• Nuclear Engineering and Technology
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• 제13권2호
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• pp.73-84
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• 1981

B$\Phi$rrensen은 3차원적 노심분석에 긴 시간이 요구되는 유한차분법의 대안으로서 경수형 원자로의 전체출력분포를 계산하는데 한가지의 coarse mesh 방법을 제안하였다. 이 방법은 계산시간이 매우 짧은 것으로 알려져 있지만. 그 계산의 정확도에 대한 것은 아직까지 알려져 있지 않다. 본 논문에서는 B$\Phi$rrensen의 방법을 IAEA benchmark 문제와 RIS$\Phi$ benchmark 문제에 적용시켜서 계산시간과 정확도에 대해서 고찰하였다. 두 문제에서 노심-반사체와의 경계조건과 B$\Phi$rrensen의 모델상수들의 개선으로 출력분포 계산의 정확도를 상당히 높힐 수 있었다.

• 한국항공운항학회지
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• 제23권2호
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• pp.69-74
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• 2015

We propose a rigorous and practical methodology to evaluate the performance of symbolic manipulation program such as Mathematica, Maple, and Maxima. First, we demonstrate an inverse method to construct the benchmark problems of an initial value problems. The benchmark problems associated with the discrete version of the Chebyshev polynomials provide a rigorous and objective measure to evaluate the performance of symbolic manipulation programs. We compare three symbolic manipulation programs, which are Mathematica, Maple and Maxima, using this methodology. The computation time, the used memory and the perturbation terms are chosen for comparison parameters.

• International Journal of Aeronautical and Space Sciences
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• 제3권2호
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• pp.46-58
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• 2002

An inverse method is introduced to construct benchmark problems for the numerical solution of initial value problems. Benchmark problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The solution is constructed such that it lies near a given approximate numerical solution, and therefore the special case solution can be generated in a versatile and physically meaningful fashion and can serve as a benchmark problem to validate approximate solution methods. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. A multi-variable orthogonal function expansion method and computer symbol manipulation are successfully used for this process. Using this special case exact solution, it is possible to directly investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given code and a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution. Illustrative examples show the utility of this method not only for the ordinary differential equations (ODEs) but for the partial differential equations (PDEs).

• Nuclear Engineering and Technology
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• 제51권1호
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• pp.13-30
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• 2019

This paper presents the recent improvements in the DeCART code for HTGR analysis. A new 190-group DeCART cross-section library based on ENDF/B-VII.0 was generated using the KAERI library processing system for HTGR. Two methods for the eigen-mode adjoint flux calculation were implemented. An azimuthal angle discretization method based on the Gaussian quadrature was implemented to reduce the error from the azimuthal angle discretization. A two-level parallelization using MPI and OpenMP was adopted for massive parallel computations. A quadratic depletion solver was implemented to reduce the error involved in the Gd depletion. A module to generate equivalent group constants was implemented for the nodal codes. The capabilities of the DeCART code were improved for geometry handling including an approximate treatment of a cylindrical outer boundary, an explicit border model, the R-G-B checker-board model, and a super-cell model for a hexagonal geometry. The newly improved and implemented functionalities were verified against various numerical benchmarks such as OECD/MHTGR-350 benchmark phase III problems, two-dimensional high temperature gas cooled reactor benchmark problems derived from the MHTGR-350 reference design, and numerical benchmark problems based on the compact nuclear power source experiment by comparing the DeCART solutions with the Monte-Carlo reference solutions obtained using the McCARD code.

• Nuclear Engineering and Technology
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• 제50권7호
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• pp.1024-1036
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• 2018

In this paper, McCARD code was verified using various models listed in the NUREG/CR-6361 benchmark guide, which provides specifications for single pin-cells, single assemblies, and the whole core classified depending on the nuclear properties and structural characteristics. McCARD code was verified by comparing its results with those of SCALE code for single pin-cell and single assembly benchmark problems. The difference in the multiplication factor obtained through the two codes did not exceed 90 pcm. The benchmark guide treats a total of 173 whole core experiments. The experiments are categorized as simple lattices, separator plates, reflecting walls, reflecting walls and separator plates, burnable absorber fuel rods, water holes, poison rods, and borated moderator. As a result of numerical simulation using McCARD, the mean value of the multiplication factors is 1.00223 and the standard deviation of the multiplication factors is 285 pcm. The difference between the multiplication factors and the experimental value is in the range of -665 pcm to + 1609 pcm. In addition, statistics of results for experiments categorized by reactor shape, additional structure, burnable poison, etc., are detailed in the main text.

• Nuclear Engineering and Technology
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• 제52권11호
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• pp.2422-2430
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• 2020

In order to improve calculational efficiency of the CAPP code in the analysis of the hexagonal reactor core, we have tried to implement a refined AFEN method with transverse gradient basis functions and interface flux moments in the hexagonal geometry. The numerical scheme for the refined AFEN method adopted here is the response matrix method that uses the interface partial currents as nodal unknowns instead of the interface fluxes used in the original AFEN method. Since the response matrix method is single-node based, it has good properties such as good calculational efficiency and parallel computing affinity. Because a refined AFEN method equivalent nonlinear FDM response matrix method tried first could not provide a numerically stable solution, a direct formulation of the refined AFEN response matrix were developed. To show the numerical performance of this response matrix method against the original AFEN method, the numerical error analyses were performed for several benchmark problems including the VVER-440 LWR benchmark problem and the MHTGR-350 HTGR benchmark problem. The results showed a more than three times speedup in computing time for the LWR and HTGR benchmark problems due to good convergence and excellent calculational efficiency of the refined AFEN response matrix method.

• 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.

• 한국IT서비스학회지
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• 제5권3호
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• pp.99-108
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• 2006

Public institutions are considering adoption of open-source software in the process of information projects. However, there doesn't exist reliable information about an adoption process for open-source software. Performance and stability problems of this software also persist, as a result, current open-source software is not widely used. As a software market and industry grows, Benchmark test has been performed more often than before in order to help customers understand and select the most appropriate product among myriad similar ones. It is certain that more objective and trustful data evidence should be obtained by way of utilizing the procedures and methods of Benchmark Test in decision making process for selecting an open-source software. For this research, Benchmark test was applied as a way of demonstrating performance verification of an open-source software in the public institutions. It is certain that more objective and trustful data evidence should be obtained by way of utilizing the procedures and methods of Benchmark Test in decision making process for selecting an open-source software. It also introduces a case study of a information system, which selected and implemented open-source software, in order to confirm the validity of this research. This research will serve as a guideline to adopt open-source software in governments as well as public institutions.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1997년도 춘계학술발표회논문집(1)
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• pp.39-44
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• 1997

The International Criticality Safety Benchmark Evaluation Project (ICSBEP) is under way for the purpose identifying, evaluating, and compiling benchmark critical experiment data into a standardized format that allows criticality analysts to easily use the data to validate calculational methods and cross sections. As part of this activity, PNL30-35 experiments, which had been adopted as benchmark problems by CSEWG in 1970s, were reevaluated, which results in some additions and modifications: changes in fuel number density, modification to the experimental keff, modifications to the soluble boron concentration for PNL-31, and addition of an uncertainty in the benchmark-model k$_{eff}$./.

• Structural Engineering and Mechanics
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• 제68권1호
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• pp.17-38
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• 2018

In this paper, we compare and assess the performance of the standard 3- and 6-node MITC shell elements (Lee and Bathe 2004) with the recently developed MITC triangular elements (Lee et al. 2014, Jeon et al. 2014, Jun et al. 2018) which were based on the partitions of unity approximation, bubble node, or both. The convergence behavior of the shell elements are measured in well-known benchmark tests; four plane stress tests (mesh distortion test, cantilever beam, Cook's skew beam, and MacNeal beam), two plate tests (Morley's skew plate and circular plate), and six shell tests (curved beam, twisted beam, pinched cylinder, hemispherical shells with or without hole, and Scordelis-Lo roof). To precisely compare and evaluate the solution accuracy of the shell elements, different triangular mesh patterns and distorted element mesh are adopted in the benchmark problems. All shell finite elements considered pass the basic tests; namely, the isotropy, the patch, and the zero energy mode tests.