• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.470-474
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• 2016

Madsen et al. (2002)이 제안한 일차원 고차 Boussinesq 방정식에 대하여 불연속갤러킨 유한요소법(Discontinuous Galerkin Finite Element Method)을 적용하였다. 연속적인 Boussinesq 방정식에서 각 요소경계에 불연속을 허용할 수 있도록 공간차분하고, 시간방향으로 4차 Runge-Kutta 시간적분법, 각 요소사이에는 Lax-Friedrichs 수치흐름률을 사용하였다. 계산영역의 양쪽에 불필요한 파랑의 반사를 억제하도록 흡수층을 설치하였으며, 영역 내부에서 조파할 수 있도록 하였다. Luth et al.(1994)의 수중잠제 실험에 적용하여 관측값과 잘 일치함을 확인하였다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.2
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• pp.87-95
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• 2018

This paper introduces a new explicit spectral element method for the simulation of SH-waves in semi-infinite domains. To simulate the wave motion in unbounded domains, it is necessary to reduce the infinite extent to a finite computational domain of interest. To prevent the wave reflection from the trunctated boundaries, perfectly matched layer(PML) wave-absorbing boundary is introduced. The forward problem for simulating SH-waves in PML-truncated domains can be formulated as second-order PDEs. The second-order semi-discrete form of the governing PDEs is constructed by using a mixed spectral elements with Legendre-gauss-Lobatto quadrature method, which results in a diagonalized mass matrix. Then the second-order semi-discrete form is transformed to a first-order, whose solutions are calculated by the fourth-order Runge-Kutta method. Numerical examples showed that solutions of SH-wave in the two-dimensional analysis domain resulted in stable and accurate, and reflections from truncated boundaries could be reduced by using PML boundaries. Elastic wave propagation analysis using explicit time integration method may be apt for solving larger domain problems such as three-dimensional elastic wave problem more efficiently.

• Membrane Journal
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• v.17 no.4
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• pp.352-358
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• 2007

A nonporous hollow fiber membrane contactor was used to control the concentration of oxygen dissolved in an aqueous solution, which was predicted along the hollow fiber membrane using a computer simulation. The governing ordinary differential equations were derived for the occurrent flows of the feed aqueous solution and the feed gas mixture in a membrane contactor and they were numerically solved using the 5th Runge-Kutta-Verner method with a personal computer, where the program was coded utilizing a software of the Compaq Visual Fortran 6.6. It is found that the concentration of oxygen dissolved in water increases from 30 to 64 ppm as the length of the hollow fiber increases from 0.4 to 1.2 m when the membrane of fibers are equal to be 16,000; the flow rate of the feed gas is kept to be 0.536 mol/sec; its pressure is maintained to be 486 kPa; the flow rate of the water is 16.69 mol/sec. As the flow rate of the water increases from 9.26 to 26.85 mol/sec, the concentration of oxygen decreases from 40 to 20 ppm with the constant fiber length of 0.4 m. Finally, it is observed that the concentration of oxygen increases from 33 to 69 ppm as the pressure of the feed gas increases from 298 to 847 kPa.

• Journal of Korea Water Resources Association
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• v.41 no.3
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• pp.243-249
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• 2008

Continuous stirred tank reactor(CSTR) model which can be applied to control and management of the surface flow wetland is developed to simulate the water quality in this research. The model solution is obtained from the optimization model using the least-squares and 4th-order Runge-Kutta methods. The model is applied to simulate BOD and TSS in the wetland database of U.S. EPA, in which the hydraulic and water quality data are enough and the number of pond is just one for simple analysis of running results. The model is tested in two different cases, one constant volume case and another constant volume and flow rate case considering only reaction term, mass flux term and both reaction and mass flux terms respectively. It is found that the model simulates the real water quality very well with both reaction and mass flux terms rather than only reaction term and the settling velocity of TSS becomes $0.3{\sim}0.4\;m/d$. The model can be applied in wetlands treatment efficiently.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.1
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• pp.38-52
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• 1991

In this paper, a semi-Lagrangian method is used to solve the nonlinear hydrodynamics of a three-dimensional body beneath the free surface in the time domain. The boundary value problem is solved by using the boundary integral method. The geometries of the body and the free surface are represented by the curved panels. The surfaces are discretized into the small surface elements using a bi-cubic B-spline algorithm. The boundary values of $\phi$ and $\frac{\partial{\phi}}{\partial{n}}$ are assumed to be bilinear on the subdivided surface. The singular part proportional to $\frac{1}{R}$ are subtracted off and are integrated analytically in the calculation of the induced potential by singularities. The far field flow away from the body is represented by a dipole at the origin of the coordinate system. The Runge-Kutta 4-th order algorithm is employed in the time stepping scheme. The three-dimensional form of the integral equation and the boundary conditions for the time derivative of the potential Is derived. By using these formulas, the free surface shape and the equations of motion are calculated simultaneously. The free surface shape and fille forces acting on a body oscillating sinusoidally with large amplitude are calculated and compared with published results. Nonlinear effects on a body near the free surface are investigated.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.11
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• pp.2090-2097
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• 1992

In this paper, fluttering behavior of mechanical monloleaflet heart valve prosthesis was analyzed taking into consideration of the impact between the valve occluder and the stopper. The motion of valve occluder was modeled as a rotating system, and equations were derived by employing the moment equilibrium conditions. Lift force, drag force, gravity and buoyancy were considered as external forces acting on the valve occluder. The 4th order Runge-Kutta method was used to solve the equations. The results demonstrated that the occluder reaches steady eguilibrium position only after damped vibration. The mean damping ratio is in the range of 0.197-0.301. Fluttering frequency does not have any specific value, but varies as a function of time. It is in the range of 11-84Hz. Valve opening appears to be affected by the orientation of the valve relative to gravitational forces.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.4
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• pp.413-420
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• 1994

Dynamics of the river plume is a very complicated non-linear problem with the free boundary changing in time and space. Mixing with the ambient water through the boundary makes the problem more complicated. In this paper we reduced 3-dimensional problem into 1-dimensional one by using the integral analysis method. Basic equations have been integrated over the lateral and vertical variations. For these integrations we adopted the well-established assumption that the flow-axis component of plume velocity and the density difference of the plume with the ambient water have Gaussian distributions in directions which are perpendicular to the flow-axis of the plume. We also used the result of our previous study on the lateral spreading velocity of the plume derived under the same assumption. And entrainment was included as a mixing process. The resultant 1-dimensional equations were solved by Runge-Kutta numerical method. Consequently, comparatively easy method of numerical analysis is presented for the 3-dimensional river plume. The method can also be used for the analysis of the thermal plume of cooling water of power plants.

• Journal of Korean Society of Water and Wastewater
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• v.19 no.4
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• pp.487-496
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• 2005

Chlorine bulk decay tests were carried out by bottle test under controlled conditions in a laboratory. Experiments were performed at different temperatures: $5^{\circ}C$, $15^{\circ}C$, $25^{\circ}C$, and the water temperatures when samples were taken from the effluent just before entering to its distribution system. 38 bulk tests were performed for water of Al (water treatment plant), 4 bulk tests for A2 (large service reservoir), and A3(pumping station). Residual chlorine concentrations in the amber bottles were measured over time till about 100 hours and bulk decay coefficients were evaluated by assuming first-order, parallel first-order, second-order. and $n^{th}-order$ reaction. The $n^{th}-order$ coefficients were obtained using Fourth-order Runge-Kutta Method. A good-fit by the average coefficient of determination ($R^2$) was first-order ($R^2=0.90$) < parallel first-order ($R^2{_{fast}}=0.92$, $R^2{_{slow}}=0.95$) < second-order ($R^2=0.95$) < $n^{th}-order$ ($R^2=0.99$). But if fast reaction of parallel first-order bulk decay were applied to the effluent of large service reservoir with ca. 20 hours of travel time and slow reaction in the water distribution system following the first 20 hours, parallel first-order bulk decay would be best and easy for application of water quality modeling technique.

• Journal of Soil and Groundwater Environment
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• v.13 no.6
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• pp.50-61
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• 2008

In this study, new integrated particle tracking algorithm was developed to reduce the inherent problem of Eulerian- Lagrangian method, or adverse effect of particle tracking error on mass balance error. The new integrated particle tracking algorithm includes numerical method, semi-analytical method, and analytical method which consider both temporal and spatial changes of velocity field during time step. Detail of mathematical derivations is well illustrated and four examples are made to verify through the comparison of the new integrated particle tracking with analytical solution or Runge-Kutta method. Additionally, It was shown that the there is better superiority of the new integrated particle tracking algorithm over other existing particle tracking method such as Lu's method.

• Journal of the Korean Society of Marine Environment & Safety
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• v.24 no.2
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• pp.140-145
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• 2018

This paper deals with the dynamical analysis of a two-point mooring vessel under surge excitations. The characteristics of nonlinear behaviors are investigated completely including bifurcation and limit cycle according to particular input parameter changes. The strong nonlinearity of the mooring system is mainly caused by linear and cubic terms of restoring force. The numerical simulation is performed based on the fourth order Runge-Kutta algorithm. The bifurcation diagram and several instability phenomena are observed clearly by varying amplitudes as well as frequencies of surge excitations. Stable periodic solutions, called the periodic windows, can be obtained in succession between chaotic clouds of dots in case of frequency ${\omega}=0.4rad/s$. In addition, the chaotic region is unexpectedly increased when external forcing amplitude exceeds 1.0 with the angular frequency of ${\omega}=0.7rad/s$. Compared to the cases for ${\omega}=0.4$, 0.7rad/s, the region of chaotic behavior becomes more fragile than in the case of ${\omega}=1.0rad/s$. Finally, various types of steady states including sub-harmonic motion, limit cycle, and symmetry breaking phenomenon are observed in the two-point mooring system at each parameter value.