• Journal of Industrial Technology
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• v.21 no.A
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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%

• Geophysics and Geophysical Exploration
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• v.22 no.2
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• pp.56-61
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• 2019

In this paper, we studied efficient modeling strategies when we simulate the 3D time-domain acoustic wave propagation using a cell-based finite difference method which can handle the variations of both P-wave velocity and density. The standard finite difference method assigns physical properties such as velocities of elastic waves and density to grid points; on the other hand, the cell-based finite difference method assigns physical properties to cells between grid points. The cell-based finite difference method uses average physical properties of adjacent cells to calculate the finite difference equation centered at a grid point. This feature increases the computational cost of the cell-based finite difference method compared to the standard finite different method. In this study, we used additional memory to mitigate the computational overburden and thus reduced the calculation time by more than 30 %. Furthermore, we were able to enhance the performance of the modeling on several media with limited density variations by using the cell-based and standard finite difference methods together.

• Steel and Composite Structures
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• v.49 no.5
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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.

• Geophysics and Geophysical Exploration
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• v.20 no.3
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• pp.121-128
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• 2017

Interpretation of time-domain electromagnetic (TEM) data has been made mostly based on one-dimensional (1-D) inversion scheme in Korea. A proper interpretation of TEM data should employ 3-D TEM forward and inverse modeling algorithms. This study developed a 3-D TEM modeling algorithm using a finite difference time-domain (FDTD) method with staggered grid. In numerically solving Maxwell equations, fictitious displacement current is included based on an explicit FDTD method using a central difference approximation scheme. The developed modeling algorithm simulated a small-coil source configuration to be verified against analytic solutions for homogeneous half-space models. Further, TEM responses for a 3-D anomaly are modeled and analyzed. We expect that it will contribute greatly to the precise interpretation of TEM data.

• Nuclear Engineering and Technology
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• v.53 no.11
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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.

• Journal of Advanced Marine Engineering and Technology
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• v.26 no.4
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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).

• Composites Research
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• v.17 no.3
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• pp.23-28
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• 2004

A method of calculating the natural frequency corresponding to the first mode of vibration of beams and tower structures, with irregular cross sections and with arbitrary boundary conditions was developed and reported by Kim, D. H. in 1974. In this paper, the result of application of this method to the three span continuous reinforced concrete bridge with elastic intermediate supports is presented. Such bridge represents either concrete or sandwich type three span bridge on polymeric supports for passive control or on actuators for active control. The concrete slab is considered as a special orthotropic plate. Any method may be used to obtain the deflection influence surfaces needed for this vibration analysis. Finite difference method is used for this purpose, in this paper, The influence of the modulus of the foundation and $D_{22}$, $D_{12}$, $D_{66}$ stiffnesses on the natural frequency is thoroughly studied.

• Nuclear Engineering and Technology
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• v.56 no.9
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• pp.3654-3667
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• 2024

Expanding upon the framework of the steady-state pin-by-pin 2D/1D decoupling method, a novel and highperformance pin-by-pin transient calculation method has been introduced. This transient method, consistent to the steady-state formulation, is designed for time-dependent calculations utilizing a 3D diffusion-based finite difference method (FDM). The inherent complexity of the large 3D problem is effectively managed by decoupling it into a series of planar (2D) and axial (1D) problems. In addition, tens of thousands of pin-cells are grouped into hundreds of boxes to reduce the computing burden for the 1D calculations without essential loss of the accuracy. Two-level coarse mesh finite difference (CMFD) formulation comprising multigroup nodewise CMFD and twogroup assemblywise CMFD is employed as well to accelerate the convergence. Errors originating from the pinlevel homogenization, energy group condensation, and the use of lower order calculation methods are simultaneously corrected by the pinwise super homogenization (SPH) equivalence factor. The transient method is evaluated with OECD/NEA PWR MOX/UO2 benchmark. Code-to-code comparison with the nTRACER direct whole core calculation code yielded highly satisfactory results for the transient scenario as well as the steady-state problems. Furthermore, comparative analyses with conventional nodal calculations show superiority of the pin-by-pin calculation.

• Journal of the Earthquake Engineering Society of Korea
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• v.15 no.3
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• pp.27-35
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• 2011

Larbi (1995) and Jeong et al. (2005) analyzed the various boundary end conditions of buried pipelines using the mode superposition method as one of the dynamic analysis methods of buried pipelines. However, it is very complicated to derive calculation equations for the solutions to be obtained by this method, and even the derived calculation equations need separate computer programming for the numerical analysis in order to obtain the solutions. For this reason, this method is extremely difficult for engineers to apply in their field works. In consideration of the shortcoming of the mode superposition method, this study's purpose is to propose a 3D dynamic finite difference method, which is more easily applicable in the field. For this purpose, we tested the accuracy of the 3D dynamic analysis and compared the results with those of the mode superposition method and certified that the 3D dynamic analysis could be an alternative method to obtain the seismic responses of the pipelines.

• Journal of Korean Society of Steel Construction
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• v.12 no.3 s.46
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• pp.303-315
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• 2000

The main object of this study is to analyze mechanical behaviors as anisotropic three-dimensional body under various static loads. This paper presents the applicability of the finite difference method to three dimensional problem of anisotropic body. The finite difference method as applied here is generalized to anisotropic three-dimensional problem of elastic body where the governing differential equations of equilibrium of such bodies are expressed in terms of the displacement u, v, and w in the coordinates axes x, y and z, care being taken to modify the finite difference expressions to satisfy the appropriate boundary conditions. By adopting a new three dimensional finite difference modelling including elimination of pivotal difference points in the case of free boundary condition, the three dimensional problem of anisotropic body was successfully completed. Several numerical results show quick convergence and numerical validity of finite difference technique in three dimensional problem.