• 한국방재학회:학술대회논문집
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• 2007.02a
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• pp.181-185
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• 2007

A free-surface correction(FSC) method is presented to solve the 3-D shallow water equations. Using the mode splitting process, FSC method can simulate shallow water flows under the hydrostatic assumption. For the hydrostatic pressure calculation, the momentum equations are firstly discretized using a semi-implicit scheme over the vertical direction leading to the tri-diagonal matrix systems. A semi-implicit scheme has been adopted to reduce the numerical instability caused by relatively small vertical length scale compare to horizontal one. and, as the free surface correction step the final horizontal velocity fields are corrected after the final surface elevations are obtained. Finally, the vertical final velocity fields can be calculated from the continuity equation. The numerical model is applied to the calculation of the simulation of flow fields in a rectangular open channel with the tidal influence. The comparisons with the analytical solutions show overall good agreements between the numerical results and analytical solutions.

• Journal of Korea Water Resources Association
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• v.38 no.6 s.155
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• pp.429-438
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• 2005

In this study, a couple of ordinary differential equations which can describe random waves are derived from the Boussinesq equations. Incident random waves are generated by using the TMA(TEXEL storm, MARSEN, ARSLOE) shallow-water spectrum. The governing equations are integrated with the 4-th order Runge-Kutta method. By using newly derived wave equations, nonlinear energy interaction of propagating waves in constant depth is studied. The characteristics of random waves propagate over a sinusoidally varying topography lying on a sloping beach are also investigated numerically. Transmission and reflection of random waves are considerably affected by nonlinearity.

• Journal of the Earthquake Engineering Society of Korea
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• v.21 no.1
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• pp.1-9
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• 2017

The scale of disaster and damage witnessed in the 2004 Indian Ocean Tsunami and the 2011 Great East Japan Tsunami has motivated researchers in developing foolproof disaster mitigation techniques for safety of coastal communities. This study focuses on developing tsunami hazard map by numerical modeling at Imwon Port to minimize losses of human beings and property damage when a real tsunami event occurs. A hazard map is developed based on inundation maps obtained by numerical modeling of 3 past and 11 virtual tsunami cases. The linear shallow-water equations with manipulation of frequency dispersion and the non-linear shallow-water equations are employed to obtain inundation maps. The inundation map gives the maximum extent of expected flooded area and corresponding inundation depths which helps in identifying vulnerable areas for unexpected tsunami attacks. The information can be used for planning and developing safety zones and evacuation structures to minimize damage in case of real tsunami events.

• Journal of Korea Water Resources Association
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• v.46 no.2
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• pp.139-153
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• 2013

For analyzing shallow-water flows over the uneven bottom, the HLLL scheme and the divergence form for bed slope source term (DFB) technique, respectively were applied to the flux gradient and the bottom gradient source terms in a finite-volume model for the shallow water equations. And also the model incorporated the volume/free-surface relationship (VFR) to consider the partially submerged cells (PSC). It was identified that a simpler version of the weighted surface-depth gradient method in the MUSCL was equivalent to the original one in the accuracy for 1D steady flows. It was verified that the flux gradient term and the bottom gradient source term were well-balanced exactly by the VFR for the 1D PSC. The VFR for the triangular PSC settled the problem which the governing equations were not well-balanced by the DFB technique for the 2D PSC. There were good agreements in simulations and experiments for 2D dam-break flows over a triangular sill and a round bump. In addition, the partial dam-break flow was successfully simulated for flooding of roughnesses in an irregular bottom as well as a sloping one. Therefore, this model is expected to be applied to the real river with uneven topography.

• Journal of Korea Water Resources Association
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• v.37 no.10
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• pp.845-855
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• 2004

The propagation and associated run-up process of nearshore tsunamis in the vicinity of shorelines have been analyzed by using a two-dimensional numerical model. The governing equations of the model are the nonlinear shallow-water equations. They are discretized explicitly by using a finite volume method and the numerical fluxes are reconstructed with a HLLC approximate Riemann solver and weighted averaged flux method. The model is applied to two problems; The first problem deals with water surface oscillations, while the second one simulates the propagation and subsequent run-up process of nearshore tsunamis. Predicted results have been compared to available analytical solutions and laboratory measurements. A very good agreement has been observed.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.32 no.6
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• pp.569-574
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• 2020

Though the discontinuous Galerkin (DG) method has been developed and applied to shallow water equations mainly in explicit schemes, they have been criticized for the limitation in treatment of bottom friction terms and severe CFL conditions. In this study, an implicit scheme is devised and applied to some representative benchmark problems. The linear triangular elements were employed and the Roe numerical fluxes were adopted for convective fluxes. To preserve TVD property, the slope limiter was employed. As the case studies, the model is applied to the flow around the cylinders and the dam-break flow. Then, the results are compared with the experimental and numerical data of previous studies and good agreements were observed.

• Journal of the Society of Naval Architects of Korea
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• v.42 no.4 s.142
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• pp.315-321
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• 2005

The effect of water depth on the wave making resistance performance is great where Froude number based on the water depth is close to one. The increase of wave making resistance due to the shallow water effect is evaluated by a numerical analysis in the present study. Three-dimensional Navier-Stokes and continuity equations are employed for the present study and the equations are discretized by finite difference method. The interface between water and air is determined by the level set method. In order to validate the numerical method, the change of resistance performance for Wigley hull according to the water depth is evaluated and the computed resistance coefficient is compared with measured one. The present numerical method is applied for the simulation of wave phenomena around a Ro-Pax hull form and the computed results are discussed in the resistance performance point of view.

• Journal of Korea Water Resources Association
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• v.56 no.12
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• pp.939-953
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• 2023

Shallow water equations (SWE) serve as fundamental equations governing the movement of the water. Traditional numerical approaches for solving these equations generally face various challenges, such as sensitivity to mesh generation, and numerical oscillation, or become more computationally unstable around shock and discontinuities regions. In this study, we present a novel approach that leverages the power of physics-informed neural networks (PINNs) to approximate the solution of the SWE. PINNs integrate physical law directly into the neural network architecture, enabling the accurate approximation of solutions to the SWE. We provide a comprehensive methodology for formulating the SWE within the PINNs framework, encompassing network architecture, training strategy, and data generation techniques. Through the results obtained from experiments, we found that PINNs could be an accurate output solution of SWE when its results were compared with the analytical method. In addition, PINNs also present better performance over the Artificial Neural Network. This study highlights the transformative potential of PINNs in revolutionizing water resources research, offering a new paradigm for accurate and efficient solutions to the SVE.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.25 no.5
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• pp.285-290
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• 2013

Both full linear and shallow water edge waves are compared to get a better understanding of edge wave behavior. By using method of separation of variables, we are able to get solution of full linear edge wave presented by Ursell (1952) without derivation. The shallow water edge waves show dispersive features despite being derived from shallow water equations. When bottom slope is mild enough, shallow water edge wave tends to linear edge wave and has some advantages of manipulation. Solution of edge wave generated by a moving landslide of Gaussian shape is constructed by an expansion of shallow water normal modes. Numerical results are presented and discussed on their main features.

• Proceedings of the Korea Water Resources Association Conference
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• 2001.05b
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• pp.949-954
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• 2001