• East Asian mathematical journal
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• v.39 no.1
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• pp.75-85
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• 2023

In this paper, a non-overlapping rectangular domain decomposition method is presented in order to numerically solve two-dimensional telegraph equations. The method is unconditionally stable and efficient. Spectral radius of the iteration matrix and convergence rate of the method are provided theoretically and confirmed numerically by MATLAB. Numerical experiments of examples are compared with several methods.

• Journal of Environmental Impact Assessment
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• v.21 no.6
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• pp.917-925
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• 2012

In this study, we report the runoff characteristics of pollutants for Tamjin A and B watershed in Tamjin river basin using statistical analysis, such as correlation analysis and regression equation. Flow rate and water qualtiy data collected from 2 sampling sites(Tamjin A and B watershed) during 3 years(2009~2011) were analyzed for biochemical oxygen demand(BOD), total nitorgen(TN), total phosphorus(TP) and suspended solid(SS). The results showed that strong correlations were observed between flow rate and SS in Tamjin A, while weak correlations were observed among the BOD, TN, and TP. In Tamjin B, strong correlations were observed among the flow rate, SS and T-P except BOD and TP. Meanwhile, the values of $R^2$ for regression equations between flow rate and pollutants load were greater than 0.7. Results of these statistics indicated that there was a good agreement between flow rate and pollutants load. Also, the flow rate exponents of regression equations for BOD, TN, and TP were smaller than 1 in Tamjin A. In Tamjin B, flow rate exponents of regression equation for BOD and TP were smaller than 1. These results indicated that concentrations of BOD, TN, TP in Tamjin A and concentrations of BOD and TP were decreased as the flow rate was increased. This means that rater than nonpoint sources, point sources affect BOD, TN and TP in Tamjin A and BOD and TP in Tamjin B.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.4
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• pp.451-460
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• 1983

Computational four-equation turbulence model is developed and is applied to predict twodimensional unsteady thermal surface discharge into a reservoir. Turbulent stresses and heat fluxes in the momentum and energy equations are determined from transport equations for the turbulent kinetic energy (R), isotropic rate of kinetic energy dissipation (.epsilon.), mean square temperature variance (theta. over bar $^{2}$), and rate of destruction of the temperature variance (.epsilon. $_{\theta}$). Computational results by four-equation model are favorably compared with those obtained by an extended two-equation model. Added advantage of the four-equation model is that it yields quantitative information about the ratio between the velocity time scale and the thermal time scale and more detailed information about turbulent structure. Predicted time scale ratio is within experimental observations by others. Although the mean velocity and temperature fields are similarly predicted by both models, it is found that the four-equation model is preferably candidate for prediction of highly buoyant turbulent flows.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.459-517
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• 2002

The purpose of this paper is to provide a careful and accessible exposition of diffusive logistic equations with indefinite weights which model population dynamics in environments with strong spatial heterogeneity. We prove that the most favorable situations will occur if there is a relatively large favorable region (with good resources and without crowding effects) located some distance away from the boundary of the environment. Moreover we prove that a population will grow exponentially until limited by lack of available resources if the diffusion rate is below some critical value; this idea is generally credited to Thomas Malthus. On the other hand, if the diffusion rate is above this critical value, then the model obeys the logistic equation introduced by P. F. Verhulst .

• Journal of the Korean Society of Combustion
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• v.17 no.2
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• pp.17-23
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• 2012

In this study, thermoacoustic analysis model was developed in order to predict both eigenfrequencies and initial growth rate of combustion instabilities for lean premixed gas turbine combustors. As a first step, a model combustor and nozzle were selected and analytical linear equations for thermoacoustic waves were derived for a given combustion system. Then, methods showing how the equations can be used for analysis of the combustion instability were suggested. It was found that the prediction results showed a good agreement with the measurements. However, there were some limitation in growth rate predictions, which were related with over-simplification of flame structure, acoustic boundary conditions, and temperature distribution in the combustor.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.849-875
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• 2018

The purpose of this paper is to present an operator method of regularization for the problem of finding a solution of a system of nonlinear ill-posed equations with a monotone hemicontinuous mapping and N inverse-strongly monotone mappings in Banach spaces. A regularization parameter choice is given and convergence rate of the regularized solutions is estimated. We also give the convergence and convergence rate for regularized solutions in connection with the finite-dimensional approximation. An iterative regularization method of zero order in a real Hilbert space and two examples of numerical expressions are also given to illustrate the effectiveness of the proposed methods.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.121-126
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• 1998

A numerical optimization procedure is developed to find the inlet velocity profile that yields the most uniform epitaxial layer in a vertical MOCVD reactor. It involves the solution of fully elliptic equations of motion, temperature, and concentration; the finite volume method based on SIMPLE algorithm has been adopted to solve the Navier-Stokes equations. The overall optimization process is highly nonlinear and has been efficiently treated by the sequential linear programming technique that breaks the non-linear problem into a series of linear ones. The optimal profile approximated by a 6th-degree Chebyshev polynomial is very successful in reducing the spatial non-uniformity of the growth rate. The optimization is particularly effective to the high Reynolds number flow. It is also found that a properly constructed inlet velocity profile can suppress the buoyancy driven secondary flow and improve the growth-rate uniformity.

• 한국전산유체공학회:학술대회논문집
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• 1995.10a
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• pp.37-42
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• 1995

In the present study, an improved version of 4-equation low-Reynolds-number 4-equation model is proposed. The equations of the temperature variance ($k_{\theta}$) and its dissipation rate(${\varepsilon}_{\theta}$) are solved, in concert with the equations of the turbulent kinetic energy(k) and its dissipation rate(${\varepsilon}$). In the present model, the near-wall effect and the non-equilibrium effect are fully taken into consideration. The validation of the model is then applied to the turbulent flow behind a backward-facing step and the flow over a blunt body. The predicted results of the present model are compared and evaluated with the relevant experiments.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.05b
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• pp.241-246
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• 1996

An analytical model to calculate rate of vapor generation due to heterogeneous wall nucleation in flashing flow is developed. In the present model, an important parameter of the vapor generation term, i.e. nucleation site density is calculated by integrating its probability distribution function with respect to active cavity radius. The limits of integration are minimum and maximum active cavity radii, and these are formulated using an active cavity model for nucleate boiling. This formulation, therefore. can statistically account for the effect of surface specific thermo-physical and geometric conditions on the vapor generation rate and flashing inception. For verifying the adequacy of the present model, steady state two-fluid and the bubble transport equations are solved with applicable constitutive equations. The applicable region of the bubble transport equation is also extended to churn-turbulent flow regime to predict interfacial area concentration at high void fraction. Predicted results in terms of axial pressure and void fraction profiles along the channels are compared with experimental data of Super Moby Dick and BNL Reasonable agreements have been achieved and this shows the applicability of the present model to flashing flow analysis.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.887-892
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• 2003

A front-end cooling fan is designed and tested in the present study. The design technique is developed using the one-dimensional inviscid flow through the fan blade, the empirical equations, and the experimental correlations. Design data for the blade can be obtained for a given flow rate and a pressure rise. A parabolic function is used to generate a sweep of the fan. Characteristics of the blade geometry are discussed between the huh and the tip. The fan is tested in the fan test unit. The measured volume flow rate at the operating point is in good agreement with that of the design specifications. Sound pressure levels of the noise are predicted with the Ffowcs Williams-Hawkings equations. Calculation results of the sound pressure level(SPL) 1m away from the fan are obtained and cpmpared with the measured data.