• Nuclear Engineering and Technology
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• v.50 no.3
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• pp.327-339
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• 2018

This article presents a new global-local hybrid coarse-mesh finite difference (HCMFD) method for efficient parallel calculation of pin-by-pin heterogeneous core analysis. In the HCMFD method, the one-node coarse-mesh finite difference (CMFD) scheme is combined with a nodal expansion method (NEM)-based two-node CMFD method in a nonlinear way. In the global-local HCMFD algorithm, the global problem is a coarse-mesh eigenvalue problem, whereas the local problems are fixed source problems with boundary conditions of incoming partial current, and they can be solved in parallel. The global problem is formulated by one-node CMFD, in which two correction factors on an interface are introduced to preserve both the surface-average flux and the net current. Meanwhile, for accurate and efficient pin-wise core analysis, the local problem is solved by the conventional NEM-based two-node CMFD method. We investigated the numerical characteristics of the HCMFD method for a few benchmark problems and compared them with the conventional two-node NEM-based CMFD algorithm. In this study, the HCMFD algorithm was also parallelized with the OpenMP parallel interface, and its numerical performances were evaluated for several benchmarks.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.03b
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• pp.467-474
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• 2000

The application of Terzaghi's theory of consolidation for analysing the settlement of multi-layered soils is not strictly valid because the theory involves an assumption that the soil is homogeneous. The settlement of stratified soils with confined aquifer can be analysed using numerical techniques whereby the governing differential equation is replaced by 2-dimensional finite difference approximations. The problems of discontinuous layer interface are very important in the algorithm and programming for the analysis of multi-layered consolidation using a numerical analysis, finite difference method(F.D.M.). Better results can be obtained by the process for discontinuous layer interface, since it can help consolidation analysis to model the actual ground The purpose of this paper provides an efficient computer algorithm based on numerical analysis using finite difference method(F.D.M) which account for multi-layered soils with confined aquifer to determine the degree of consolidation and excess pore pressures relative to time and positions more realistically.

• Journal of Advanced Marine Engineering and Technology
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• v.18 no.3
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• pp.94-101
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• 1994

To develope the new simulator for the analysis of fluid flow information, the influence of various convective difference schemes were evaluated. General curvilinear coordinate system with nonorthogonal grids was adopted for the successful analysis of various complex geometries. Computation results show that if we can not obtain full grid numbers within available computational environment, we need to use higher order finite difference schemes to keep the prediction accuracy.

• Steel and Composite Structures
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• v.19 no.3
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• pp.679-695
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• 2015

A numerical solution using finite difference method to evaluate the thermal buckling of simply supported FGM plate with variable thickness is presented in this research. First, the governing differential equation of thermal stability under uniform temperature through the plate thickness is derived. Then, the governing equation has been solved using finite difference method. After validating the presented numerical method with the analytical solution, the finite difference formulation has been extended in order to include variable thickness. The accuracy of the finite difference method for variable thickness plate has been also compared with the literature where a good agreement has been found. Furthermore, a parametric study has been conducted to analyze the effect of material and geometric parameters on the thermal buckling resistance of the FGM plates. It was found that the thickness variation affects isotropic plates a bit more than FGM plates.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.91-98
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• 2005

The straight rectangular fin is analyzed using the one-dimensional analytic method and the finite difference method. For the finite difference method, the numbers of nodes vary from 20 to 100. The relative errors of heat loss and temperature between the analytic method and the finite difference method are represented as a function of Biot Number and dimensionless fin length. One of the results shows that the relative error between the analytic method and the finite difference method decreases as the numbers of nodes for finite difference method increase.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.10
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• pp.2724-2730
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• 1996

In this paper, the dispersive characteristics of the Finite-Difference Frqequency-Domain method based on the Multi-Resolution Technique(MR-FDFD) are numerically analyzed. A dispersion analysis of the MR-FDFD ority of the MR-FDFD method to the spatial discretization is shown. We expect that the multi-resoluation technique will improve the disavantage of the finite difference techqnique which needs the large comutational memory for accurate electromagnetic analysis.

• Structural Engineering and Mechanics
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• v.31 no.4
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• pp.383-392
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• 2009

The static and dynamic analyses of simply supported beams are studied by using the U-transformation method and the finite difference method. When the beam is divided into the mesh of equal elements, the mesh may be treated as a periodic structure. After an equivalent cyclic periodic system is established, the difference governing equation for such an equivalent system can be uncoupled by applying the U-transformation. Therefore, a set of single-degree-of-freedom equations is formed. These equations can be used to obtain exact analytical solutions of the deflections, bending moments, buckling loads, natural frequencies and dynamic responses of the beam subjected to particular loads or excitations. When the number of elements approaches to infinity, the exact error expression and the exact convergence rates of the difference solutions are obtained. These exact results cannot be easily derived if other methods are used instead.

• Journal of the Korea institute for structural maintenance and inspection
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• v.9 no.4
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• pp.159-168
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• 2005

This study carries out a finite difference nonlinear analysis of anisotropic advanced composite plate structures with various layer sequences. In the numerical analysis of various mechanical problems involving complex partial differential equations, the finite difference method (FDM) developed in this study has an advantage over the finite element method in its ability to avoid mesh generation and numerical integration. Many studies in FDM have been made on clamped or simple boundary conditions using merely an energy approach. These approaches cannot be satisfied, however, with pivotal points along the free boundary. Therefore, this study addresses the nonlinear problem of anisotropic plates by adopting a finite difference modeling elimination of pivotal difference points in the case of a free boundary condition. Complex nonlinear behaviors of composite plate structures for various parameters, especially for layer sequences, are analyzed using the proposed approach.

• Journal of KSNVE
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• v.8 no.2
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• pp.267-273
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• 1998

This study aims at performing sensitivity analysis of piezoelectric smart structure for minimizing radiated noise from the structure, The structure consists of a flat plate on which disk shaped piezoelectric actuator is mounted, and finite element modeling is used for the structure. The finite element modeling uses a combination of three dimensional piezoelectric, flat shell and transition elements so thus it can take into account the coupling effects of the piezoelectric device precisely and it can also reduce the degrees of freedom of the finite element model. Electric potential on the piezoelectric actuator is taken as a design variable and total radiated power of the structure is chosen as an objective function. The objective function can be represented as Rayleigh's integral equation and is a function of normal displacements of the structure. For the convenience of computation, all degrees of freedom of the finite element equation is condensed out except the normal displacements of the structure. To perform the design sensitivity analysis, the derivative of the objective function with respect to the normal displacements is found, and the derivative of the norma displacements with respect to the design variable is calculated from the finite element equation by using so called the adjoint variable method. The analysis results are compared with those of the finite difference method, and shows a good agreement. This sensitivity analysis is faster and more accurate than the finite difference method. Once the sensitivity analysis program is used for gradient-based optimizations, one could achieve a better convergence rate than non-derivative methods for optimal design of piezoelectric smart structures.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.27 no.6
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• pp.782-786
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• 1994

Integrated finite difference method (IFDM) is used to solve one dimensional free oscillation problem in the coastal area. To evaluate the solution accuracy of IFDM in free oscillation analysis, two finite difference equations based on area discretization method and point discretization method are derived from the governing equations of free oscillation, respectively. The difference equations are transformed into a generalized eigenvalue problem, respectively. A numerical example is presented, for which the analytical solution is available, for comparing IFDM to conventional finite difference equation (CFDM), qualitatively. The eigenvalue matrices are solved by sub-space iteration method. The numerical results of the two methods are in good agreement with analytical ones, however, IFDM yields better solution than CFDM in lower modes because IFDM only includes first order differential operator in finite difference equation by Green's theorem. From these results, it is concluded that IFDM is useful for the free oscillation analysis in the coastal area.