• 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).

• Journal of the Geological Society of Korea
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• v.54 no.6
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• pp.683-694
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• 2018

Subduction has been the focal point of numerical studies for decades because it plays an important role in the Earth's mass and energy circulations and generates earthquakes and arc volcanoes which are closely related to the human lives. Among the studies on subduction, numerical modeling has been broadly applied to the quantitative studies on the subducting slab in the mantle which cannot be directly observed. In this study, we benchmark the numerical subduction modeling using a finite element package, COMSOL $Multiphysics^{(R)}$ and the results are consistent with the previously reported benchmark results.

• Nuclear Engineering and Technology
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• v.52 no.11
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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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• v.51 no.1
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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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• v.53 no.3
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• pp.752-762
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• 2021

The Smoothed Particle Hydrodynamics is one of the most widely used mesh-free numerical method for thermo-fluid dynamics. Due to its Lagrangian nature and simplicity, it is recently gaining popularity in simulating complex physics with large deformations. In this study, the 3D single/two-phase numerical simulations are performed on the Liquid Metal Reactor (LMR) centralized sloshing benchmark experiment using the SPH parallelized using a GPU. In order to capture multi-phase flows with a large density ratio more effectively, the original SPH density and continuity equations are re-formulated in terms of the normalized-density. Based upon this approach, maximum sloshing height and arrival time in various experimental cases are calculated by using both single-phase and multi-phase SPH framework and the results are compared with the benchmark results. Overall, the results of SPH simulations show excellent agreement with all the benchmark experiments both in qualitative and quantitative manners. According to the sensitivity study of the particle-size, the prediction accuracy is gradually increasing with decreasing the particle-size leading to a higher resolution. In addition, it is found that the multi-phase SPH model considering both liquid and air provides a better prediction on the experimental results and the reality.

• Korean Management Science Review
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• v.29 no.3
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• pp.1-11
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• 2012

This paper considers a localization problem in time difference of arrival (TDOA)-based radio frequency identification (RFID) systems. To estimate the position of a target tag, this paper suggests three localization algorithms that use benchmark tags. The benchmark tags are the same type as the target tag, but either the locations or distance of the benchmark tags are known. Two algorithms use the benchmarks for auxiliary information to improve the estimation accuracy of the other localization algorithms such as least squared estimator (LSE). The other one utilizes the benchmarks as essential tags to estimate the location. Numerical tests show that the localization accuracy can be improved by using benchmark tags especially when an algorithm using the LSE is applied to the localization problem. Furthermore, this paper shows that our benchmark algorithm is valuable when the measurement noise is large.

• Tunnel and Underground Space
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• v.34 no.2
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• pp.127-142
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• 2024

The robustness of a numerical method means that its computational performance is maintained under various modeling conditions. New numerical methods or codes need to be assessed for robustness through benchmark testing. The TOUGH-FLAC modeling approach has been applied to various fields such as subsurface carbon dioxide storage, geological disposal of spent nuclear fuel, and geothermal development both domestically and internationally, and the modeling validity has been examined by comparing the results with experimental measurements and other numerical codes. In the present study, a benchmark test of the TOUGH-FLAC approach was performed based on a coupled thermal-hydro-mechanical behavior problem with an analytical solution. The analytical solution is related to the temperature, pore water pressure, and mechanical behavior of a fully saturated porous medium that is subjected to a point heat source. The robustness of the TOUGH-FLAC approach was evaluated by comparing the analytical solution with the results of numerical simulation. Additionally, the effects of thermal-hydro-mechanical coupling terms, fluid phase change, and timestep on the computation of coupled behavior were investigated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.110-117
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• 2004

The aim of a benchmark study is carried out nine methods are employed for ULS analysis which implicitly predict the ultimate strength of aluminium stiffened panels under axial compression. For this purpose, DNV PULS, experimental and numerical data on the ultimate strength of panels were collected. Comparison of these experimental / numerical, DNV PULS / numerical, results with theoretical solutions by the candidate methods is performed. Also it's compared that ALPS/ULSAP program is based on closed-form formula for the ULS of plates and grillages under axial compression. It is considered that ALPS/ULSAP methodology provides quite accurate and reasonable ULS calculations by a comparison with more refined FEA. Comparison of these experimental data, numerical, computational software results with the simplified solutions obtained by the candidate methods is then performed. The model uncertainties associated with the candidate methods are studied in terms of mean bias and COV (i.e., coefficient of variation) against experiments and numerical solutions, and the relative performance of the various methods is discussed.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.37 no.6
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• pp.973-980
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• 2017

The purpose of this study is to develop VDFT (Visual Basic based Density-coupled Flow and Transport), a numerical modeling code used to simulate density coupled flow equations used to simulate seawater intrusion in a two dimensional finite difference method. The VDFT code has the advantage of being intuitive and simple to use and has the advantage of utilizing the EXCEL Visual Basic platform, which is widely used for general business purposes. Generally, code developed for numerical simulation can be verified through representative example models called benchmark problem. In this study, we verified the VDFT code using benchmark problem called Henry Problem and Modified Henry Problem as well as two laboratory test data. The results of this study are analyzed the importance of each benchmark problems, validated VDFT code compared to those problems. In conclusion, the possibility of using VDFT code is diagnosed and the direction of future research is suggested.

• Nuclear Engineering and Technology
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• v.50 no.7
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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.