• International Journal of Aeronautical and Space Sciences
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• v.3 no.2
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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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• v.55 no.10
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• pp.3639-3647
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• 2023

This paper defines a 3D full core neutronics benchmark which is based on the NuScale small modular reactor (SMR) concept. The paper provides a detailed description of the NuScale-like core, a list of expected outputs, and a reference solution to the benchmark exercises obtained with the Monte Carlo code Serpent. The benchmark was developed in the framework of the Euratom McSAFER project and can be used for verification of computational chains dedicated to 3D full-core neutronics simulations of water cooled SMRs. The paper is supplemented with a digital data set to ease the modeling process.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1326-1338
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• 2017

The continuous energy Monte Carlo neutron transport code, MC21, was coupled to the CTF subchannel thermal-hydraulics code using a combination of Consortium for Advanced Simulation of Light Water Reactors (CASL) tools and in-house Python scripts. An MC21/CTF solution for VERA Core Physics Benchmark Progression Problem 6 demonstrated good agreement with MC21/COBRA-IE and VERA solutions. The MC21/CTF solution for VERA Core Physics Benchmark Progression Problem 7, Watts Bar Unit 1 at beginning of cycle hot full power equilibrium xenon conditions, is the first published coupled Monte Carlo neutronics/subchannel T-H solution for this problem. MC21/CTF predicted a critical boron concentration of 854.5 ppm, yielding a critical eigenvalue of $0.99994{\pm}6.8E-6$ (95% confidence interval). Excellent agreement with a VERA solution of Problem 7 was also demonstrated for integral and local power and temperature parameters.

• Nuclear Engineering and Technology
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• v.27 no.3
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• pp.374-384
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• 1995

The mathematical adjoint solution of the Analytic Function Expansion (AFEN) method is found by solving the transposed matrix equation of AFEN nodal equation with only minor modification to the forward solution code AFEN. The perturbation calculations are then performed to estimate the change of reactivity by using the mathematical adjoint The adjoint calculational scheme in this study does not require the knowledge of the physical adjoint or the eigenvalue of the forward equation. Using the adjoint solutions, the exact and first-order perturbation calculations are peformed for the well-known benchmark problems (i.e., IAEA-2D benchmark problem and EPRI-9R benchmark problem). The results show that the mathematical adjoint flux calculated in the code is the correct adjoint solution of the AFEN method.

• Structural Engineering and Mechanics
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• v.68 no.1
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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.

• Structural Engineering and Mechanics
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• v.38 no.6
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• pp.767-802
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• 2011

Developers of new finite elements or nonlinear solution techniques rely on discriminative benchmark tests drawn from the literature to assess the advantages and drawbacks of new formulations. Buckling benchmark tests provide a rigorous evaluation of finite elements applied to thin structures, and a complete and detailed set of reference results would therefore prove very useful in carrying out such evaluations. Results are usually presented in the form of load-deflection curves that developers must reconstruct by extracting the points, a procedure which is often tedious and inaccurate. Moreover the curves are usually given without accompanying information such as the calculation time or number of iterations it took for the model to converge, even though this type of data is equally important in practice. This paper presents ten different limit-point buckling benchmark tests, and provides for each one the reference load-deflection curve, all the points necessary to recreate the curve in tabulated form, analysis data such as calculation time, number of iterations and increments, and all of the inputs used to obtain these results.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.59
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• pp.11-20
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• 2000

The Job Shop Scheduling Problem(JSSP) is one of the most general and difficult of all traditional scheduling problems. The goal of this research is to develop an efficient scheduling method based on single genetic algorithm(SGA) and parallel genetic algorithm (PGA) to address JSSP. In this scheduling method, new genetic operator, generating method of initial population are developed and island model PGA are proposed. The scheduling method based on PGA are tested on standard benchmark JSSP. The results were compared with SGA and another GA-based scheduling method. The PGA search the better solution or improves average of solution in benchmark JSSP. Compared to traditional GA, the proposed approach yields significant improvement at a solution.

• Journal of Mechanical Science and Technology
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• v.15 no.6
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• pp.752-763
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• 2001

Although there are many different solution schemes proposed for multidimensional radiative transfer, reference solutions to benchmark these methods are very rare in the literature. In this paper we produced some accurate solutions for purely absorbing gray and nongray gases including H$_2$O and CO$_2$by using the discrete transfer method with sufficiently accurate T(sub)95 quadrature set. The spectral transmittances of the mixtures of H$_2$O and CO$_2$are estimated by using the narrow band model. The gray gas solutions are obtained for different absorption coefficients, and the nongray real gas solutions are obtained for different mixture fractions of H$_2$O and CO$_2$. The numerical solutions presented in this paper are proved to be sufficiently accurate as compared to the available exact solutions and they may be used as reference solutions in evaluating various solution schemes.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.18 no.9
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• pp.722-728
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• 2006

Natural convection flows in a cubical air-filled slanted cavity that has one pair of opposing faces isothermal at different temperatures, $T_h\;and\;T_c$, respectively, the remaining four faces having a linear variation from $T_c\;toT_h$ are numerically simulated by a solution code (PowerCFD) using unstructured cell-centered method. Special attention is paid to three-dimensional flow and thermal characteristics according to a new orientation (diamond type) for the cubical-cavity benchmark problem in natural convection. Comparisons of the average Nusselt number at the cold face are made with experimental benchmark solutions found in the literature. It is found that the code is capable of producing accurately the nature of the laminar convection in a cubical air-filled slanted cavity with differentially heated walls.

• Smart Structures and Systems
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• v.10 no.4_5
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• pp.427-442
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• 2012

An effective approach for updating finite element model is presented which can provide reliable estimates for structural updating parameters from identified operational modal data. On the basis of the dynamic perturbation method, an exact relationship between the perturbation of structural parameters such as stiffness change and the modal properties of the tested structure is developed. An iterative solution procedure is then provided to solve for the structural updating parameters that characterise the modifications of structural parameters at element level, giving optimised solutions in the least squares sense without requiring an optimisation method. A regularization algorithm based on the Tikhonov solution incorporating the generalised cross-validation method is employed to reduce the influence of measurement errors in vibration modal data and then to produce stable and reasonable solutions for the structural updating parameters. The Canton Tower benchmark problem established by the Hong Kong Polytechnic University is employed to demonstrate the effectiveness and applicability of the proposed model updating technique. The results from the benchmark problem studies show that the proposed technique can successfully adjust the reduced finite element model of the structure using only limited number of frequencies identified from the recorded ambient vibration measurements.