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Journal ArticleDOI

Numerical analysis of breaking waves using the moving particle semi-implicit method

TL;DR: In this paper, a moving particle semi-implicit (MPS) algorithm is used for two-dimensional incompressible non-viscous flow analysis and two types of breaking waves, plunging and spilling breakers, are observed in the calculation results.
Abstract: SUMMARY The numerical method used in this study is the moving particle semi-implicit (MPS) method, which is based on particles and their interactions. The particle number density is implicitly required to be constant to satisfy incompressibility. A semi-implicit algorithm is used for two-dimensional incompressible non-viscous flow analysis. The particles whose particle number densities are below a set point are considered as on the free surface. Grids are not necessary in any calculation steps. It is estimated that most of computation time is used in generation of the list of neighboring particles in a large problem. An algorithm to enhance the computation speed is proposed. The MPS method is applied to numerical simulation of breaking waves on slopes. Two types of breaking waves, plunging and spilling breakers, are observed in the calculation results. The breaker types are classified by using the minimum angular momentum at the wave front. The surf similarity parameter which separates the types agrees well with references. Breaking waves are also calculated with a passively moving float which is modelled by particles. Artificial friction due to the disturbed motion of particles causes errors in the flow velocity distribution which is shown in comparison with the theoretical solution of a cnoidal wave. © 1998 John Wiley & Sons, Ltd.
Citations
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Journal ArticleDOI
TL;DR: In this article, an incompressible smoothed particle hydrodynamics (SPH) method is presented to simulate Newtonian and non-Newtonian flows with free surfaces.

923 citations

Journal ArticleDOI
TL;DR: In this paper, a new formulation for enforcing incompressibility in Smoothed Particle Hydrodynamics (SPH) is introduced, which uses a fractional step with the velocity field integrated forward in time.

862 citations

Journal ArticleDOI
TL;DR: Several improvements that are implemented are presented here to handle turbulence, the fluid viscosity and density, and a different time-stepping algorithm is used.

691 citations

Journal ArticleDOI
TL;DR: A multi-phase smoothed particle hydrodynamics (SPH) method for both macroscopic and mesoscopic flows is proposed, and a new simple algorithm capable for three or more immiscible phases is developed.

610 citations


Cites background from "Numerical analysis of breaking wave..."

  • ...r(r) is a measure of the particle number density which has a larger value in a dense particle region than in a dilute particle region [20]....

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Journal ArticleDOI
TL;DR: A new divergence-free ISPH approach is proposed here which maintains accuracy and stability while remaining mesh free without increasing computational cost by slightly shifting particles away from streamlines, although the necessary interpolation of hydrodynamic characteristics means the formulation ceases to be strictly conservative.

572 citations

References
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Book
01 Jan 2007

3,984 citations


"Numerical analysis of breaking wave..." refers methods in this paper

  • ...The simultaneous linear equations are solved using the incomplete Cholesky decomposition conjugate gradient (ICCG) method [16]....

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Journal ArticleDOI
TL;DR: In this paper, a moving-particle semi-implicit (MPS) method for simulating fragmentation of incompressible fluids is presented, where the motion of each particle is calculated through interactions with neighboring particles covered with the kernel function.
Abstract: A moving-particle semi-implicit (MPS) method for simulating fragmentation of incompressible fluids is presented. The motion of each particle is calculated through interactions with neighboring particles covered with the kernel function. Deterministic particle interaction models representing gradient, Laplacian, and free surfaces are proposed. Fluid density is implicitly required to be constant as the incompressibility condition, while the other terms are explicitly calculated. The Poisson equation of pressure is solved by the incomplete Cholesky conjugate gradient method. Collapse of a water column is calculated using MPS. The effect of parameters in the models is investigated in test calculations. Good agreement with an experiment is obtained even if fragmentation and coalescence of the fluid take place.

1,653 citations


"Numerical analysis of breaking wave..." refers background or methods in this paper

  • ...1 was selected to avoid the concentration of particles near the free surfaces [4]....

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  • ...This value was selected by a test calculation [4]....

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  • ...0 was selected by the balance between computation time and accuracy [4]....

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  • ...The weight function which was used in the particle interaction models was improved to enhance the numerical stability of the MPS method [4]....

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Journal ArticleDOI
TL;DR: Breaker type, for waves on smooth concrete slopes, depends on beach slope m, wave period T, and either deep-water or breaker height, H 0 or Hb as discussed by the authors.
Abstract: Breaker type, for waves on smooth concrete slopes, depends on beach slope m, wave period T, and either deep-water or breaker height, H0 or Hb. For forty-three varied laboratory conditions, breaker type can be sorted fairly well by either of two dimensionless combinations of these variables, an offshore parameter, H0/(L0m2) or an inshore parameter, Hb/(gmT2). As either of these parameters increases, breaker type changes from surging or collapsing to plunging to spilling. For the offshore and inshore parameters, respectively, the surge-plunge transition values are about 0.09 and 0.003 and the plunge-spill transition values are about 4.8 and 0.068. The deep-water heights in the offshore parameter were computed from linear, wave-generator theory. Breaker type data were obtained from films of breaking waves for conditions that produced a dominant breaker type, free from interference by secondary waves.

387 citations


"Numerical analysis of breaking wave..." refers background or methods or result in this paper

  • ...The relation between the breaker types and the surf similarity parameter is compared with the experiments in References [13,14]....

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  • ...In fact, it was written in Galvin’s paper [14] that...

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  • ...This agrees with Galvin’s result [14], but is a little larger than Patrick–Wiegel’s result [13] of j=0....

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  • ...Two experimental results are also included in the figure [13,14]....

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  • ...These tendencies agree with experiments [13,14]....

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