Numerical analysis of breaking waves using the moving particle semi-implicit method
15 Apr 1998-International Journal for Numerical Methods in Fluids (Wiley)-Vol. 26, Iss: 7, pp 751-769
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.
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TL;DR: In this article, an incompressible smoothed particle hydrodynamics (SPH) method is presented to simulate Newtonian and non-Newtonian flows with free surfaces.
Abstract: An incompressible smoothed particle hydrodynamics (SPH) method is presented to simulate Newtonian and non-Newtonian flows with free surfaces. The basic equations solved are the incompressible mass conservation and Navier–Stokes equations. The method uses prediction–correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting deviation of particle density is then implicitly projected onto a divergence-free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. Various SPH formulations are employed in the discretization of the relevant gradient, divergence and Laplacian terms. Free surfaces are identified by the particles whose density is below a set point. Wall boundaries are represented by particles whose positions are fixed. The SPH formulation is also extended to non-Newtonian flows and demonstrated using the Cross rheological model. The incompressible SPH method is tested by typical 2-D dam-break problems in which both water and fluid mud are considered. The computations are in good agreement with available experimental data. The different flow features between Newtonian and non-Newtonian flows after the dam-break are discussed.
923 citations
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.
Abstract: A new formulation is introduced for enforcing incompressibility in Smoothed Particle Hydrodynamics (SPH). The method uses a fractional step with the velocity field integrated forward in time without enforcing incompressibility. The resulting intermediate velocity field is then projected onto a divergence-free space by solving a pressure Poisson equation derived from an approximate pressure projection. Unlike earlier approaches used to simulate incompressible flows with SPH, the pressure is not a thermodynamic variable and the Courant condition is based only on fluid velocities and not on the speed of sound. Although larger time-steps can be used, the solution of the resulting elliptic pressure Poisson equation increases the total work per time-step. Efficiency comparisons show that the projection method has a significant potential to reduce the overall computational expense compared to weakly compressible SPH, particularly as the Reynolds number, Re, is increased. Simulations using this SPH projection technique show good agreement with finite-difference solutions for a vortex spin-down and Rayleigh?Taylor instability. The results, however, indicate that the use of an approximate projection to enforce incompressibility leads to error accumulation in the density field.
862 citations
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.
Abstract: Smoothed Particle Hydrodynamics (SPH) is a relatively new method for examining the propagation of highly nonlinear and breaking waves. At Johns Hopkins University, we have been working since 2000 to develop an engineering tool using this technique. However, there have been some difficulties in taking the model from examples using a small number of particles to more elaborate and better resolved cases. Several improvements that we have implemented are presented here to handle turbulence, the fluid viscosity and density, and a different time-stepping algorithm is used. The final model is shown to be able to model breaking waves on beaches in two and three dimensions, green water overtopping of decks, and wave–structure interaction.
691 citations
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.
Abstract: A multi-phase smoothed particle hydrodynamics (SPH) method for both macroscopic and mesoscopic flows is proposed. Since the particle-averaged spatial derivative approximations are derived from a particle smoothing function in which the neighboring particles only contribute to the specific volume, while maintaining mass conservation, the new method handles density discontinuities across phase interfaces naturally. Accordingly, several aspects of multi-phase interactions are addressed. First, the newly formulated viscous terms allow for a discontinuous viscosity and ensure continuity of velocity and shear stress across the phase interface. Based on this formulation thermal fluctuations are introduced in a straightforward way. Second, a new simple algorithm capable for three or more immiscible phases is developed. Mesocopic interface slippage is included based on the apparent slip assumption which ensures continuity at the phase interface. To show the validity of the present method numerical examples on capillary waves, three-phase interactions, drop deformation in a shear flow, and mesoscopic channel flows are considered.
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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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.
Abstract: The stability and accuracy of three methods which enforce either a divergence-free velocity field, density invariance, or their combination are tested here through the standard Taylor-Green and spin-down vortex problems. While various approaches to incompressible SPH (ISPH) have been proposed in the past decade, the present paper is restricted to the projection method for the pressure and velocity coupling. It is shown that the divergence-free ISPH method cannot maintain stability in certain situations although it is accurate before instability sets in. The density-invariant ISPH method is stable but inaccurate with random-noise like disturbances. The combined ISPH, combining advantages in divergence-free ISPH and density-invariant ISPH, can maintain accuracy and stability although at a higher computational cost. Redistribution of particles on a fixed uniform mesh is also shown to be effective but the attraction of a mesh-free method is lost. 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. This avoids the highly anisotropic particle spacing which eventually triggers instability. Importantly pressure fields are free from spurious oscillations, up to the highest Reynolds numbers tested.
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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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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01 Jan 1995
424 citations
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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01 Jan 1970
365 citations