• Environmental Engineering Research
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• v.23 no.4
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• pp.442-448
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• 2018

This paper presents the numerical simulation of advection-diffusion mechanism of BOD concentration which was used as an indicator of waste only in one flow-direction of waste stabilization ponds (1-dimension (1-D)). This model was represented in partial differential equation order 2. The purpose of this paper was to determine the simulation of the model 1-D of wastewater transport phenomena based advection-diffusion mechanism and did validate the model. Numerical methods which was used for the solution of this model is finite difference method with Forward Time Central Space scheme. The simulation results which was obtained would be compared with field observation data as a validation model. Collection of field data was carried out in the Wastewater Treatment Plant Sewon, Bantul, D.I. Yogyakarta. The results of numerical simulations were indicate that the advection-diffusion mechanism takes place continuously over time. Then validation of the model was state that there was a difference between the calculation results with the field data, with a correlation value of 0.998.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.419-435
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• 2021

This paper deals with numerical treatment of singularly perturbed differential equations involving small delays. The highest order derivative in the equation is multiplied by a perturbation parameter 𝜀 taking arbitrary values in the interval (0, 1]. For small 𝜀, the problem involves a boundary layer of width O(𝜀), where the solution changes by a finite value, while its derivative grows unboundedly as 𝜀 tends to zero. The considered problem contains delay on the convection and reaction terms. The terms with the delays are approximated using Taylor series approximations resulting to asymptotically equivalent singularly perturbed BVPs. Inducing exponential fitting factor for the term containing the singular perturbation parameter and using central finite difference for the derivative terms, numerical scheme is developed. The stability and uniform convergence of difference schemes are studied. Using a priori estimates we show the convergence of the scheme in maximum norm. The scheme converges with second order of convergence for the case 𝜀 = O(N^-1) and for the case 𝜀 ≪ N^-1, the scheme converge uniformly with first order of convergence, where N is number of mesh intervals in the domain discretization. We compare the accuracy of the developed scheme with the results in the literature. It is found that the proposed scheme gives accurate result than the one in the literatures.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.415-417
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• 2005

In order to retrieve the latent and sensible heat fluxes, high-resolution airborne imageries with visible, near infrared, and thermal infrared bands and ground-base meteorology measurements are utilized in this paper. The retrieval scheme is based on the balance of surface energy budget and momentum equations. There are three basic surface parameters including surface albedo $(\alpha)$, normalized difference vegetation index (NOVI) and surface kinetic temperature (TO). Lowtran 7 code is used to correct the atmosphere effect. The imageries were taken on 28 April and 5 May 2003. From the scattering plot of data set, we observed the extreme dry and wet pixels to derive the fitting of dry and wet controlled lines, respectively. Then the sensible heat and latent heat fluxes are derived from through a partitioning factor A. The retrieved latent and sensible heat fluxes are compared with in situ measurements, including eddy correlation and porometer measurements. It is shown that the retrieved fluxes from our scheme match with the measurements better than those derived from the S-SEBI model.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.881-898
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• 2018

This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible Navier-Stokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudo-time derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.

• 한국방재학회:학술대회논문집
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• 2008.02a
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• pp.431-434
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• 2008

Pratical dispersion-correction scheme is applicated to simulate the distant propagation of tsunami. This scheme is based on the leap-frog finite difference scheme for the linear shallow-water equations. The new scheme has the advantage of using the constant spatial grid size and time step size even in area of variable depths. And this new model constructed by using the 2nd upwind scheme, dynamic linking method, and staggered grid system. This model is simulated to near Sokcho harbor about The Central East Sea Tsunami in 1983. And this result is compared to tide gage and result of former model.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2001.05a
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• pp.52-57
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• 2001

Laminar two-dimensional time-dependent flow past a circular cylinder is numerically investigated using direct numerical simulation for the low Reynolds number (Re=164∼280). The higher-order finite difference scheme is employed for the spatial distributions along with the second order Adams-Bashforth and the first order backward-Euler time integration. The convection term is applied by the 7th order up wind scheme and the pressure and viscosity terms are applied by the 4th order central difference. The grid system makes use of the regular grid system and it is generated by an equation. The calculated results of drag coefficients, lift coefficients, pressure distributions, and vorticity contours and other information are compared with experimental and numerical ones. These results obtained by the present DNS show good agreement with the previous studies.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.16 no.5
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• pp.119-125
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• 2017

In this paper, the characteristics and load carrying capacity of square pocket surfaces on a slider bearing are discussed for the thin film effect by the square pocket slider bearing. To study the lubrication, a Reynolds equation is used in this paper for the analysis of the slider bearing characteristics with square pocket surfaces. For numerical analysis, the central differencing scheme finite difference method is used. In a slider bearing with square pocket surfaces, the simulation dependent parameters such as pressure and load carrying capacity of the bearing can be acquired from the independent parameters, the slope of the slider bearing and number of pockets on the upper slider. These results can be acquired by the programmed softwar,e and they can be analyzed and stored in a sequential data file for later analysis. Furthermore, their pressure and load capacity distribution can be displayed easily by using the developed program with the Matlab GUI.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.2
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• pp.77-94
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• 1991

A finite difference method based on MAC method is used to simulate free-surface waves around a ship. Euler equations and continuity equation are differentiated using the forward time and central space, and solved by time marching scheme. By the employment of variable mesh system in horizontal and vertical direction, the numerical accuracy of wave simulation results is grossly improved. To verify the improvement of numerical accuracy, some numerical simulations are accomplished for Wigley, Series 60($C_{b}$=0.6) and a bulk carrier model. The computational results are compared to the various experimental data and show good agreements.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2010.04a
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• pp.179-182
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• 2010

본 연구에서는 MLS 차분법을 이용하여 동역학 문제를 해석하기 위한 explicit 동적해석 알고리즘을 제시한다. 격자망이 없는 장점을 부각시키기 위해 이동최소제곱법에 근거한 Taylor 전개로부터 미분근사를 얻고 차분식을 구성했다. 지배 미분방정식의 시간항을 CDM(Central difference Method) 차분하여 빠른 속도로 동적해석을 수행하였다. 수치결과를 통해 본 연구에서 제시한 알고리즘의 정확성과 안정성을 확인할 수 있었다.

• Journal of Advanced Marine Engineering and Technology
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• v.40 no.5
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• pp.412-417
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• 2016

A fin of finite width with infinitely small thickness is assumed to be placed horizontally between two horizontal parallel plates of infinite extension in the exactly central position. The lower plate and the half of the upper plate are kept at a constant lower temperature, and the remaining upper plate is kept at a constant higher temperature. The fin is also kept at a constant temperature (variable). Steady-state two-dimensional laminar natural convection is analyzed as a problem of boundary value under a boundary-fitted conformal mapping system, using a spectral finite difference scheme, with a condition of doubly-connectedness. The steady-state solution is obtained as a limit of the transient solution.