• 산업기술연구
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• 제21권A호
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• pp.41-50
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• 2001

A comparison is made of the temperature distribution and heat loss from a trapezoidal profile fin using two different 3-dimensional methods. These two methods are analytical and finite difference methods. In the finite difference method 78 nodes are used for a fourth of the fin. A trapezoidal profile fin being the height of the fin tip is half of that of the fin base is chosen arbitrarily as the model. One of the results shows that the relative error in the total convection heat loss obtained by using 78 nodes in the finite difference method as compared to the heat conduction through the fin root obtained by analytic method seems to be good (i.e., -3.5%

• 대한수학회보
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• 제61권3호
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• pp.745-762
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• 2024

In this paper, we study the existence of finite order meromorphic solutions of the following non-linear difference equation fⁿ(z) + P_d(z, f) = p₁e^α1z + p₂e^α2z + p₃e^α3z, where n ≥ 2 is an integer, P_d(z, f) is a difference polynomial in f of degree d ≤ n - 2 with small functions of f as its coefficients, p_j (j = 1, 2, 3) are small meromorphic functions of f and α_j (j = 1, 2, 3) are three distinct non-zero constants. We give the expressions of finite order meromorphic solutions of the above equation under some restrictions on α_j (j = 1, 2, 3). Some examples are given to illustrate the accuracy of the conditions.

• Steel and Composite Structures
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• 제49권5호
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• pp.587-602
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• 2023

This article presents the numerical modelling of transient heat transfer in highly heterogeneous composite materials where the thermal conductivity, specific heat and density are assumed to be directional-dependent. This article uses a coupled finite element-finite difference scheme to perform the transient heat transfer analysis of unidirectional (1D) and multidirectional (2D/3D) functionally graded composite panels. Here, 1D/2D/3D functionally graded structures are subjected to nonuniform heat source and inhomogeneous boundary conditions. Here, the multidirectional functionally graded materials are modelled by varying material properties in individual or in-combination of spatial directions. Here, fully spatial-dependent material properties are evaluated using Voigt's micromechanics scheme via multivariable power-law functions. The weak form is obtained through the Galerkin method and solved further via the element-space and time-step discretisation through the 2D-isoparametric finite element and the implicit backward finite difference schemes, respectively. The present model is verified by comparing it with the previously reported results and the commercially available finite element tool. The numerous illustrations confirm the significance of boundary conditions and material heterogeneity on the transient temperature responses of 1D/2D/3D functionally graded panels.

• 지구물리와물리탐사
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• 제22권2호
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• pp.56-61
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• 2019

셀 기반 유한 차분법을 사용하여 P파 속도와 밀도 변화를 고려한 3차원 시간 영역 음향 파동 전파 모델링에서 성능을 향상시킬 수 있는 방법을 살펴보았다. 일반적인 유한 차분법에서는 격자점에 탄성파 속도 또는 밀도와 같은 물성을 할당하고 계산하지만 셀 기반 유한 차분법에서는 이러한 물성을 격자점 사이의 셀에 할당한다. 격자점에서의 차분식 계산을 위해서는 주변 셀의 물성 평균값을 이용하는데 이로 인해 일반적인 유한 차분법에 비해 계산량이 증가하게 된다. 이 연구에서는 이러한 계산량 문제를 개선하기 위해 메모리를 추가로 사용하여 모델링 시간을 30 % 이상 줄일 수 있었다. 또한 밀도가 제한적으로 변화하는 매질에서 셀 기반 유한 차분법과 일반 유한 차분법을 함께 사용하여 모델링 성능을 추가로 향상시킬 수 있었다.

• 지구물리와물리탐사
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• 제20권3호
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• pp.121-128
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• 2017

국내에서 시간영역 전자탐사(time-domain/transient electromagnetic, TEM) 자료의 해석은 1차원 알고리듬에 주로 의존하고 있는 실정이기 때문에 정밀한 해석을 위하여 3차원 모델링 및 역산 해석 프로그램의 개발이 필요한 상황이다. 이 연구에서는 엇갈린 격자를 이용한 시간영역 유한차분(staggered-grid finite-difference time-domain, FDTD)법에 기초하여 3차원 TEM 반응 모델링 알고리듬을 개발하였다. 시간영역 전자탐사의 모델링을 위해 맥스웰 방정식을 현시적 중앙점 FDTD법을 이용하여 이산화하였으며 수치 안정성을 높이기 위해 가상 변위전류항을 도입하였다. 일반적으로 많이 활용되는 소형 코일 송신원을 수치적으로 구현하여 균질 반무한 공간에서의 해석해와 비교 검증하고 3차원 이상체에 대한 반응을 분석하였다. 이 연구에서 개발된 모델링 프로그램은 향후 TEM 전자탐사 자료의 정밀 해석에 기초가 될 것으로 기대한다.

• 한국강구조학회 논문집
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• 제12권3호통권46호
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• pp.303-315
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• 2000

본 논문에서는 일반화된 21개 강성 매트릭스의 독립 변수를 모두 사용하였고 비등방성 3차원 탄성체의 지배 방정식 및 수치 해석 근사식을 유도하였다. 일반화된 3차원 해석은 2차원 해석의 제한성을 극복하는 정밀해를 보여줄 수 있으며, 두꺼운 보나 판, 또는 쉘에서 전단 변형 효과에 의한 처짐의 증가 효과를 더욱 정밀하게 해석할 수 있다. 따라서 본 논문은 3차원 비등방성 탄성체에 대하여 다양한 경계조건에 따른 유한 차분식을 유도하였으며 이를 전산화하여 해석 프로그램을 개발하였다. 특히, 본 논문에서는 자유경계조건에 대하여 개선된 유한차분법의 적용 방식을 제시하였다. 또한 탄성체의 각 방향 자유경계면에서 경계조건을 해결할 수 있는 일반화된 방식을 제시하였다. 몇가지 수치예제를 통하여 이러한 유한차분 경계처리 방식에 의한 비등방성 3차원 탄성체 해석의 타당성 및 거동을 분석하였다.

• Journal of Advanced Marine Engineering and Technology
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• 제26권4호
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• pp.485-492
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• 2002

The present study is aimed to reveal macroscopic aerodynamic characteristics of two-dimensional rectangular prisms with three aspect ratios(D/H=1, 2 and 3) and six angles of attack($0^{circ}, 10^{circ}, 13.5^{circ}, 20^{circ}, 30^{circ} and 45^{\circ}$). The Reynolds number is fixed as $1\times10^4$. The SOLA-based revised finite difference method for the conservation form on irregular grid was adopted as a new numerical method. Instantaneous flow patterns at $45^{\circ}$ in case of D/H=2 and D/H=3 show larger asymmetric wake development which is closely related to the sharp decrease of drag coefficients at higher angles of attack range. Vorticity propagation into enlarged wake region is conjectured to be responsible for this phenomenon. The Strouhal number is found to be sensitive to the angle of attack at higher aspect ratios(D/H=2 and 3).

• Nuclear Engineering and Technology
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• 제53권11호
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• pp.3543-3562
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• 2021

The methods and performance of a 3D pin-by-pin neutronics code based on the 2D/1D decoupling method are presented. The code was newly developed as an effort to achieve enhanced accuracy and high calculation performance that are sufficient for the use in practical nuclear design analyses. From the 3D diffusion-based finite difference method (FDM) formulation, decoupled planar formulations are established by treating pre-determined axial leakage as a source term. The decoupled axial problems are formulated with the radial leakage source term. To accelerate the pin-by-pin calculation, the two-level coarse mesh finite difference (CMFD) formulation, which consists of the multigroup node-wise CMFD and the two-group assembly-wise CMFD is implemented. To enhance the accuracy, both the discontinuity factor method and the super-homogenization (SPH) factor method are examined for pin-wise cross-section homogenization. The parallelization is achieved with the OpenMP package. The accuracy and performance of the pin-by-pin calculations are assessed with the VERA and APR1400 benchmark problems. It is demonstrated that pin-by-pin 2D/1D alternating calculations within the two-level 3D CMFD framework yield accurate solutions in about 30 s for the typical commercial core problems, on a parallel platform employing 32 threads.

• Geomechanics and Engineering
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• 제17권4호
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• pp.317-322
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• 2019

This paper presents the results of parametric analyses to compute the axial capacity of a suction pile using 2D and 3D finite element approaches. The study is intended to simplify the process of analyzing suction piles from 3D to 2D model. The research focuses on obtaining the coefficient to be applied into the 2D model in order to obtain results that are as close as possible to the 3D model. Two 2D models were used in the analysis, namely the plane strain and axisymmetric models. The analyses were performed using two actual offshore soil data of the North and West Java Indonesia. The study reveals that the simplification of model through 2D Finite Element is achievable by applying the appropriate coefficient to the stiffness parameters. The results show that the simplified model of the 2D FEA provides more conservative results (with the difference between 2% to 7%) than the 3D FEA.

• 대한수학회지
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• 제44권3호
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• pp.627-645
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• 2007

We investigate the eigenvalues of the semi-circulant preconditioned matrix for the finite difference scheme corresponding to the second-order elliptic operator with the variable coefficients given by $L_vu\;:=-{\Delta}u+a(x,\;y)u_x+b(x,\;y)u_y+d(x,\;y)u$, where a and b are continuously differentiable functions and d is a positive bounded function. The semi-circulant preconditioning operator $L_cu$ is constructed by using the leading term of $L_vu$ plus the constant reaction term such that $L_cu\;:=-{\Delta}u+d_cu$. Using the field of values arguments, we show that the eigenvalues of the preconditioned matrix are clustered at some number. Some numerical evidences are also provided.