• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.1757-1760
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• 2008

본 연구에서는 유한요소 모델인 RMA-2를 이용하여 격자의 구성방법에 따른 만곡수로에서의 흐름특성분석을 비교하였다. 수치모의는 격자구성에 따라 균일격자망의 모형과 타원형 편미분 방정식을 이용한 모형에 대하여 실시하였다. 균일 격자망의 모형은 직선부에서는 가로세로비율에 따라 직사각형 격자를 구성하였고 곡선부에서는 곡률구간을 일정한 각도로 나누어 구성하였으며, 타원형 편미분 방정식을 이용한 모형은 격자간의 직교성을 만족하도록 구성하였다. 본 연구의 수치 모의는 Shukry(1950)의 $180^{\circ}$ 만곡수로실험과 동일한 조건으로 실시하였으며 각 지점에서의 합성 유속분포를 실험값과 비교하였다. 실험결과, 만곡부에서 타원형 편미분 방정식을 이용한 모형의 수치모의 결과는 균일격자를 이용한 모형에 비해 실험값과 잘 일치함을 알 수 있었다.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 1992.08a
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• pp.84-89
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• 1992

파랑변형 예측모델로서는 타원형 편미분 방정식 형태인 완경사 방정식(Berkhoff, 1972)이 있으며 이는 파랑의 굴절, 회절, 반사등의 변형을 재현할 수 있으나 수치해석상 어려운점이 있으며 많은 기억용량과 계산시간이 소요되어 일반적이지 못한 단점이 있다.(중략)

• Journal of Industrial Technology
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• v.14
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• pp.19-28
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• 1994

We can get a tridiagonal block Toeplitz linear system by the finite difference approximation of 2-D Poisson equation. To exploit the nice property of this linear equation, we transform the equation into a Lyapunov equation and apply DST (discrete sine transform) to get diagonal matrix based Lyapunov equation. DST can be performed using FFT, which enables high-speed computaion. All the computations are performed on an SIMD parallel computer, the MasPar MP-2 with 4,096 processing elements. In this paper, parallel algorithm, mapping method of the algorithm onto the MP-2, and timing results are presented.

• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.159-163
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• 2008

본 연구에서는 2-방정식 난류모형을 이용하여 사면을 따라 발달하는 하층밀도류의 시간에 따른 이동현상에 대해 살펴보았다. 이를 위해 타원형의 편미분 방정식을 지배방정식으로 구성하고, 난류 완결을 위해 k-$\varepsilon$ 난류모형을 이용하였다. 개발된 모형을 이용하여 경사의 사면을 따라 진행하는 연속 유입 밀도류를 수치모의 하였다. 완전 발달된 하층밀도류의 거리에 따른 주흐름방향 유속 분포, 체적 농도를 계산하였고, 이를 기존의 실험결과와 비교하였다. 실험과 수치모의 결과가 잘 일치함을 확인하였다. 또한, 불연속 유입 밀도류의 시간에 따른 진행 상황을 수치모의하여 밀도류와 주변수체의 경계부에서 Kelvin-Helmholtz 불안정에 의한 와(渦)가 형성되는 것을 확인하였으며, 밀도류 선단부의 진행 속도와 주변수체의 유입에 대해 고찰하였다.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.3
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• pp.80-86
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• 1994

A numerical method for simulations of inviscid incompressible flow fields around a ship advancing on the free surface is developed. A body fitted coordinate system, generated by numerically solving elliptic type partial differential equations is used to conform the ship and free surface configurations. Three dimensional Euler equations transformed to the non-staggered body fitted coordinate system are discretised by finite difference method. Time and spatial derivatives are discretised by forward and centered differencings, respectively, and artificial dissipations are added to discretised convection terms for improvements of numerical stability. At each time steps, free surface elevations are recomputed to satisfy nonlinear free surface conditions. Poisson equations for pressure field are solved iteratively and the velocity field for next time step is extrapolated. To verify the developed numerical method, flow fields around a Wigley model are simulated(Fn=0.250-0.408) and compared with experimental data to show good agreements.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.3B
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• pp.231-237
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• 2009

This study presents a numerical model to simulate density currents developing two dimensionally. The ${\kappa}-{\varepsilon}$ model is used for the turbulence closure. Elliptic flow equations are solved by the finite volume method. In order to investigate the applicability of the numerical model, discontinuous density currents are simulated numerically. The vortices due to the instability at the interface are simulated, showing a good agreement with the experimental visualizations in the literature. It is also investigated that the transition from slumping phase to inertial phase occurs when a bore generated at the end wall overtakes the front. However, the propagation of the density current is retarded compared with the experimental results. Two-dimensional modeling seems to have an effect on underestimating the front velocity of the density current.

• Journal of Radiation Protection and Research
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• v.28 no.2
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• pp.97-108
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• 2003

A three-dimensional wind field model based on the variational technique has been developed for estimating the overall wind patterns over a complex terrain. The three-dimensional elliptic partial differential equations on Cartesian and terrain-following coordinates have been established to obtain the Lagrangian multiplier and the adjusted wind velocity. The simulations were performed to evaluate the variations of the velocity vectors on the hemisphere, half-cylinder, and saddle type obstacles. Also, the wind field model in the terrain-following coordinate has been applied for evaluating the characteristics of wind patterns according to the variations of Gauss precision moduli on the hemispheric topography. The results showed that the horizontal and vertical wind components were strongly governed by the selection of the values of Gauss precision moduli.

• The KIPS Transactions:PartA
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• v.10A no.2
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• pp.137-140
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• 2003

Recently, CG (Conjugate Gradient) scheme for the optimization of the Rayleigh quotient has been proven a very attractive and promising technique for interior eigenvalues for the following eigenvalue problem, Ax＝λx (1) The given matrix A is assummed to be large and sparse, and symmetric. Also, the method is very amenable to parallel computations. A proper choice of the preconditioner significantly improves the convergence of the CG scheme. We compare the parallel preconditioners for the computation of the interior eigenvalues of a symmetric matrix by CG-type method. The considered preconditioners are Point-SSOR, ILU (0) in the multi-coloring order, and Multi-Color Block SSOR (Symmetric Succesive OverRelaxation). We conducted our experiments on the CRAY­T3E with 128 nodes. The MPI (Message Passing Interface) library was adopted for the interprocessor communications. The test matrices are up to $512{\times}512$ in dimensions and were created from the discretizations of the elliptic PDE. All things considered the MC-BSSOR seems to be most robust preconditioner.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.5
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• pp.413-420
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• 2012

In this study, the Kernel integration scheme for 2D linear elastic direct boundary element method has been discussed on the basis of subparametric element. Usually, the isoparametric based boundary element uses same polynomial order in the both basis function and mapping function. On the other hand, the order of mapping function is lower than the order of basis function to define displacement field when the subparametric concept is used. While the logarithmic numerical integration is generally used to calculate Kernel integration as well as Cauchy principal value approach, new formulation has been derived to improve the accuracy of numerical solution by algebraic modification. The subparametric based direct boundary element has been applied to 2D elliptical partial differential equation, especially for plane stress/strain problems, to demonstrate whether the proposed algebraic expression for integration of singular Kernel function is robust and accurate. The problems including cantilever beam and square plate with a cutout have been tested since those are typical examples of simple connected and multi connected region cases. It is noted that the number of DOFs has been drastically reduced to keep same degree of accuracy in comparison with the conventional isoparametric based BEM. It is expected that the subparametric based BEM associated with singular Kernel function integration scheme may be extended to not only subparametric high order boundary element but also subparametric high order dual boundary element.