• 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.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.531-551
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• 2021

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing p(x)-Laplacian. More precisely, we consider the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.87-118
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• 1997

This paper is concerned with a mixed Lagrangian formulation of the wiscous, stationary, incompressible Navier-Stokes equations $$ (1.1) -\nu\Delta u + (u \cdot \nabla)u + \nabla_p = f in \Omega $$ and $$ (1.2) \nubla \cdot u = 0 in \Omega $$ along with inhomogeneous Dirichlet boundary conditions on a portion of the boundary $$ (1.3) u = ^{0 on \Gamma_0 _{g on \Gamma_g, $$ where $\Omega$ is a bounded open domain in $R^d, d = 2 or 3$, or with a boundary $\Gamma = \partial\Omega$, which is composed of two disjoint parts $\Gamma_0$ and $\Gamma_g$.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.585-598
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• 2014

In this paper we consider the nonlinear parabolic problems with mixed boundary condition. Under comparatively mild conditions of the coefficients related to the problem, we construct the discontinuous Galerkin approximation of the solution to the nonlinear parabolic problem. We discretize spatial variables and construct the finite element spaces consisting of discontinuous piecewise polynomials of which the semidiscrete approximations are composed. We present the proof of the convergence of the semidiscrete approximations in $L^{\infty}(H^1)$ and $L^{\infty}(L^2)$ normed spaces.

• Structural Engineering and Mechanics
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• v.4 no.2
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• pp.191-202
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• 1996

This paper presents a construction of adaptive boundary element for the problem with mixed boundary conditions such as heat transfer between heated body surface and surrounding medium. The scheme is based on the sample point error analysis and on the extended error indicator, proposed earlier by the authors for the potential and elastostatic problems, and extended successfully to multidomain and thermoelastic analyses. Since the field variable is connected with its derivative on the boundary, their errors are also interconnected by the specified condition. The extended error indicator on each boundary element is modified to meet with the situation. Two numerical examples are shown to indicate the differences due to the prescribed boundary conditions.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.31-37
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• 2002

In this paper, we find explicitly the eigenvalues and the eigenfunctions of Laplace operator on a triangle domain with a mixed boundary condition. We also show that a weaker form of the principle of spatial averaging holds for this domain under suitable boundary condition.

• Journal of IKEEE
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• v.13 no.3
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• pp.55-61
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• 2009

The heat transfer analysis applying finite element method has been carried out. Particularly, the convection boundary condition associated with the mixed boundary condition is numerically formulated by the Galerkin method analogous to the magnetic field problem. Also, the coupled electromagnet-thermal field analysis by the proposed heat transfer coefficient computation algorithm is executed to enhance the accuracy of solutions. Finally, the validity of the proposed results is verified by comparison with the measured ones.

• Tribology and Lubricants
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• v.15 no.3
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• pp.248-256
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• 1999

Many tribological components in automobile engine undergo high load and sliding speed with thin film thickness. The lubrication characteristics of the components are regarded as ether hydrodynamic lubrication or boundary lubrication, whereas in a working cycle they actually have both characteristics. Many modem engine lubricants have various additives for better performance which make boundary film formation even under hydrodynamic lubrication regime. Conventional Reynolds equation with the viewpoints of continuum mechanics concerns only bulk viscosity of lubricant, which means that its simulation does not give insights on boundary lubrication characteristics. However, many additives of modern engine lubricant provide mixed modes of boundary lubrication characteristics and hydrodynamic lubrication. Especially, high molecular weight polymeric viscosity index improvers form boundary film on the solid surface and cause non-Newtonian fluid effect of shear thinning. This study has performed the investigation about journal bearing system with the mixed concepts of boundary lubrication and hydrodynamic lubrication which happen concurrently in many engine components under the condition of viscosity index improver added.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.579-590
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• 2009

The precise form of singular functions, singular function representation and the extraction form for the stress intensity factor play an important role in the singular function methods to deal with the domain singularities for the Poisson problems with most common boundary conditions, e.q. Dirichlet or Mixed boundary condition [2, 4]. In this paper we give an elementary step to get the singular functions of the solution for Poisson problem with Neumann boundary condition or Robin boundary condition. We also give singular function representation and the extraction form for the stress intensity with a result showing the number of singular functions depending on the boundary conditions.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1137-1152
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• 2005

In this article we prove the existence of the solution to the mixed problem for Euler-Bernoulli beam equation with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We proved that the energy decay with the same rate of decay of the relaxation function, that is, the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially.