• Journal of Korea Water Resources Association
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• v.32 no.6
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• pp.607-616
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• 1999

A fractional step finite difference model for the longitudinal dispersion of nonconservative contaminants is developed. It is based on splitting the longitudinal dispersion equation into a set of three equations each to be solved over a one-third time step. The fourth-order Holly-Preissmann scheme, an analytic solution, and the Crank-Nicholson scheme are used to solve the equations for the pure advection, the first-order decay, and the diffusion, respectively. To test the model, it is applied to simulate the longitudinal dispersion of continuous source released into a nonuniform flow field as well as the dispersion of an instantaneous source in a uniform flow field. The results are compared with the exact solution and those computed by an existing model. Compared to the existing model which uses Euler method for the first-order decay equation, the present model yield more accurate results as the decay coefficient increases.

• Korean Journal of Mineralogy and Petrology
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• v.36 no.3
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• pp.199-212
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• 2023

Diffusion is a powerful tool to understand geological processes recorded in terrestrial rocks as well as extraterrestrial materials. Since the diffusive exchange of elements or isotopes may have occurred differently in the solar nebula (high temperature and rapid cooling) and on the parent bodies (fluid-assisted thermal metamorphism at relatively low temperature), it is particularly important to model elemental or isotopic diffusion profiles within the mineral grains to better understand the evolution of the early solar system. A numerical model with the finite difference method for the fast grain boundary diffusion was established for the exchange of elements or isotopes between constituent minerals in a closed system. The fast grain boundary diffusion numerical model was applied to 1) ²⁶Mg variation in plagioclase of an amoeboid olivine aggregate (AOA) from a CH chondrite and 2) Fe-Mg interdiffusion between chondrules, AOA, and matrix minerals in a CO chondrite. Equilibrium isotopic fractionation and equilibrium partitioning were also included in the numerical model, based on the assumption that equilibrium can be reached at the interfaces of mineral crystals. The numerical model showed that diffusion profiles observed in chondrite samples likely resulted from the diffusive exchange of elements or isotopes between the constituent minerals. This study also showed that the closure temperature is determined not only by the mineral with the slowest diffusivity in the system, but also strongly depends on the constituent mineral abundances.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.1
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• pp.131-141
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• 1994

Three characteristics-based split-operator methods were applied to a longitudinal pollutant dispersion problem, and the results were compared with those of several Eulerian schemes. The split-operator methods consisted of generalized upwind, two-point fourth-order and sixth-order Holly-Preissmann schemes, respectively, for the advection calculation, and the Crank-Nicholson scheme for the diffusion calculation. Compared with the Eulerian schemes tested, split-operator methods using the Holly-Preissmann schemes gave much more accurate computational results. Eulerian schemes using centered difference approximations for the advection term resulted in numerical oscillations, and those using backward difference resulted in numerical diffusion, both of which were more severe for smaller value of the longitudinal dispersion coefficient.

• Journal of Korea Water Resources Association
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• v.45 no.5
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• pp.473-480
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• 2012

A two-dimensional depth-integrated hydrodynamic and a depth-averaged passive scalar transport models were developed by using a Compact Finite Volume Method (CFVM) which can assure a higher order accuracy. A typical wave current interaction experimental data set was compared with the computed results by the proposed CFVM model, and resonable agreements were observed from the comparisons. One and two dimensional scalar advection tests were conducted, and very close agreements were observed with very little numerical diffusion. Finally, a turbulent mixing simulation was done in an open channel flow, and a reasonable similarity with LES data was observed.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 1998.09a
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• pp.24-30
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• 1998

고도의 산업발달은 인간환경과 밀접한 하구와 해안의 오염을 심화시켜 최근 사회적 문제로 대두되고 있으며, 이에 오염물질의 이동을 예측하고 제어하려는 노력이 꾸준이 진행되어 왔다. 이 같은 노력은 수치모형을 이용한 수질관리 연구에도 많은 진전을 가지고 왔으며, 오일러적 모형, 라그랑쥐적 모형, 오일러-라그랑쥐 적 모형이 대표적이다. 오일러-라그랑쥐적 모형은 이류에 대해 라그랑쥐적 방법, 확산에 대해 오일러적 방법으로 해석함으로서 각 방법들의 장점을 취하여 수치적 진동, 수치적 확산이 적고 효율성이 뛰어나 최근 많이 연구되고 있다. (중략)

• Journal of the Society of Naval Architects of Korea
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• v.31 no.1
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• pp.94-101
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• 1994

This paper describes a short-term prediction model for the movement of an oil slick in shallow waters. Under the assumption that the initial movement of the oil slick is governed by spreading and advection, the model has been developed and applied to Kyungki-Bay near Incheon Harbor. The initial spreading is estimated by using an empirical formula. The depth-averaged momentum equations are solved numerically for the volume transport velocities, in which the $M_2$ tide is the main driving source. A staggered grid system is adopted fur spatial discretization and the half-time method is implemented for time marching. The numerical result is visualized with the help of animation and thus the contaminated area is displayed on a monitor in time sequence. The input data are the time, the location and the volume of spill accident as well as environmental data such as md and $M_2$ tide.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.5B
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• pp.557-562
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• 2006

In order to predict the dispersion of suspended sediment arising from dredging operation in port and navigation channel, a hybrid model for dispersive transport of turbidity plume was developed using Lee's(1998) hybrid method. Using hybrid modeling scheme advection-diffusion equation was solved by the forward particle-tracking method for advection process and by the fixed Eulerian grid method for diffusion process. To examine numerical model simulation in accuracy, the simulated results for 1-D, 2-D, and 3-D cases were compared with the analytical solutions including Kuo, et al's (1985) 3-D mathematical model. The model results were in a good agreement with the analytical solutions and mathematical model for the dispersion of turbidity plume.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.557-561
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• 2006

매년 영산강 본류 수질이 악화되고 있는 영산강 유역주변은 최근 전남도청 이전에 따른 남악 신도시개발, J-Project 및 환경 문화 복원사업의 추진, 기업도시개발등과 관련하여 수질관리개선 및 주요환경현안으로 대두되고 있다. 따라서 영산강 하구역 관리방안 중 담수호 수질개선대책의 일환으로 수문개방을 통한 해수 유입에 의한 수질 개선을 효과를 도모하는 방안이 제시되고 있다. 이에 하구호 방조제의 수문 개통 및 완전 개방에 따른 수질개선 문제에 앞서 발생할 수 있는 환경변화 중 영산강 및 연안역 염분의 확산범위를 평가하기 위하여 수치모형 실험이 실시되었다. 담수 유입에 따른 염분 확산 범위 및 해수 유입에 따른 염분의 역상 범위를 평가 하기위해 수치 모델로는 EFDC를 적용하였고, 하천형상과 연안역을 동시에 고려하기 위해 수평좌표계는 직교곡선좌표로 격자 크기는 $120{\sim}1000m$, 연직방향으로 시그마좌표를 사용하였다. 담수 방류 및 염분역상 효과를 알아보기 위해 1997년부터 2005년까지의 하구 수문 방류량 및 하천 유입량으로부터 홍수기와 갈수기를 선택하여 현재 상황 및 수문의 부분 개통 하구둑 완전 개방에 시나리오를 설정하여 실시하였다. 수문의 부분개통과 하구둑 완전 개방에 따른 염분 확산 범위는 영산강 하구둑을 기준으로 홍수기에는 $13{\sim}17km$, 갈수기에는 36km 이상의 상류지역에서 해수와 담수의 분리 기준인 0.3 psu 범위가 계산됨을 알 수 있다.

• Journal of Korean Society of Environmental Engineers
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• v.33 no.1
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• pp.16-24
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• 2011

EFDC model was applied to reproduce velocity fields and to evaluate the dispersion characteristics of suspended sediments (SS) around a Daesan port. Numerical results using two-dimensional hydrodynamic model of EFDC showed good agreements through comparison with the time series and harmonic analysis of the tidal elevations. The dispersion patterns of the suspended sediments using the calculated velocity fields were calculated to move from east to northeast direction in flood tide and from west to southwest in ebb tide for dredging of sea route, respectively. Also, the suspended sediments were widely dispersed into the front areas of a Daesan port, Nanji-do and Garorim bay in the long-term. Therefore, it was inferred that the environmental problems for sea pollution would be occurred seriously if the dredging for sea route would be continued in the long-term.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.4
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• pp.261-270
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• 1992

To investigate the flow patterns and diffusions in the Taean coastal waters of the eastern Yellow Sea, hydraulic and numerical experiments of tidal currents and diffusions of dye and cooling water were performed during spring tide along with field observations. Flow patterns obtained by the hydraulic and numerical experiments approximately coincide with those of the field observations. In the fold observations of tidal current, currents flow southwestward during the ebb tide, while currents flow northeastward during the flood tide. and the maximum velocity is 2.13 ㎧ toward WSW direction. The Eulerian diffusion coefficient estimated from field measmements of current is 7.82$\times$10$^{5}$ $\textrm{cm}^2$/s. Diffusion coefficients obtained from the area of dye plume in the model are given by the expression 0.18 $r^{4}$3/, and the coefficients have the range of 10$^{5}$ ~10$^{6}$ $\textrm{cm}^2$/s. These values are similar to the Eulerian diffusion coefficient estimated fram field measurements. Diffusion coefficients obtained in the hydraulic model are one to two orders higher than those obtained in the Onsan Bay in the eastern waters and two to three orders higher than those obtained in the Chinhae Bay in the southern waters of the Korean Peninsula. Diffusion patterns of cooling water by numerical experiments are similar to those of dye plume by hydraulic experiments. Both hydraulic and numerical experiment results of diffusions of dye plume and cooling water in the Taean coastal waters, have shown that the diffusion during the ebb tide is more prevalent than one during the flood tide.