Boussinesq Equation Model Research Articles

NUMERICAL CALCULATION OF SURFACE WAVES DURING A FLOOD ON THE TOYOHIRA RIVER USING ONE-DIMENSIONAL BOUSSINESQ EQUATION MODEL

Numerical simulation of a flood event is made, using a one-dimensional Boussinesq equation model. Flood generation factors and occurrence conditions are employed for model calibration. The simulated results are verified by comparison with video images of surface waves taken during the flood period. The numerical simulation is used to study the mechanism whereby the surface waves are generated. The numerical model seems to be able to accurately reproduce the water waves that occurred during flood period in 1981. The simulated results show that the surface waves grew when they came into phase with the antidunes. The simulated results confirm that the phenomenon is related to Froude number.

Comparing numerical methods for Boussinesq equation model problem

AbstractThis article applies three methods to solve a class of nonlinear differential equations. We obtain the exact solution and numerical solution of the Boussinesq equation for certain initial condition. Comparsion of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions. The numerical results demonstrate that those methods are quite accurate and readily implemented. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009

Boussinesq 방정식을 이용한 동해지진해일 수치실험 연구

Most seismic sea waves in the East Sea originate from earthquakes occurring near the Japanese west coast. While the waves propagate in the East Sea, they are deformed by refraction, diffraction and scattering. Though the Boussinesq equation is most applicable for such wave phenomena, it was not used in numerical modelling of seismic sea waves in the East Sea. To examine characteristics of seismic sea waves in the East Sea, numerical models based on the Boussinesq equation are established and used to simulate recent tsunamis. By considering Ursell parameter and Kajiura parameter, it is proved that Boussinesq equation is a proper equation for seismic sea waves in the East Sea. Two models based on the Boussinesq equation and linear wave equation are executed with the same initial conditions and grid size (<TEX>$1min{\times}1min$</TEX>), and the results are compared in various respects. The Boussinesq equation model produced better results than the linear model in respect to wave propagation and concentration of wave energy. It is also certified that the Boussinesq equation model can be used for operational purpose if it is optimized. Another Boussinesq equation model whose grid size is <TEX>$40sec{\times}30sec$</TEX> is set up to simulate the 1983 and 1993 tsunamis. As the result of simulation, new propagation charts of 2 seismic sea waves focused on the Korean east coast are proposed. Even though the 1983 and 1993 tsunamis started at different areas, the propagation paths near the Korean east coast are similar and they can be distinguished into 4 paths. Among these, total energy and propagating time of the waves passing over North Korea Plateau(NKP) and South Korea Plateau(SKP) determine wave height at the Korean east coast. In case of the 1993 tsunami, the wave passing over NKP has more energy than the wave over SKP. In case of the 1983 tsunami, the huge energy of the wave passing over SKP brought about great maximum wave heights at Mukho and Imwon. The Boussinesq equation model established in this study is more useful for simulation of seismic sea waves near the Korean east coast than it is the Japanese coast. To improve understanding of seismic sea waves in shallow water, a coastal area model based on the Boussinesq equation is also required.

A BASIC STUDY OF A HYBRID CODE OF PARTICLE METHOD AND BOUSSINESQ MODEL

Because the Boussinesq equation is governing equation of an ideal fluid, a sea bottom friction and a wave breaking, which are the phenomena related to energy dispersion, cannot be handled precisely. A particle method on the basis of the Navier-Stokes equation is effective for numerical analysis of wave breaking with a splash. In this study, an Euler-Lagrange coupling for boundary interface between the Boussinesq equation model and the particle method are proposed. As basic studies to build a multi-purpose numerical wave basin, a wave motion in a wave flume is simulated by the present coupling model. Agreement of predicted water surface profiles by both models in the vicinity of a boundary interface is confirmed.

Justification of the nonlinear Schroedinger equation for a resonant Boussinesq model

The nonlinear Schrodinger equation formally describes slow modulations in time and space of an underlying spatially and temporarily oscillating wave packet. It is the purpose of this paper to prove estimates between the formal approximation, obtained via the nonlinear Schrodinger equation, and true solutions of the original system. The method developed in an earlier paper in case of non-trivial quadratic resonances is improved to cover also the additional problem of a trivial resonance at the wavenumber k = 0 as it occurs for the water wave problem. For a Boussinesq equation, a formal and phenomenological model for surface water waves subject to gravity and surface tension, we establish the approximation property in case the formal NLS approximation is stable in the system for the three wave interaction associated to the resonance. Although we restrict ourselves to a Boussinesq equation we believe that the result is also true for the full water wave problem.

Parallel computation of a highly nonlinear Boussinesq equation model through domain decomposition

AbstractImplementations of the Boussinesq wave model to calculate free surface wave evolution in large basins are, in general, computationally very expensive, requiring huge amounts of CPU time and memory. For large scale problems, it is either not affordable or practical to run on a single PC. To facilitate such extensive computations, a parallel Boussinesq wave model is developed using the domain decomposition technique in conjunction with the message passing interface (MPI). The published and well‐tested numerical scheme used by the serial model, a high‐order finite difference method, is identical to that employed in the parallel model. Parallelization of the tridiagonal matrix systems included in the serial scheme is the most challenging aspect of the work, and is accomplished using a parallel matrix solver combined with an efficient data transfer scheme. Numerical tests on a distributed‐memory super‐computer show that the performance of the current parallel model in simulating wave evolution is very satisfactory. A linear speedup is gained as the number of processors increases. These tests showed that the CPU time efficiency of the model is about 75–90%. Copyright © 2005 John Wiley &amp; Sons, Ltd.

THE DIFFERENCE OF BEACH PROCESS ACCORDING TO OFFHSORE DISTANCE OF ARTIFICIAL ISLAND

In recent years, large scale structures have been built on offshore for utilization of coastal zone as offshore airport and marine terminals. Those big scale structures, however, may act as significant barriers against wave and severe beach erosion may take place on the coast.The present study deals nearshore topography change affected by construction of an offshore structure with different distance from the shore. The series of three dimensional movable bed experiments have been examined in detail. Moreover, in order to make clear the relation of nearshore currents and local erosions behind offshore structure, the nearshore currents are calculated by boussinesq equation model with the same scale condition of the experiments.

拡張型Boussinesq方程式の沿岸波浪場・海浜流場への適用性に関する研究

The modified Boussinesq equation model which was proposed by Madsen et al was applied for wave motion and nearshore current fields and its applicability was discussed. Numerical simulations of the circular reef, half-unlimited breakwater and beach topographies with an offshore breakwater were performed The accuracy of this model was verified thorough comparison with laboratory experiments and previous theory. Furthermore, numerical analysis of wave transformation for typhoon No.9918 in the vicinity of the Kumamoto New Port were carried out Results demonstrated that wave height increased in the estuary of Shirakawa river and the velocity scale of nearshore currents was as large as that of tidal currents.

EVALUATION OF SUITABILITY FOR NON-LINEAR DISPERSIVE WAVE MODEL AND A NUMERICAL METHOD BY CONNECTION WITHLINEAR WAVE MODEL

A Boussinesq equation model was connected with parabolic mild-slope equation model in order to relieve their burden of calculation. The method of connection was that first, the wave motions, refraction, shoaling deformation and diffraction in relatively deep water were calculated based on the parabolic mild-slope equation, and then the wave motions in shallow water were calculated by the Boussinesq equation. It was demonstrated that the connection of two models was efficient for a wide area calculation in practical use.Moreover, in order to verify the Boussinesq equation model for the calculation of wave motion around a offshore barrier in shallow water, laboratory experiments were made with offshore detached breakwater. The wave height and depth-averaged velocity distributions were measured in detail and compared with results of numerical simulation.