• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.419-431
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• 2010

A low-order finite element preconditioner is analyzed for a cubic spline collocation method which is used for discretizations of coupled elliptic problems derived from an optimal control problrm subject to an elliptic equation. Some numerical evidences are also provided.

• 한국전산유체공학회:학술대회논문집
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• 2000.10a
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• pp.72-77
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• 2000

This paper presents the results of the application of a computational fluid dynamics algorithm for the simulation of plasma flows of arc-heated jet. The underlying physical model is based on the axisymmetric form of the conservation equations that are coupled with an arc model including Ohm heating, electromagnetic forces. The arc model given as a source term in fluid dynamic equations is determined by a solution of electric potential field governed by an elliptic partial differential equation. The governing equation of electric field is loosely coupled with fluid dynamic equations by an electric conductivity that is a function of state variables. However, the electric fields and flow fields cannot be solved In fully coupled manner, but should be solved iteratively due to the different characteristics of governing equations. With this solution approach, several applications of arc flow analysis will be presented including Arc Thruster and Circuit Breaker.

• Water for future
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• v.23 no.3
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• pp.319-328
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• 1990

The Parameter Identification of 2-demensional estuarine model was carried out using new output ADI-FDM numerical semi-implicit schem transformed in boundary fitted(BF) - coordinate. The hydrodynamic equations which is coupled with the transport equations were used as basic equations in the model. Thompson's equations were used to transform governing equations into rectangular plane equations and his elliptic grid generation scheme was used to generate curvilinear grid system. in BF - coordinates. The parameters to be identified are friction coefficient and disperse coefficient embedded in the governing equations. The numerical output scheme is tidally averaged salinity model in BF - coordinates. The algorithm to optimize norm of error between observations and calculations is the influence coefficinet algorithm associated with least square criterion. The lumped model is conssidered in identification. This paper was concetrated on checking whether the new output scheme might be useful to identify parameters in estuarine salinity model or not. The proposed method was tested through experimental application with hypothetical simple model. The result of the test shows that the proposed method can be used for parameter identification in estuarine model.

• 한국전산유체공학회:학술대회논문집
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• 2002.05a
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• pp.128-133
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• 2002

The heat transfer characteristics of a turbulent flow in a ribbed two-dimensional channel have been investigated numerically. The fully elliptic governing equations, coupled with a four-equation turbulence model, $\kappa-\omega-\bar{t^2}-\epsilon_t$, are solved by a finite volume method of SIMPLE type. Calculations have been carried out for three rib cross-sections : square, triangular, and semicircular, with various rib pitches and Reynolds numbers. The procedure appears to be satisfactory as the results for the square rib compare favorably with available experimental data and earlier calculation. The optimal rib pitch that yields the maximum heat transfer has been identified. It is also found that the square rib is most effective in enhancing the heat transfer. The semicircular rib, on the other hand, incurs the least amount of pressure drop but the improvement in heat transfer is substantially lower.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1140-1149
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• 2004

The absorption characteristics of water vapor into a LiBr-H$_2$O solution flowing down on finned inclined surfaces are numerically investigated in order to study the absorbing performances of different surface shapes of finned tubes as an absorber element. A three-dimensional numerical model is developed. The momentum, energy, and diffusion equations are solved simultaneously using a finite difference method. In order to obtain the temperature and concentration distributions, the Runge-Kutta and the Successive over relaxation methods are used. The flat, circular, elliptic, and parabolic shapes of the tube surfaces are considered in order to find the optimal surface shapes for absorption. In addition, the effects of the fin intervals and Reynolds numbers are studied. The results show that the absorption mainly happens near the fin tip due to the temperature and concentration gradient, and the absorbing performance of the parabolic surface is better than those of the other surfaces.

• Solar Energy
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• v.17 no.3
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• pp.67-73
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• 1997

In order to development of a new wall structure type thermal diode for energy saving, the numerical studies have been performed for natural convection across an rectangular enclosure with the various lengthes of the heat source and sink plate. The governing equations for the two-dimensional, laminar, natural convection process in an enclosure are discretized by the control volume approach which insures the conservative characteristics to be satisfied in the calculation domain, and solved by a elliptic SIMPLE algorithm. The momentum and energy equations are coupled through the buoyancy term.

• The Transactions of the Korea Information Processing Society
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• v.2 no.4
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• pp.535-542
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• 1995

In this paper we present two preconditioners for solving large sparse linear systems arising from elliptic partial differential equations on massively parallel machines, such as the CM-5. Most massively parallel machines do heavily rely on the message-passing for the interprocessor communications. but according to the current manufacturing standards the cost of communications is very high compared to that of floating point arithmetic computations. Due to this we need an algorithm which minimizes the amount of interprocessor communication on the massively parallel machines. We will show that Block SOR(Successive Over Relaxation) method coupled with the multi-coloring technique is one of such preconditioner on the massively parallel machines, by conducting experiments in the CM-5. Also, we implemented the ADI(Alternation Direction Implicit) method in the CM-5, which has been conventionally one of the most powerful parallel preconditioner. Our experiment shows that Block SOR method coupled with the multi-coloring technique could yield a speedup with 50% efficiency with the range of number of processors form 16 to 512 for a matrix with dimension 512x512. On the other hand, the ADI method shows a very poor performance.