Simulation of wave phenomena in the nearshore through application of O(μ2) and O(μ4) pressure-Poisson Boussinesq type models

Donahue, Aaron S.; Kennedy, Andrew; Westerink, Joannes J.; Zhang, Yao; Dawson, Clint

doi:10.1016/j.coastaleng.2016.03.010

Cited by 2 publications

(6 citation statements)

References 56 publications

(85 reference statements)

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“…In this study, we use the fully nonlinear

scriptO false(μ^{2} false)

PPBOUSS model, which truncates all terms of order greater than

scriptO false(μ^{2} false)

in terms of a measure of frequency dispersion, μ . We adopt the same optimal value of the constant,

{\overset{ϕ}{true}}_{m l}

, as used in the work of Donahue et al,

{\overset{ϕ}{true}}_{12} = - \frac{4}{3}

. Under these conditions, the pressure expansion can be written as follows:

p^{*} = sans-serifg H false(1 - q false) + c_{1} false(1 - q false) + c_{2} ({}, - \frac{4}{3} false(1 - q false) + false(1 - q^{2} false)) .

The distribution of c 1 is obtained by solving the following equation:

α_{3} \nabla^{2} c_{1} + α_{2} \cdot false(\nabla c_{1} false) + α_{1} c_{1} = α_{0},

α_{3} = - \frac{1}{2} H^{2},

α_{2} = - \frac{2}{3} H \nabla ζ - \frac{1}{4} H \nabla h,

α_{1} = \frac{1}{2} H \nabla^{2} h - \frac{1}{3} H \nabla^{2} ζ + \frac{1}{4} false| \nabla h |^{2} + \frac{2}{3} false| \nabla ζ |^{2} - \frac{1}{3} false(\nabla h false) \cdot false(\nabla ζ false) + \frac{5}{4}

…”

Section: Pressure‐poisson Boussinesq‐type Modelmentioning

confidence: 99%

“…Synolakis reported that wave breaking occurs between t ∗ = 15 and 20. It has been demonstrated that the incorporation of a wave breaking scheme will improve the near‐shore prediction of the PPBOUSS model …”

Section: Verification and Validation Of The Proposed Coupling Modelmentioning

confidence: 99%

“…It has been demonstrated that the incorporation of a wave breaking scheme will improve the near-shore prediction of the PPBOUSS model. 32 Using the results obtained by the PPBOUSS computation as shown in Figure 17, local computations based on the EMPS method are conducted. The coupling interface is set at x = 2.5 m (L I = 2.5 m in Figure 16) because wave breaking occurs in this area, x > 2.5 m. This seems appropriate considering the detailed wave shapes between t * = 15 and 20 shown in Figure 18.…”

Section: Solitary-wave Breaking On a Mild Slopementioning

confidence: 99%

“…Our main target is the simulation of tsunamis, and our strategy and the goals of this modeling are as follows. We adopt a domain‐wide Boussinesq‐type wave model to make the 3D region small as possible while improving the physics in the 2D region over standard shallow water equation models. We use a particle method for 3D computation to take the advantage of robustness in the moving boundary and free‐surface treatments. We model the interfaces between the 2D and 3D (2D‐3D interfaces) computations as moving interfaces in a Lagrangian fashion to get rid of particle generation and elimination around the interface. We propose a reproduction method of the nonconstant vertical velocity profile based on the results of 2D computations to achieve higher reproducibility of waves from 2D to 3D computations. We adopt the explicit moving‐particle semi‐implicit (EMPS) method as a particle method and the pressure‐Poisson Boussinesq‐type (PPBOUSS) model as a Boussinesq‐type wave model, which has nonhydrostatic components that are not considered in the shallow water equations. In the proposed coupling model, 2D computation based on the PPBOUSS model in the global domain is conducted preliminarily, and the velocity profile in the vertical direction is reproduced using the nonhydrostatic pressure components.…”

Section: Introductionmentioning

confidence: 99%

“…We adopt the explicit moving-particle semi-implicit (EMPS) method 29,30 as a particle method and the pressure-Poisson Boussinesq-type (PPBOUSS) model [31][32][33] as a Boussinesq-type wave model, which has nonhydrostatic components that are not considered in the shallow water equations. In the proposed coupling model, 2D computation based on the PPBOUSS model in the global domain is conducted preliminarily, and the velocity profile in the vertical direction is reproduced using the nonhydrostatic pressure components.…”

Section: Introductionmentioning

confidence: 99%

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Coupling methods between finite element–based Boussinesq‐type wave and particle‐based free‐surface flow models

Mitsume

Donahue

Westerink

et al. 2018

Numerical Methods in Fluids

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Summary We develop one‐way coupling methods between a Boussinesq‐type wave model based on the discontinuous Galerkin finite element method and a free‐surface flow model based on a mesh‐free particle method to strike a balance between accuracy and computational cost. In our proposed model, computation of the wave model in the global domain is conducted first, and the nonconstant velocity profiles in the vertical direction are reproduced by using its results. Computation of the free‐surface flow is performed in a local domain included within the global domain with interface boundaries that move along the reproduced velocity field in a Lagrangian fashion. To represent the moving interfaces, we used a polygon wall boundary model for mesh‐free particle methods. Verification and validation tests of our proposed model are performed, and results obtained by the model are compared with theoretical values and experimental results to show its accuracy and applicability.

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“…In this study, we use the fully nonlinear