A particle-in-cell method for the solution of two-layer shallow-water equations

Cushman-Roisin, Benoı̂t; Esenkov, Oleg E.; Mathias, Benedict J.

doi:10.1002/(sici)1097-0363(20000315)32:5<515::aid-fld933>3.0.co;2-l

Cited by 9 publications

(6 citation statements)

References 15 publications

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“…Pavia (1992), Pavia and Lopez (1994), and Sanson et al (1998) performed similar simulations of evolving oceanic eddies and frontal filaments. Ochoa et al (1998) generalized a PIC shallow water model so that it allowed variable particle densities, and Esenkov and Cushman-Roisin (1999) and Cushman-Roisin et al (2000) discuss the application of the PIC approach to a single layer within a two-layer system.…”

Section: The Pic Methodsmentioning

confidence: 99%

Could a Pile of Slippery Sacks Behave Like an Ocean?

Haertel

Randall

2002

Mon. Wea. Rev.

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A method for simulating fluid motions that shows promise for application to the oceans is explored. Incompressible inviscid fluids with free surfaces are represented as piles of slippery sacks. A system of ordinary differential equations governs the motions of the sacks, and this system is solved numerically in order to simulate a nonlinear deformation, internal and external gravity waves, and Rossby waves. The simulations are compared to analytic and finite-difference solutions, and the former converge to the latter as the sizes of the sacks are decreased.The slippery-sack method appears to be well suited to ocean modeling for the following reasons: 1) it perfectly conserves a fluid's distributions of density and tracers; 2) unlike existing isopycnic models the slippery-sack method is capable of representing a continuum of fluid densities and vertically resolving neutral regions; 3) the inclusion of continuous topography adds no numerical complexity to the slippery-sack method; 4) the slipperysack method conserves energy in the limit as the time step approaches zero; and 5) the slippery-sack method is computationally efficient.

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Section: The Pic Methodsmentioning

confidence: 99%

Could a Pile of Slippery Sacks Behave Like an Ocean?

Haertel

Randall

2002

Mon. Wea. Rev.

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“…FLIC uses an Eulerian grid but computes the motion of continuous fluid rather than particle motion. The classic PIC method stores mass and position information on particles while other physical quantities remain on the grid (Cushman-Roisin et al, 2000). The momentum transfer between the grid and particles results in considerable numerical dissipation, severely impairing computational accuracy.…”

Section: Introductionmentioning

confidence: 99%

An Overview of Coupled Lagrangian–Eulerian Methods for Ocean Engineering

Qian,

Yang,

Liu

2024

J. Marine. Sci. Appl.

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Combining the strengths of Lagrangian and Eulerian descriptions, the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects. This work reviews their development and application in ocean engineering. Initially, we briefly outline the advantages and disadvantages of the Lagrangian and Eulerian descriptions and the main characteristics of the coupled Lagrangian–Eulerian approach. Then, following the developmental trajectory of these methods, the fundamental formulations and the frameworks of various approaches, including the arbitrary Lagrangian–Eulerian finite element method, the particle-in-cell method, the material point method, and the recently developed Lagrangian–Eulerian stabilized collocation method, are detailedly reviewed. In addition, the article reviews the research progress of these methods with applications in ocean hydrodynamics, focusing on free surface flows, numerical wave generation, wave overturning and breaking, interactions between waves and coastal structures, fluid-rigid body interactions, fluid–elastic body interactions, multiphase flow problems and visualization of ocean flows, etc. Furthermore, the latest research advancements in the numerical stability, accuracy, efficiency, and consistency of the coupled Lagrangian–Eulerian particle methods are reviewed; these advancements enable efficient and highly accurate simulation of complicated multiphysics problems in ocean and coastal engineering. By building on these works, the current challenges and future directions of the hybrid Lagrangian–Eulerian particle methods are summarized.

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“…A gain of CPU time is possible by solving the Poisson's equation on a Cartesian grid. This SPH‐mesh coupling is equivalent to the particle in cell method introduced by Harlow in 1955 59‐62 . In this work, we propose to use the work by Ramos Ortega et al for developing a ISPH method to study the damp of a waves train on an inclined porous structure.…”

Section: Introductionmentioning

confidence: 99%

Modified incompressible smooth particle hydrodynamics in porous media method for modeling the damping of a waves train on an inclined porous structure

Ortega

Beaudoin

2021

Numerical Methods in Fluids

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In this work, the ISPHP method proposed by Akbari and Namin in 2013 has been modified by implementing the Taylor expansion of a classical smoothing function. The modified ISPHP method with the Taylor expansion of the smoothing function, the optimization of the solving of Poisson's equation and the wave maker, has been used to simulate the damping of a waves train on an inclined porous structure. The comparison between the numerical results obtained with the modified ISPHP method and the experimental data obtained by Carrasco et al. in 2020 has shown on the one hand that the modified ISPHP method could be used to study the damping of a waves train on an inclined porous structure and on the other hand that the dimensionless number χ could be used to characterize the energy transformations of the interaction of a waves train and an inclined porous structure.

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A particle-in-cell method for the solution of two-layer shallow-water equations

Cited by 9 publications

References 15 publications

Could a Pile of Slippery Sacks Behave Like an Ocean?

Could a Pile of Slippery Sacks Behave Like an Ocean?

An Overview of Coupled Lagrangian–Eulerian Methods for Ocean Engineering

Modified incompressible smooth particle hydrodynamics in porous media method for modeling the damping of a waves train on an inclined porous structure

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