• Nuclear Engineering and Technology
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• v.28 no.3
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• pp.311-319
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• 1996

We reconstruct the assembly pinwise flux using several types of boundary conditions and confirm that the reconstructed fluxes are the same with the reference flux if the boundary condition is exact. We test EPRI-9R benchmark problem with four boundary conditions, such as Dirichlet boundary condition, Neumann boundary condition, homogeneous mixed boundary condition (albedo type), and inhomogeneous mixed boundary condition. We also test reconstruction of the pinwise flux from nodal values, specifically from the AFEN [1, 2] results. From the nodal flux distribution we obtain surface flux and surface current distributions, which can be used to construct various types of boundary conditions. The result show that the Neumann boundary condition cannot be used for iterative schemes because of its ill-conditioning problem and that the other three boundary conditions give similar accuracy. The Dirichlet boundary condition requires the shortest computing time. The inhomogeneous mixed boundary condition requires only slightly longer computing time than the Dirichlet boundary condition, so that it could also be an alternative. In contrast to the fixed-source type problem resulting from the Dirichlet, Neumann, inhomogeneous mixed boundary conditions, the homogeneous mixed boundary condition constitutes an eigenvalue problem and requires longest computing time among the three (Dirichlet, inhomogeneous mixed, homogeneous mixed) boundary condition problems.

• International Journal of Aeronautical and Space Sciences
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• v.6 no.1
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• pp.1-7
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• 2005

The inlet boundary condition of computations about the supersonic turbine flow is commonly applied as far-field inlet boundary condition with specified velocity. However, the inflow condition of supersonic turbine is sometimes affected by the shocks or expansion waves propagated from leading edges of blade. These shocks and expansion waves alter the inlet boundary condition. In this case, the inlet boundary condition can not be specified Therefore, in this paper, numerical analyses for three different inlet conditions - fa-field inlet boundary condition, inlet boundary condition with a linear nozzle and inlet boundary condition with a converging-diverging nozzle - have been performed and compared with experimental results to solve the problem. It is found that the inlet condition with a linear nozzle or a converging-diverging nozzle can prevent changing of inlet boundary condition, and thus predict more accurately the supersonic flow within turbine cascade than a far-field inlet boundary condition does.

• East Asian mathematical journal
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• v.32 no.5
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• pp.621-633
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• 2016

We establish the existence of positive solutions to nonlocal boundary value problems with integral boundary condition and non-negative real boundary parameter by mainly using the Schauder-Fixed point theorem.

• Journal of computational fluids engineering
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• v.21 no.1
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• pp.10-18
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• 2016

Numerical boundary conditions are as important as the governing equations when analyzing the fluid flows numerically. An explicit boundary condition method updates the solutions at the boundaries with extrapolation from the interior of the computational domain, while the implicit boundary condition method in conjunction with an implicit time integration method solves the solutions of the entire computational domain including the boundaries simultaneously. The implicit boundary condition method, therefore, is more robust than the explicit boundary condition method. In this paper, steady compressible 2-Dimensional Navier-Stokes solver is developed. We present the implicit boundary condition method coupled with LU-SGS(Lower Upper Symmetric Gauss Seidel) method. Also, the explicit boundary condition method is implemented for comparison. The preconditioning Navier-Stokes equations are solved on unstructured meshes. The numerical computations for a number of flows show that the implicit boundary condition method can give accurate solutions.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.637-647
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• 1999

In this paper, we consider a free boundary problem with Pushchino dynamics satisfying the Dirichlet boundary condition. We shall the stationary solutions ($v^{*}(x),s^{*}$) exist and the Hopf bifurcation occurs at a critical point when s $\in$ (1/3,1).

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.7 s.262
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• pp.620-627
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• 2007

In this paper, we adapt a modified internal energy non-equilibrium first-order extrapolation thermal boundary condition to the thermal lattice Boltzmann model (TLBM). This model is the double populations approach to simulate hydrodynamic and thermal fields. The bounce-back boundary condition which is a traditional boundary condition of lattice Boltzmann method has only a first order in numerical accuracy at the boundary and numerical instability. A non-equilibrium first-order extrapolation boundary condition has been verified to be of better numerical stability than the bounce-back boundary condition and this boundary condition is proved to be of second-order accuracy for the flat boundaries. The two-dimensional natural convection flow in a square cavity with Pr=0.71 and various Rayleigh numbers are simulated. The results are found to be in good agreement with those of previous studies.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.525-530
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• 2000

The vibration shape of the structure with arbitrary boundary condition under excitation is determined by the governing equation and the boundary condition and driving force. In this paper, driving point impedance that is defined by the ratio of the driving force at one point to the velocity of that point is selected as a measure to identify the boundary condition. First, this paper deals with a string with arbitrary boundary condition. It is selected because of its simplicity, but generality of which exhibits the desired physical phenomena. Particularly the relation among the driving point impedance, the boundary condition and the vibration shape is dealt as a primary step to identify the boundary condition by using the driving point impedance.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.2077-2081
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• 2005

A symmetry breaking nonlinear fluid flow in a two-dimensional wall-driven square cavity taking symmetric boundary condition after some transients has been investigated numerically. It has been shown that the symmetry breaking critical Reynolds number is dependent on the time history of the boundary condition. The cavity has at least three stable steady state solutions for Re=300-375, and two stable solutions if Re>400. Also, it has also been showed that a particular solution among several possible solutions can be obtained by a controlled boundary condition.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1123-1148
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• 2016

The aim of this note is to provide detailed proofs for local estimates near the boundary for weak solutions of second order parabolic equations in divergence form with time-dependent measurable coefficients subject to Neumann boundary condition. The corresponding parabolic equations with Dirichlet boundary condition are also considered.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.497-502
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• 2022

Existence and uniqueness for fractional differential equations satisfying a general nonlocal initial or boundary condition are proven by means of Schauder's fixed point theorem. The nonlocal condition is given as an integral with respect to a signed measure, and includes the standard initial value condition and multi-point boundary value condition.