressed the consistency of the SPH formulation in presence of a free surface, but for inviscid flow.…”

Section: Introductionmentioning

confidence: 99%

Theoretical analysis and numerical verification of the consistency of viscous smoothed-particle-hydrodynamics formulations in simulating free-surface flows

et al. 2011

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The theoretical formulation of the smoothed particle hydrodynamics (SPH) method deserves great care because of some inconsistencies oceurring when considering free-surface inviscid flows. Actually, in SPH formulations one usually assumes that (i) surface integral terms on the boundary of the interpolation kernel support are neglected, (ii) free-surface conditions are implicitly verified. These assumptions are studied in detail in the present work for free-surface Newtonian viscous flow. The consistency of classical viscous weakly compressible SPH formulations is investigated. In particular, the principie of virtual work is used to study the verification of the free-surface boundary conditions in a weak sense. The latter can be related to the global energy dissipation induced by the viscous term formulations and their consistency. Numerical verification of this theoretical analysis is provided on three free-surface test cases including a standing wave, with the three viscous term formulations investigated.

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Section: Introductionmentioning

confidence: 99%

Theoretical analysis and numerical verification of the consistency of viscous smoothed-particle-hydrodynamics formulations in simulating free-surface flows

et al. 2011

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“…An interesting discussion about the influence of the truncation of differential operators close to the boundaries in WCSPH can be found in Ref. 11) where a complete analysis of several formulations of the pressure gradient and velocity divergence operators is performed when an inviscid flow is considered in the presence of a free surface. These ideas were extended to the Laplacian operator in Ref.…”

Section: §1 Introductionmentioning

confidence: 99%

A Boundary Integral SPH Formulation: Consistency and Applications to ISPH and WCSPH

Macià

González

Cercos-Pita

et al. 2012

Progress of Theoretical Physics

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One of the historical problems appearing in SPH formulations is the inconsistencies coming from the inappropriate implementation of boundary conditions. In this work, this problem has been investigated; instead of using typical methodologies such as extended domains with ghost or dummy particles where severe inconsistencies are found, we included the boundary terms that naturally appear in the formulation. First, we proved that in the 1D smoothed continuum formulation, the inclusion of boundary integrals allows for a consistent O (h) formulation close to the boundaries. Second, we showed that the corresponding discrete version converges to a certain solution when the discretization SPH parameters tend to zero. Typical tests with the first and second derivative operators confirm that this boundary condition implementation works consistently. The 2D Poisson problem, typically used in ISPH, was also studied, obtaining consistent results. For the sake of completeness, two practical applications, namely, the duct flow and a sloshing tank, were studied with the results showing a rather good agreement with former experiments and previous results.Subject Index: 024 §1. IntroductionThe SPH scheme is a Lagrangian model based on a smoothing of the spatial differential operators of fluid-dynamics equations and on their subsequent discretization through a finite number of fluid particles. The smoothing procedure is performed at the continuum level using a compact support kernel function whose characteristic length is the smoothing length h. The resolution of the discrete SPH scheme is a function of the smoothing length h and the mean particle distance Δx. In this framework, the (continuous) equations of the fluid-dynamics should be recovered as both h and Δx/h simultaneously tend to zero. 1) Colagrossi and Landrini 2) demonstrated that when boundaries are not present, the SPH approximation of a function u (x) differs O(h 2 ) from the analytical function u (x). Quinlan et al. 3) studied the errors in the first-order derivatives of a classical SPH implementation and its dependence on the particle spacing and smoothing length when no boundaries were considered. In Ref. 4), this work was extended to 3D and a complete consistency study was performed for first-and second-order derivatives.The SPH simulations in engineering usually involve solid boundary conditions (BC) for both the velocity and pressure fields. In the SPH framework, these conditions have been implemented in the past in a number of different ways: by using boundary force-type models, 5), 6) by modifying the structure of the kernel in the Downloaded from https://academic.oup.

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“…For conservation and consistency reasons (see Colagrossi et al, 2009Colagrossi et al, , 2011Colagrossi et al, , 2013, the above differential operators are not directly approximated using equation Eq. (5), but are conveniently symmetrized.…”

Section: Discretizationmentioning

confidence: 99%

Time domain simulation of coupled sloshing–seakeeping problems by SPH–FEM coupling

et al. 2016

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The aim of this work is to carry out numerical simulations in the time domain of seakeeping problems taking into account internal flow in tanks, including sloshing. To this aim, a Smooth Particle Hydrodynamics (SPH) solver for simulating internal flows in tanks is coupled in the time domain to a Finite Element Method (FEM) diffraction-radiation solver developed for seakeeping problems. Validations are carried out comparing against available experimental data. Good agreement between obtained numerical results and experimental data is found.

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Theoretical considerations on the free-surface role in the smoothed-particle-hydrodynamics model

Cited by 168 publications

References 10 publications

Theoretical analysis and numerical verification of the consistency of viscous smoothed-particle-hydrodynamics formulations in simulating free-surface flows

Theoretical analysis and numerical verification of the consistency of viscous smoothed-particle-hydrodynamics formulations in simulating free-surface flows

A Boundary Integral SPH Formulation: Consistency and Applications to ISPH and WCSPH

Time domain simulation of coupled sloshing–seakeeping problems by SPH–FEM coupling

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