• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.181-192
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• 2023

This work deals with the numerical modeling of dam-break flow over erodible bed. The mathematical model consists of the shallow water equations, the transport diffusion and the bed morphology change equations. The system is solved by central upwind scheme. The obtained results of the resolution of dam-beak problem is presented in order to show the performance of the numerical scheme. Also a comparison of central upwind and Roe schemes is presented.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2008.09a
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• pp.204-207
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• 2008

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2008.09b
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• pp.204-207
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• 2008

• Proceedings of the Korea Water Resources Association Conference
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• 2023.05a
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• pp.171-171
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• 2023

This study investigates the capability of Physics-Informed Neural Networks (PINNs) for solving the solution of partial differential equations. Particularly, the 1D Saint-Venant Equations (SVEs) were considered, which describe the movement of water in a domain with shallow depth compared to its horizontal extent, and are widely adopted in hydrodynamics, river, and coastal engineering. The core contribution of this work is to combine the robustness of neural networks with the physical constraints of the SVEs. The PINNs method utilized a neural network to approximate the solutions of SVEs, while also enforcing the underlying physical principles of the equations. This allows for a more effective and reliable solution, especially in areas with complex geometry and varying bathymetry. To validate the robustness of the PINNs method, numerical experiments were conducted on several benchmark problems. The results show that the PINNs could be achieved high accuracy when compared with the solution from the numerical solution. Overall, this study demonstrates the potential of using PINNs and highlights the benefits of integrating neural network and physics information for improved efficiency and accuracy in solving SVEs.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.5
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• pp.1383-1393
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• 2014

Recently, with rapid improvement in computer hardware and theoretical development in the field of computational fluid dynamics, high-order accurate schemes also have been applied in the realm of computational hydraulics. In this study, numerical solutions of 1D shallow water equations are presented with TVD Runge-Kutta discontinuous Galerkin (RKDG) finite element method. The transcritical flows such as dam-break flows due to instant dam failure and transcritical flow with bottom elevation change were studied. As a formulation of approximate Riemann solver, the local Lax-Friedrichs (LLF), Roe, HLL flux schemes were employed and MUSCL slope limiter was used to eliminate unnecessary numerical oscillations. The developed model was applied to 1D dam break and transcritical flow. The results were compared to the exact solutions and experimental data.

• The Journal of the Korea Contents Association
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• v.13 no.3
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• pp.428-434
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• 2013

With the increase of the frequency in large-scale floods and natural disasters, the demands for highly accurate numerical river models are also rapidly growing. Generally, flows in rivers are modeled with previously developed and well-established numerical models based on shallow water equations. However, the so-far-developed models reveal a lot of limitations in the analysis of discontinuous flow or flow which needs accurate modeling. In this study, the numerical shallow water model based on the discontinuous Galerkin method was applied to the simulation of one-dimensional transcritical flow, including dam break flows and a flow over a hump. The favorable agreement was observed between numerical solutions and analytical solutions.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.05b
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• pp.1174-1178
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• 2005

In this study, flood inundations have been simulated by using the numerical model FLUMEN solving the shallow-water equations with a finite volume method. Before applying to a real problem, the numerical model is first applied to simplified problems. Obtained numerical results are verified by comparing to available analytical solutions and laboratory measurements. Reasonable agreements are observed. The model is then applied to a simulation of flood events with real geometries. The results of the present study provide basic informations for a flood inundation map.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.221-223
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• 2003

The tidal bores of the Qiantang River on the East coast of China are simulated numerically based on the shallow water theory. The governing equations, which were traditionally formulated using water depth, are formulated in terms of water surface level, and the fractional-step method is applied in conjunction with a Godunov-type scheme. In addition, the source terms due to bottom gradient are discretized centrally to exactly balance the flux terms. Our numerical simulation produces tidal bores in excellent agreement with field measurements.

• Journal of Korea Water Resources Association
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• v.44 no.10
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• pp.819-830
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• 2011

The multi-slope MUSCL, proposed by T. Buffard and S. Clain, determines slopes of conserved variables at each edge of a cell in the linear reconstructions of data. In this study, the second order accurate numerical model was developed according to the multi-slope MUSCL to solve the shallow water equations on the unstructured grids. The HLLL scheme of approximate Riemann solvers was used to calculate fluxes. For the review of the applicability of the developed model, the results of the model were compared to the 'isolated building test' and the 'model city flooding experiment' conducted as part of the IMPACT (Investigation of extreMe flood Processes And unCerTainty) project in Europe. There were limitations to predict abrupt rising of water depths by the resistance of model buildings and water depths at the specific locations among the buildings. But they were identified as the same problems also revealed in results of the other models to the same experiment. On the more refined meshes to the 'model city flooding experiment' simulated results showed good agreement with measurements. It was verified that the developed model simulated well the complex phenomena such as a dam-break problem and the urban inundation by flash floods.

• Journal of Industrial Technology
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• v.20 no.A
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• pp.139-148
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• 2000

A numerical model is represented to calculate the wave fields such as the reflected waves, the transmitted waves, and depth averaged velocities over submerged breakwaters for the normally incident wave trains of nonlinear monochromatic wave. The numerical model is correctly formulated by using both the finite amplitude shallow water equations with the effects of bottom friction and the explicit dissipative Lax-Wendroff finite difference scheme, also satisfactorily verified by comparison with the other results. The behaviors of reflected and transmitted waves with respect to geometric parameters of submerged breakwater such as the slope, crest depth, and crest width are numerically analyzed in this study. In particular, the reflection and transmission coefficients are quantitatively calculated as the function of geometric parameter of submerged breakwater. It is found that the crest depth among parameters related to practical design may be the most important parameter in designing the submerged breakwater. Therefore, the effective and economic performances of submerged breakwater should be depended on the determination of optimal crest depth.