• Journal of Energy Engineering
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• v.16 no.1 s.49
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• pp.46-52
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• 2007

The piecewise constant angular approximation is developed to replace the conventional angular quadrature sets in the solution of the second-order, multi-dimensional $S_{N}$ neutron transport equations. The newly generated quadrature sets by this method substantially mitigate ray effects and can be used in the same manner as the conventional quadrature sets are used. The discrete-ordinates and the piecewise-constant approximations are applied to both the first-order Boltzmann and the second-order form of neutron transport equations in treating angular variables. The result is that the mitigation of ray effects is only achieved by the piecewise-constant method, in which new angular quadratures are generated by integrating angle variables over the specified region. In other sense, the newly generated angular quadratures turn out to decrease the contribution of mixed-derivative terms in the even-parity equation that is one of the second-order neutron transport equation. This result can be interpreted as the entire elimination or substantial mitigation of ray effect are possible in the simplified even-parity equation which has no mixed-derivative terms.

• Proceeding of EDISON Challenge
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• 2012.04a
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• pp.121-124
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• 2012

비정상 유동 해석을 수행하는데 있어서 비정상 Navier-Stokes 방정식을 적용한 결과와 정상 N-S 지배 방정식을 적용한 결과의 차이를 비교하려한다. 적용하고자 하는 비정상 유동은 대칭형 에어포일 NACA0012 에어포일 주위 유동으로 정하였으며, 이 때 에어포일 시위(chord) 길이와 자유류(free stream) 속도 기준으로 Re=100,000에 해당한다. 계산결과 비정상 지배 방정식을 적용한 경우 비정상 유동박리(flow separation)를 모사 할 수 있었으며, 평균 양력계수($C_L$)와 항력계수($C_D$)는 실험치와 비교적 잘 일치하였다. 하지만 정상 N-S 방정식을 적용했을 경우 비정상 유동을 모사하기 어려웠으며 평균양력, 항력계수도 실험치와 차이를 보였다. 이러한 결과는 비정상 유동 해석시 시간에 따라 변화하는 유동의 특성을 고려해 비정상 N-S 지배 방정식을 적용해야한다는 사실을 보이고 있다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.35 no.5
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• pp.1061-1071
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• 2015

In the present study, the Navier-Stokes (N-S) equations delineating water flows inside porous media were derived applying Reynolds transport theorem in order to provide a basis for analyzing water wave problems inside the porous media. Then, the derived N-S equations were compared with the same species of equations in existing researches. Based on the N-S equations, a set of Boussinesq equations was then derived in such a form that the dispersiveness and nonlinearity of water waves inside the porous media can be properly reproduced. Finally, numerical analyses were carried out to demonstrate the validity of the equations. The reflection and transmission coefficients of porous breakwaters were calculated and compared with the results of existing hydraulic experiments. The numerical results showed a rather sensitive dependency on the virtual mass coefficient of grains constituting the porous media. The selection of the coefficient with zero turned out to give nice agreements with numerical and experimental results.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.2
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• pp.71-82
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• 1984

A programme, called BIPOLE, for the numerical analysis of twotimensional n-p-n bipolar transistors was developed. It has included the SRH and Auger recolnbination processes, the mobility dependence on the impurity density and the electric field, and the band-gap narrowing effect. The finite difference equations of the fundamental semiconductor equations are formulated using Newton's method for Poisson's equation and the divergence theorem for the hole and electron continuity equations without physical restrictions. The matrix of the linearized equations is sparse, symmetric M-matrix. For the solution of the linearized equations ICCG method and Gummel's algorithm have been employed. The programme BIPOLE has been applied to various kinds of the steady-state problems of n-p-n transistors. For the examples of applications the variations of common emitter current gain, emitter and diffusion capacitances, and input and output characteristics are calculated. Three-dimensional representations of some D.C. physical quantities such as potential and charge carrier distributions were displayed. This programme will be used for the nome,rical analysis of the distortion phenom ana of two-dimensional n-p-n transistors. The BIPOLE programme is available for everyone.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.05a
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• pp.173-178
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• 1996

특정한 방향성분에 대한 방향중성자속을 정의하는 방향차분 수송 방정식(discrete ordinates or S$_{N}$ transport equation)과 달리 방향변수를 구분된 방향영역에 대하여 적분하고, 해당 방향영역 내에서의 방향중성자속이 일정하다고 가정하는 영역상수법(piecewise constant method)을 이용하여 유사방향차분방정식(discrete ordinates-like equation)을 유도하여, 이를 Boltzmann 수송식과 2계 우성수송식(even-parity transport equation)에 적용하여 기존의 방향차분법의 단점인 광첨두현상(ray effects)을 감소시키고, 우성수송식의 교차미분항을 제거한 단순우성방정식(simplified even-parity equation)을 사용하여 광첨두현상을 제거하였다. 이는 단순우성방정식의 또 다른 장점을 제시한다.

• Journal of the Korean Chemical Society
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• v.16 no.6
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• pp.349-353
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• 1972

The Faddeev-type equations for systems of more than four particles are derived from Weinberg's equation. The derivation is considerably simpler than that by others. The Faddeev-type equations thus derived can be expressed in a matrix form and the rules for constructing the inhomogeneous term and the matrix kernel of the matrix integral equation are formulated and verified explicitly for N=3, 4, and 5.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.3
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• pp.62-71
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• 1995

In the numerical analysis of incompressible unsteady Navier-stokes equation, large time is required for solving the pressure Poisson equation of the elliptic type at each time step. In this paper, a numerical analysis by the direct method is carried out to solve the pressure Poisson equation and the computing time is analyzed as mesh size increases. The pressure Poisson equation can be transformed to the boundary value problem by the Green theorem. The computing time for the convolution type of the domain integral can be reduced by using F.F.T. and the computing time in the direct method depends entirely on obtaining the solution of the boundary value problem. The numerical analysis on the known solutions is carried out and compared for the verification of the direct method. And the numerical analysis on the body boundary and domain decomposition problem are carried out with the computing time less than O($n^{3}$) in the (n.n) mesh.

• Journal of the Korean Vacuum Society
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• v.17 no.5
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• pp.400-407
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• 2008

In this study, Two dimensional spatial profile of electromagnetic field for capacitively coupled plasma source is calculated. Based on one dimensional fluid equation, spatial profile for the axial direction of electric field and conduction current density is firstly calculated. The two dimensional spatial profile for the electromagnetic field is calculated from solution of Maxwell equation that is expanded to power series for ${\omega}r/c$ into the radial direction.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.15 no.7
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• pp.553-564
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• 1990

The co-efficient matrix of linear second-order partial differential equations in the general form is partitioned with (n-1)x(n-1) submartices and is transformed into the block tridiagonal system. Then the cyclic odd-even reduction technique is applied to this system with the large-grain data granularity and the block cyclic reduction algorithm to solve unknown vectors of this system is created. But this block cyclic reduction technique is not suitable for the parallel processing system because of its parallelism chanigng at every computing stages. So a new algorithm for solving linear second-order partical differential equations is presentes by the block cyclic reduction technique which is modified in order to keep its parallelism constant, and to reduce gteatly its execution time. Both of these algoriths are compared and studied.

• Journal of the Korean Society of Safety
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• v.7 no.4
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• pp.101-104
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• 1992

It is shown that for a characteristic equation of continuous linear system, stability can be determined by conditions srggested in this paper. And also It Is of interest to Know how much coefficients of the low-order characteristic equation(N$\leq$5) can be perturbed while simutanously preserving the stable condition of the equation. This result is analogous to result by Anderson et al. based on the Kharitonov's conditions and Hermite - Biehler theorem.