• Journal of the Korean Data and Information Science Society
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• v.11 no.1
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• pp.103-110
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• 2000

Suppose that there is a population of hidden objects of which the total number N is unknown. From such data, we derive second-order approximations to the stopping time with fixed proportional accuracy.

• Journal of computational fluids engineering
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• v.10 no.1
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• pp.99-106
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• 2005

Performance of first, second and third order accurate methods for calculation of in viscid fluxes in fluid flow governing equations are investigated here. For the purpose, an upwind method based on Roe's scheme is used to solve 2-dimensional Euler equations. To increase the accuracy of the method two different schemes are applied. The first one is a second and third order upwind-based algorithm with the MUSCL extrapolation Van Leer (1979), based on primitive variables. The other one is an upwind-based algorithm with the Chakravarthy extrapolation to the fluxes of mass, momentum and energy. The results show that the thickness of shock layer in the third order accuracy is less than its value in second order. Moreover, applying limiter eliminates the oscillations near the shock while increases the thickness of shock layer especially in MUSCL method using Van Albada limiter.

• Journal of Electrical Engineering and Technology
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• v.8 no.4
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• pp.780-786
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• 2013

In the reliability-based design optimization of electromagnetic devices, the accurate and efficient reliability assessment method is very essential. The first-order sensitivity-assisted Monte Carlo Simulation is proposed in the former research. In order to improve its accuracy for wide application, in this paper, the second-order sensitivity analysis is presented by using the hybrid direct differentiation-adjoint variable method incorporated with the finite element method. By combining the second-order sensitivity with the Monte Carlo Simulation method, the second-order sensitivity-assisted Monte Carlo Simulation algorithm is proposed to implement reliability calculation. Through application to one superconductor magnetic energy storage system, its accuracy is validated by comparing calculation results with other methods.

• Nuclear Engineering and Technology
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• v.53 no.5
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• pp.1391-1402
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• 2021

The aim of this work is to prepare a neutron noise calculator based on the second order of average current nodal expansion method (ACNEM). Generally, nodal methods have the ability to fulfill the neutronic analysis with adequate precision using coarse meshes as large as a fuel assembly size. But, for the zeroth order of ACNEM, the accuracy of neutronic simulations may not be sufficient when coarse meshes are employed in the reactor core modeling. In this work, the capability of second order ACNEM is extended for solving the neutron diffusion equation in the frequency domain using coarse meshes. For this purpose, two problems are modeled and checked including a slab reactor and 2D BIBLIS PWR. For validating of results, a semi-analytical solution is utilized for 1D test case, and for 2D problem, the results of both forward and adjoint neutron noise calculations are exploited. Numerical results indicate that by increasing the order of method, the errors of frequency dependent coarse mesh solutions are considerably decreased in comparison to the reference. Accordingly, the accuracy of second order ACNEM can be acceptable for the neutron noise calculations by using coarse meshes in the nuclear reactor core.

• Ocean Science Journal
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• v.40 no.4
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• pp.201-208
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• 2005

An accurate particle tracking method for a finite difference method model is developed using a constant acceleration method. Being assumed constant temporal and spatial gradients, the new method permits temporal-spatial variability of particle velocity. Test results in a solid rotating flow show that the new method has second-order accuracy. The performance of the new method is compared with that of other methods; the first-order Euler forward method, and the second-order Euler predictor-corrector method. The new method is the most efficient method among the three. It is more accurate and efficient than the other two.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.410-415
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• 2001

An analytical and numerical examination of second-order fractional-step methods and boundary condition for the incompressible Navier-Stokes equations is presented. In this study, the compatibility condition for pressure Poisson equation and its boundary conditions, stability, and numerical accuracy of canonical fractional-step methods has been investigated. It has been found that satisfaction of compatibility condition depends on tentative velocity and pressure boundary condition, and that the compatible boundary conditions for type D method and approximately compatible boundary conditions for type P method are proper for divergence-free velocity for type D and approximately divergence-free for type P method. Instability of canonical fractional-step methods is induced by approximation of implicit viscous term with explicit terms, and the stability criteria have been founded with simple model problems and numerical experiments of cavity flow and Taylor vortex flow. The numerical accuracy of canonical fractional-step methods with its consistent boundary conditions shows second-order accuracy except $D_{MM}$ condition, which make approximately first-order accuracy due to weak coupling of boundary conditions.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.05b
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• pp.1063-1067
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• 2005

A second-order accuracy upwind scheme is used to investigate the run-up heights of tsunamis in the East Sea and the predicted results are compared with field observed data and results of a first-order accuracy upwind scheme, In the numerical model, the governing equations solved by the finite difference scheme are the linear shallow-water equations in deep water and nonlinear shallow-water equations in shallow water The target events is 1993 Hokktaido Nansei Oki Tsunami. The predicted results represent reasonably the run-up heights of tsunamis in the East Sea. And, The results of simulation is used to design inundation map.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.46.1-46.1
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• 2019

We present an accurate and efficient method to calculate the gravitational potential of an isolated system in three-dimensional Cartesian and cylindrical coordinates subject to vacuum (open) boundary conditions. Our method consists of two parts: an interior solver and a boundary solver. The interior solver adopts an eigenfunction expansion method together with a tridiagonal matrix solver to solve the Poisson equation subject to the zero boundary condition. The boundary solver employs James's method to calculate the boundary potential due to the screening charges required to keep the zero boundary condition for the interior solver. A full computation of gravitational potential requires running the interior solver twice and the boundary solver once. We develop a method to compute the discrete Green's function in cylindrical coordinates, which is an integral part of the James algorithm to maintain second-order accuracy. We implement our method in the {\tt Athena++} magnetohydrodynamics code, and perform various tests to check that our solver is second-order accurate and exhibits good parallel performance.

• Journal of the Society of Naval Architects of Korea
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• v.58 no.3
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• pp.182-190
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• 2021

Computational simulations of turbulent flows around a model ship have been performed to investigate an influence of TVD schemes on the accuracy of advective terms associated with ship resistances. Several TVD schemes including upwind, second-order upwind, vanLeer, and QUICK as well as a nonTVD linear scheme were studied by examining temporal and spatial characteristics of accuracy transition in adjacent cells to the hull. Even though vanLeer scheme was the most accurate among TVD schemes in both structured and unstructured grid systems, the ratio of accuracy switch from 2^nd order to 1^st order in vanLeer scheme was considerable compared with the 2^nd order linear scheme. Also, the accuracy transition was observed to be overally scattered in the unstructured grid while the accuracy transition in the structured grid appeared relatively clustered. It concluded that TVD schemes had to be carefully used in computational simulations of turbulent flows around a model ship due to the loss of accuracy despite its attraction of numerical stability.

• Structural Engineering and Mechanics
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• v.35 no.5
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• pp.631-643
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• 2010

A numerical procedure for the geometrical and material nonlinear analysis of concrete beams prestressed with external tendons is described, where the effects of external prestressing are treated as the equivalent loads applied on the concrete beams. The geometrical nonlinearity is considered not only the eccentricity variations of external tendons (second-order effects) but also the large displacement effects of the structure. The numerical method can predict the nonlinear response of externally prestressed concrete beams throughout the entire loading history with considerable accuracy. An evaluation of second-order effects of externally prestressed concrete beams is carried out using the proposed analysis. The analysis shows that the second-order effects have significant influence on the response characteristics of externally prestressed concrete beams. They lead to inferior ultimate load and strength capacities and a lower ultimate stress increase in tendons. Based on the current analysis, it is recommended that, for simply-supported externally prestressed beams with straight horizontal tendons, one deviator at midspan instead of two deviators at one-third span be furnished to minimize these effects.