Linear and nonlinear wave diffraction using the nonlinear time dependent mild slope equations

Abohadima, Samir; Isobe, Masahiko

doi:10.1016/s0378-3839(99)00020-4

Cited by 9 publications

(4 citation statements)

References 12 publications

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“…Introducing a slow coordinate for the time variable, Li [12] obtained a ÿrst-order wave evolution equation with the use of the perturbation method. Recently, Abohadima and Isobe [13] extended Madsen and Larsen's [11] approach to the non-linear wave di raction computation. The deÿciency of such approach is that a pre-step of equation splitting is always needed that introduces the artiÿcial ux and therefore requires the additional e ort of solving it.…”

Section: Introductionmentioning

confidence: 99%

A compact numerical algorithm for solving the time‐dependent mild slope equation

Lin

2004

Numerical Methods in Fluids

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SUMMARYThe mild slope equation has been widely used to describe combined wave refraction and di raction. In this study, a new numerical algorithm is developed to solve the time-dependent mild slope equation in a second-order hyperbolic form. The numerical algorithm is based on a compact and explicit ÿnite di erence method that is second-order accurate in both time and space. The algorithm has the similar structure to the leap-frog method but is constructed on three time levels for the second-order time derivative term. The numerical model has the capability of simulating transient wave motion by correctly predicting the speed of wave energy propagation, which is important for the real-time forecast of the arrival time of storm waves generated in the far ÿeld. The model is validated against analytical solution for wave shoaling and experimental data for combined wave refraction and di raction over a submerged elliptic shoal on a slope (Coastal Eng. 1982; 6:255). Lastly, the realistic scale Homma's island (Geophys. Mag. 1950; 21:199) is studied with the use of various wave periods of T = 720 s, T = 120 s, and T = 24 s. These wave periods correspond to long, intermediate, and short waves for the given topography, respectively. Comparisons are made between numerical results and existing analytical solutions in terms of the wave ampliÿcation around the island, which serves as the indicator for the potential wave runup. Excellent agreements are obtained. The model runs on a PC (Pentium IV 1:8GHz) and the computer capacity allows the computation of a mesh system up to 3000 × 3000, which is equivalent to about 150 × 150 waves or a large area of 540 km × 540 km for a wave train with the period of T = 60 s.

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Section: Introductionmentioning

confidence: 99%

A compact numerical algorithm for solving the time‐dependent mild slope equation

Lin

2004

Numerical Methods in Fluids

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“…Finally, it can be seen that the non-linear wave height contours are more widely spread in the lateral direction compared with the linear ones, suggesting that inclusion of amplitude dispersion accentuates diffraction. This is in agreement with the findings of Abohadima and Isobe (1999) who concluded that generally inclusion of non-linearity increases the lateral energy spreading. The non-linear amplitude dispersion inclusion is further and more extensively verified in Section 5.7.…”

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confidence: 93%

“…The extended Boussinesq equations (e.g. Battjes and Beji, 1991) or the non-linear mild-slope equations (Kaihatu and Kirby, 1995;Abohadima and Isobe, 1999;etc) could be used for that purpose. However, the accurate prediction of non-linear surface profiles is not the primary interest of this study and hence was not pursued.…”

Section: Comments On the Treatment Of Wave Breakingmentioning

confidence: 99%

Physical and numerical modelling of irregular wave propagation in coastal waters

Μπόκαρης¹

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The present research work concentrates on the development and verification of a numerical model capable of simulating wave transformation in coastal waters over uneven, two-dimensional bathymetry.The so-called mild-slope equation, which includes the combined effects of shoaling, refraction, diffraction and reflection is adopted as the basis of the numerical model. Solutions are obtained on unstructured triangular meshes using a Godunov-type, secondorder, upwind, cell-centred finite volume formulation, whereby the numerical fluxes are computed using Roe's flux function. Appropriate conditions for driving, transparent and fully reflecting boundaries are derived. The unknown variables are updated in time through an accurate implicit scheme. It is the first time that such a solution methodology is used for the solution of the mild-slope equation.Apart from monochromatic waves, irregular waves which are those actually encountered in nature are also taken into account. Furthermore, the processes of non-linear wave phase speed distortion due to amplitude dispersion as well as energy dissipation due to bottom friction, whose effects are intensified in shallow waters, are also incorporated in I would like to express my gratitude to my supervisor Dr. K. Anastasiou for his consistent and truly inspired guidance. His support and encouragement throughout the course of this research work are highly appreciated.

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“…The design of the model of wave propagation and penetration into the harbour basin has been performed according to the placement of the breakwater arms and the probable and effective directions of the waves. To increase the speed of the model execution, the areas where the wave characteristics and the wave diffraction pattern are not needed are defined in [7,[16][17][18][19][20]. In this study, to increase the capacity of Genaveh port, which is facing a number of problems, research was done to minimize the obstacles to the development of the port.…”

Section: Introductionmentioning

confidence: 99%

Investigating the Harbour Basin Tranquillity in the Genaveh Port Development Plan

Sharif

Gorbanpour

Ghassemi

et al. 2023

Polish Maritime Research

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The Genaveh commercial port was placed on the agenda of the Iranian PMO (ports and maritime organization) to consider economic, commercial and residential development in Bushehr province and specifically in Genaveh city. In order to increase the water capacity of the port, it is necessary to build a new harbour basin for exploitation and commercial purposes at a depth of 5 to 6 meters by extending the existing jetties arms in front of the port. This research aims to investigate the harbour basin’s tranquillity for providing vessels with safe berthing. For this purpose, three modules, namely the flow model (FM), spectral wave (SW) and Boussinesq waves model (BW) from the MIKE 21 software package, were utilized. According to the monitoring data, which is provided by the Iranian PMO, the harbour basin’s tranquillity based on the prevailing wave directions was investigated. Based on the diffraction graph in the harbour basin, the results showed that, according to the percentage of permissible diffraction recommended by different valid regulations, there is a need to modify the geometry of the breakwater arms to increase the harbour basin’s tranquillity at the port in the development plan.

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Linear and nonlinear wave diffraction using the nonlinear time dependent mild slope equations

Cited by 9 publications

References 12 publications

A compact numerical algorithm for solving the time‐dependent mild slope equation

A compact numerical algorithm for solving the time‐dependent mild slope equation

Physical and numerical modelling of irregular wave propagation in coastal waters

Investigating the Harbour Basin Tranquillity in the Genaveh Port Development Plan

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