• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.53-65
• /
• 2003

Here we present a study of small-amplitude, shallow water waves on sloping beds. The beds considered in this analysis are linear and quadratic in nature. First we start with stating the relevant governing equations and boundary conditions for the theory of water waves. Once the complete prescription of the water-wave problem is available based on some assumptions (like inviscid, irrotational flow), we normalize it by introducing a suitable set of non-dimensional variables and then we scale the variables with respect to the amplitude parameter. This helps us to characterize the various types of approximation. In the process, a summary of equations that represent different approximations of the water-wave problem is stated. All the relevant equations are presented in rectangular Cartesian coordinates. Then we derive the equations and boundary conditions for small-amplitude and shallow water waves. Two specific types of bed are considered for our calculations. One is a bed with constant slope and the other bed has a quadratic form of surface. These are solved by using separation of variables method.

• 한국방재학회:학술대회논문집
• /
• 2007.02a
• /
• pp.163-167
• /
• 2007

For numerical analysis of a tidal flow, a two-dimensional hydrodynamic model is developed by solving the nonlinear shallow-water equations. The governing equations are discretized explicitly with a finite difference leap-frog scheme and a first-order upwind scheme on adaptive hierarchical quadtree grids. The developed model is verified by applying to prediction of tidal behaviors. The calculated tidal levels are compared to available field measurements. A very reasonable agreement is observed.

• 한국방재학회:학술대회논문집
• /
• 2007.02a
• /
• pp.395-398
• /
• 2007

In this study, new dispersion-correction terms are added to leap-frog finite difference scheme for the linear shallow-water equations with the purpose of considering the dispersion effects of the linear Boussinesq equations for the propagation of tsunamis. The new model is applied to near Gadeok island in Pusan about The Central East Sea Tsunami in 1983 and The Hokkaldo Nansei Oki Earthquake Tsunami in 1993 one simulated in the study.

• 한국방재학회:학술대회논문집
• /
• 2008.02a
• /
• pp.237-240
• /
• 2008

Numerical Analysis for exchanging seawater experiment is carried out in Do-Jang fish port. The change of tidal velocity and water level is derived by the two-dimensional nonlinear shallow-water numerical model. To calculate exchange rate of seawater with the change of tidal velocity and water level, a two-dimensional numerical model is employed which governing equations are Fokker-Plank equations. The calculated exchange rates of each time are described in tables and figures.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.21 no.12
• /
• pp.1679-1689
• /
• 1997

In this paper, a precise description is given to the basic theory as well as the detailed algorithms for the numerical treatment of the method of POD (proper orthogonal decomposition). This method is then applied to analysing the numerical solutions of one-dimensional shallow-water equations to show how the method is affected by various parameters such as the sampling time, sampling numbers, and the spatial resolution for the autocorrelation function. A few curious features associated with this flow model found through the analysis are further explained and discussed.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.43 no.6
• /
• pp.749-762
• /
• 2023

A depth-integrated model with an approximate Riemann solver for flux computation of the shallow water equations was applied to hydraulic jump experiments. Due to the hydraulic jump, different flow regimes occur simultaneously in a single channel. Therefore, the Weisbach resistance coefficient, which reflects flow conditions rather than the Manning roughness coefficient that is independent of depth or flow, has been employed for flow resistance. Simulation results were in good agreement with experimental results, and it was confirmed that Manning coefficients converted from Weisbach coefficients were appropriately set in the supercritical and subcritical flow reaches, respectively. Limitations of the shallow water equations that rely on hydrostatic assumptions have been revealed in comparison with hydraulic jump experiments, highlighting the need for the introduction of a non-hydrostatic shallow-water flow model.

• Journal of Korea Water Resources Association
• /
• v.31 no.4
• /
• pp.449-457
• /
• 1998

Using a numerical model solving the shallow-water equations, unusual huge run-up heights observed in the lees of both Babi and Okushiri islands were investigated in detail. The effects of incident tsunami widths were particularly examined by adjusting the transverse length of the wave-maker in laboratory and numerical experiments. The calculated run-up heights were compared with the laboratory experimental data. It has been found that the run-up heights in the lee of a conical island are strongly dependent on the ratio of a transverse length of incident tsuanmis to a base diameter of the island. Keywords : shallow-water equations, tsunami, run-up height, conical island.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.31 no.4
• /
• pp.229-239
• /
• 2019

A model of landslides is developed using the shallow water equations to simulate time-dependent performance of landslides. The shallow water equations are derived using the (b, s) coordinate system which can be applied in both river and ocean. The finite volume scheme employing the HLL approximate Riemann solver and the total variation diminishing (TVD) limiter is applied to deal with the numerical discontinuities occurring in landslides. For dam-break water flow and debris flow, numerical results are compared with analytical solutions and experimental data and good agreements are observed. The developed landslide model is successfully applied to predict subaerial and submarine landslides. It is found that the subaerial landslide propagates faster than the submarine landslide and the speed of propagation becomes faster with steeper bottom slope and less bottom roughness.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2003.05b
• /
• pp.1063-1066
• /
• 2003

• Journal of The Korean Society of Agricultural Engineers
• /
• v.54 no.6
• /
• pp.65-76
• /
• 2012

Agricultural reservoir water quality simulation model (ARSIM-rev) was developed in this study for water quality simulation of a small and shallow agricultural reservoir with limited observed water quality data. Developed ARSIM-rev is a zero-dimensional water quality model because of little spatial differences in water quality between stations in a small and shallow agricultural reservoir. ARSIM-rev used same water quality reaction equations with WASP except for several equations, and daily based input parameters such as settling rate, release rate from sediment, and light extinction coefficient changed yearly based input parameters in ARSIM-rev. A number of pre- and post-processors were developed such as auto calibration and scenario analysis for ARSIM-rev. CE-QUAL-W2, WASP, and developed ARSIM-rev were applied to Mansu agricultural reservoir to evaluate model performance, and ARSIM-rev demonstrated similar model performance with CE-QUAL-W2 and WASP when low number of observed data was used for agricultural reservoir water quality simulation. Overall, developed ARSIM-rev was feasible for water quality simulation in a small and shallow agricultural reservoir with limited observed water quality data, and it can simulate agricultural reservoir water quality precisely enough like common water quality model such as CE-QUAL-W2 and WASP within a limited time.