• The Journal of the Acoustical Society of Korea
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• v.18 no.4
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• pp.71-77
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• 1999

Exact forward modeling of acoustic propagation is crucial in MFP such as inverse problems and various other acoustic applications. As acoustic propagation in shallow water environments become important, range dependent modeling has to be considered of which PE method is considered as one of the most accurate and relatively fast. In this paper higher order numerical rode employing the PE method is developed. To approximate the depth directional operator, Galerkin's method is used with partial collocation to lessen necessary calculations. Linearization of tile depth directional operator is achieved via expansion into a multiplication form of (equation omitted) approximation. To approximate the range directional equation, Crank-Nicolson's method is used. Final1y, numerical self stater is employed. Numerical tests are performed for various occan environment scenarios. The results of these tests are compared to exact solutions, OASES and RAM results.

• Korean Journal of Soil Science and Fertilizer
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• v.28 no.3
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• pp.233-240
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• 1995

Fick's diffusion equation was transformed into algebraic subsidiary equation with its initial and boundary conditions through Laplace transformation, and the subsidiary equation was transformed back on the basis of Burington's table of inverse transformations so that it became the solution of Fick's equation. The initial and boundary condition was for upward diffusion of salts into flooding water of constant depth from uniform polder soil of infinite depth containing constant concentration of salt. The derived solution was tested through comparison for its conformability with other solutions of simpler initial and boundary conditions. The importance of shallow transplanting of rice seedlings and salt removing by growing rice was mentioned on the basis of very slow desalting rate by diffusion calculated from the derived solutions.

• Journal of Navigation and Port Research
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• v.27 no.5
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• pp.527-537
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• 2003

The characteristics of ship induced waves caused by navigation become widely different from both ship's speed and water depth condition. The ship induced waves specially generated in coastwise routes frequently give rise to call unforeseen danger for swimmers and small boats as well as shoreline erosion or sea wall destruction in coastal zones. The main concern of ship induced wave study until now is either how to reduce ship resistance or how to manoeuvre the ship safely under a constant water depth in the view point of shipbuilding engineers. Moreover, due to the trends for appearance of the high speed ships at the shallow coastal water, we are confronted with the danger of damages from those ship induced waves. Therefore, it is necessary to examine the development of ship induced waves and the influence of their deformation effects according to its propagation ray. In present study, in order to predict the development of the ship induced waves and their propagation under the conditions of complicate and variable shallow water depth with varying ship's speed, we constructed a computer model using Boussinesq equation with a fixed coordinate system and verified the model results by comparison with experimental results. Additionally, the model was applied under the variable water depth based on actual passage and we then confirmed the importance of the variable water depth consideration.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.18 no.4
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• pp.308-320
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• 2006

An analytic solution to the mild-slope equation is derived for waves propagating over an axi-symmetric pit. The water depth inside the pit varies in proportion to a power of radial distance from the pit center. The governing equation is transformed into ordinary differential equations by using separation of variables, and the coefficients of the equations are transformed into explicit forms by using Hunt's (1979) approximate solution. Finally, by using the Frobenius series, the analytic solution is derived. Due to the feature of Hunt's equation, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth water. The validity of the analytic solution is demonstrated by comparison with numerical solutions. The analytic solution is also used to examine the effects of pit geometry and relative depth on wave transformation.

• Journal of Korea Water Resources Association
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• v.44 no.3
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• pp.249-262
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• 2011

In this study, in order to reduce the numerical oscillation due to the unbalance between source and flux terms as the HLLC scheme is applied to the flow analysis on the irregular bed topography, a unstructured finite volume model based on the well-balanced HLLC scheme and the shallow water equations is developed and applied to problems of dam-break waves. The well-balanced HLLC scheme considers directly the gradient of bed topography as the flux terms is calculated. This scheme provides the good numerical balance between the source and flux terms in the case of the application to the steady-state transcritical flow. To verify the numerical model developed in this study, it is applied to three cases of hydraulic model experiments and a field case study of Mapasset dam failure (France). As a result of the verification, the predicted numerical results agree relatively well with available laboratory and field measurements. The model provides slightly more accurate results compared with the existing models.

• Water Engineering Research
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• v.6 no.1
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• pp.17-30
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• 2005

The bed evolution of the stretch of the River Rhine between km-812.5 and km-821.5 is characterised by general bed degradation as a result of the river training works and dredging activities of the last two centuries. The degradation of the river bed affects the water levels, and so the navigation conditions. To combat the erosion of the river bed with the aim to keep up the shipping traffic and to avoid the ecological system damages due to water level reductions, sand-gravel-mixtures were added to the river (so called artificial grain feeding activities). This paper presents the results of an application of a graded sediment transport model in order to study morpholodynamical characteristics due to artificial grain feeding activities in the river stretch. The finite element code TELEMAC2D was used for flow calculation by solving the 2D shallow water equation on non-structured grids. The sediment transport module SISYPHE has been developed for graded sediment transport using a multiple layer model. The needs to apply such graded sediment transport approaches to study morphological processes in the domain are discussed. The calculations have been carried out for the case of middle water flow and different size-fraction distributions. The results show that the grain feeding process could be well simulated by the model.

• Journal of Ocean Engineering and Technology
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• v.32 no.6
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• pp.474-484
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• 2018

In this study, a new numerical modeling system was proposed to predict oil spills, which increasingly occur at sea as a result of abnormal weather conditions such as global warming. The hydrodynamic conditions such as the flow velocity needed to calculate oil dispersion were estimated using a three dimensional hydrodynamic model based on the Navier-Stokes equation, which considered all of the physical variations in the vertical direction. This improved the accuracy compared to those estimated by the conventional shallow water equation. The advection-diffusion model for the spilled oil was combined with the hydrodynamic model to predict the movement and fate of the oil. The effects of absorption, weathering, and wind were also considered in the calculation process. The combined model developed in this study was then applied to various test cases to identify the characteristics of oil dispersion over time. It is expected that the developed model will help to establish initial response and disaster prevention plans in the event of a nearshore oil spill.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.4B
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• pp.333-341
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• 2011

This study analyzed the propagation of dam-break waves in an area directly downstream of a dam by using 3D numerical modeling with RANS as the governing equation. In this area, the flow of the waves has three dimensional characteristics due to the instantaneous dam break. In particular, the dam-break flows are characterized by a highly unsteady and discontinuous flow, a mixture of the sharp flood waves and their reflected waves, a mixture of subcritical and supercritical flow, and propagation in a dry and movable bed. 2D numerical modeling, in which the governing equation is the shallow water equation, was regarded as restricted in terms of dealing with the sharp fluctuation of the water level at the dam-breaking point and water level vibration at the reservoir. However, in this 30 analysis of flood wave propagation due to partial dam breaking and dam-break in channels with $90^{\circ}$ bend, those phenomena were properly simulated. In addition, the flood wave and bed profiles in a movable bed with a flat/upward/downward bed step, which represents channel aggradation or degradation, was also successfully simulated.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.4
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• pp.389-396
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• 1994

We analyze existing time-dependent mild-slope equations, which were developed by Smith and Sprinks (1975) (or, equivalently, Radder and Dingemans (1985)) and Kubo et al. (1992), in terms of the dispersion relation and energy transport. One-dimensionally in the horizontal direction, we compare the modulation of wave amplitudes for the time-dependent mild-slope equations against the linear Scrodinger equation. In view of the dispersion relation and modulation of wave amplitudes, Smith and Sprinks' model is more accurate in shallower water (kh$\leq$0.2$\pi$) and satisfies the linear Scrodinger equation in very shallow water (kh>0.2$\pi$) and satisfies the linear Scrodinger equation at a point of intermediate water depth (kh=0.3$\pi$). In view of the energy transport, Kubo et al.'s model is more accurate but yields singular solutions at some higher frequency range.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.3
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• pp.212-220
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• 1993

A numerical model for the transformation of irregular waves in a coastal area is developed, which takes account of shoaling, refraction, diffraction, bottom friction and wave breaking. The governing equations are the usual energy conservation equation and kinematic conservation equations, but to consider the diffraction effects additional terms are included in the usual kinematic conservation or wave number equations. A linear superposition technique is used to represent the spectral formation. and an explicit formula is developed for the estimation of friction factor of irregular waves. A breaking criterion of component waves, which is the modified form of the Kitaigorodskii saturation relation, is employed to restrict the growth of shoaling waves in very shallow waters. The model was applied to a laboratory test and satisfactory agreement was obtained between the computation and measurement.