• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.405-413
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• 2001

The inverse boundary value problem for the steady state heat equation with convection term is considered in a simply connected bounded domain with smooth boundary. Taking the Dirichlet to Neumann map which maps the temperature on the boundary to the that flux on the boundary as an observation data, the global uniqueness for identifying the convection term from the Dirichlet to Neumann map is proved.

• Nuclear Engineering and Technology
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• v.49 no.5
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• pp.953-967
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• 2017

In this paper, a complete station blackout (SBO) or complete loss of electrical power supplies is simulated and analyzed in a downward cooling 5-MW pool-type Material Testing Reactor (MTR). The scenario is traced in the absence of active cooling systems and operators. The code nodalization is successfully benchmarked against experimental data of the reactor's operating parameters. The passive heat removal system includes downward water cooling after pump breakdown by the force of gravity (where the coolant streams down to the unfilled portion of the holdup tank), safety flapper opening, flow reversal from a downward to an upward cooling direction, and then the upward free convection heat removal throughout the flapper safety valve, lower plenum, and fuel assemblies. Both short-term and long-term natural core cooling conditions are simulated and investigated using the RELAP5 code. Short-term analyses focus on the safety flapper valve operation and flow reversal mode. Long-term analyses include simulation of both complete SBO and long-term operation of the free convection mode. Results are promising for pool-type MTRs because this allows operators to investigate RELAP code abilities for MTR thermal-hydraulic simulations without any oscillation; moreover, the Tehran Research Reactor is conservatively safe against the complete SBO and long-term free convection operation.

• East Asian mathematical journal
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• v.35 no.5
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• pp.569-587
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• 2019

In this paper, we consider a split least-squares characteristic mixed element method for Sobolev equations with a convection term. First, to manipulate both convection term and time derivative term efficiently, we apply a characteristic mixed element method to get the system of equations in the primal unknown and the flux unknown and then get a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares characteristic mixed element scheme for the given problem whose system is uncoupled in the unknowns. We prove the optimal order in $L^2$ and $H^1$ normed spaces for the primal unknown and the suboptimal order in $L^2$ normed space for the flux unknown.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.4
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• pp.291-306
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• 2011

We consider the second order Strang splitting method to approximate the solution to the KdV equation. The model equation is split into three sets of initial value problems containing convection and dispersal terms separately. TVD MUSCL or MUSCL scheme is applied to approximate the convection term and the second order centered difference method to approximate the dispersal term. In time stepping, explicit third order Runge-Kutta method is used to the equation containing convection term and implicit Crank-Nicolson method to the equation containing dispersal term to reduce the CFL restriction. Several numerical examples of weakly and strongly dispersive problems, which produce solitons or dispersive shock waves, or may show instabilities of the solution, are presented.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1279-1292
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• 2009

In this paper, a numerical method that uses standard finite difference scheme defined on Shishkin mesh for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a discontinuous source term is presented. An error estimate is derived to show that the method is uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented to illustrate the theoretical results.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.357-382
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• 2019

In this paper, we consider boundary value problem for a weakly coupled system of two singularly perturbed differential equations of convection diffusion type with discontinuous source term. In general, solution of this type of problems exhibits interior and boundary layers. A numerical method based on streamline diffusiom finite element and Shishkin meshes is presented. We derive an error estimate of order $O(N^{-2}\;{\ln}^2\;N$) in the maximum norm with respect to the perturbation parameters. Numerical experiments are also presented to support our theoritical results.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.113-131
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• 2024

In this paper we give conditions for the existence of, and describe the asymtotic behavior of, radial positive solutions of the nonlinear elliptic equation of Emden-Fowler type with convection term ∆_p u + 𝛼|u|^q-1u + 𝛽x.∇(|u|^q-1u) = 0 for x ∈ ℝ^N, where p > 2, q > 1, N ≥ 1, 𝛼 > 0, 𝛽 > 0 and ∆_p is the p-Laplacian operator. In particular, we determine ${\lim}_{r{\rightarrow}}{\infty}\,r^{\frac{p}{q+1-p}}\,u(r)$ when $\frac{{\alpha}}{{\beta}}$ > N > p and $q\,{\geq}\,{\frac{N(p-1)+p}{N-p}}$.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.19-34
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• 2016

In this paper, we present a split least-squares characteristic mixed finite element method(MFEM) to get the approximate solutions of the convection dominated Sobolev equations. First, to manage both convection term and time derivative term efficiently, we apply a least-squares characteristic MFEM to get the system of equations in the primal unknown and the flux unknown. Then, we obtain a split least-squares characteristic MFEM to convert the coupled system in two unknowns derived from the least-squares characteristic MFEM into two uncoupled systems in the unknowns. We theoretically prove that the approximations constructed by the split least-squares characteristic MFEM converge with the optimal order in L² and H¹ normed spaces for the primal unknown and with the optimal order in L² normed space for the flux unknown. And we provide some numerical results to confirm the validity of our theoretical results.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.3 no.5
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• pp.376-385
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• 1991

The purpose of this paper is to propose basic data on convection heat-transfer coefficients in Ondol-heated room. Surface temperatures and several temperatures around each inside surface of wall, floor and ceiling composed of heating room are measured vertically in Ondol-heated model rooms, and the vertical temperature profiles could be expressed by nonlinear equation models. Also, the convection heat transfer phenomena are analysed from the nonlinear equation models. In the results, the convection heat-transfer coefficients of Ondol heated space are suggested by the term of temperature difference between each wall surface and room air temperature and by the relationship between Nusselt number and Rayleigh number of dimensionless numbers.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1601-1606
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• 2004

In this paper, the unsteady behavior of the viscous flow field past an impulsively started elliptic cylinder is studied numerically. In order to analyze flow field, we introduce vortex particle method. The vorticity transport equation is solved by fractional step algorithm which splits into convection term and diffusion term. The convection term is calculated with Biot-Savart law, the no-through boundary condition is employed on solid boundaries. The diffusion term is modified based on the scheme of particle strength exchange. The particle redistributed scheme for general geometry is adapted. The flows around an elliptic cylinder are investigated for various attack angles at Reynolds number 200. The comparison between numerical results of present study and experimental data shows good agreements.