• Journal of Mechanical Science and Technology
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• v.14 no.1
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• pp.84-92
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• 2000

A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.2
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• pp.93-99
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• 1998

Parabolic approximation and sponge layer are applied as open boundary condition for elliptic finite difference wave model. Generalized conjugate gradient method is used as a solution procedure. Using parabolic approximation a large part of spurious reflection is removed at the spherical shoal experiment and sponge layer boundary condition needs more than 2 wave lengths of sponge layer to give similar results. Simulating the propagation of waves on a rectangular harbor, it is identified that iterative scheme can be applied easily for the non-rectangular computational region.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.483-493
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• 2013

We investigate the multiplicity of the solutions for a class of the system of the biharmonic equations with some singular potential nonlinearity. We obtain a theorem which shows the existence of the nontrivial weak solution for a class of the system of the biharmonic equations with singular potential nonlinearity and Dirichlet boundary condition. We obtain this result by using variational method and the generalized mountain pass theorem.

• Korean Journal of Mathematics
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• v.4 no.2
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• pp.179-193
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• 1996

This paper is concerned with the penalized stationary incompressible Navier-Stokes system with the inhomogeneous Dirichlet boundary condition on the part of the boundary. By taking a generalized velocity space on which the homogeneous essential boundary condition is imposed and corresponding trace space on the boundary, we pose the system to the weak form which the stress force is involved. We show the existence and convergence of the penalized system in the regular branch by extending the div-stability condition.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.277-288
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• 2010

We consider the nonlinear biharmonic equation with coefficient exponential growth term and Dirichlet boundary condition. We show that the nonlinear equation has at least one bounded solution under the suitable conditions. We obtain this result by the variational method, generalized mountain pass theorem and the critical point theory of the associated functional.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.379-391
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• 2015

We investigate the existence of solutions of the nonlinear biharmonic equation with variable coefficient polynomial growth nonlinear term and Dirichlet boundary condition. We get a theorem which shows that there exists a bounded solution and a large norm solution depending on the variable coefficient. We obtain this result by variational method, generalized mountain pass geometry and critical point theory.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.179-202
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• 2019

This paper presents second derivative generalized extended backward differentiation formulas (SDGEBDFs) based on the second derivative linear multi-step formulas of Cash [1]. This class of second derivative linear multistep formulas is implemented as boundary value methods on stiff problems. The order, error constant and the linear stability properties of the new methods are discussed.

• Tribology and Lubricants
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• v.37 no.1
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• pp.14-24
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• 2021

This study shows the effect of the thermal boundary condition around the tilting pad journal bearing on the static and dynamic characteristics of the bearing through a high-precision numerical model. In many cases, it is very difficult to predict or measure the exact thermal boundary conditions around bearings at the operating site of a turbomachine, not even in a laboratory. The purpose of this study is not to predict the thermal boundary conditions around the bearing, but to find out how the performance of the bearing changes under different thermal boundary conditions. Lubricating oil, bearing pads and shafts were modeled in three dimensions using the finite element method, and the heat transfer between these three elements and the resulting thermal deformation were considered. The Generalized Reynolds equation and three-dimensional energy equation that can take into account the viscosity change in the direction of the film thickness are connected and analyzed by the relationship between viscosity and temperature. The numerical model was written in in-house code using MATLAB, and a parallel processing algorithm was used to improve the analysis speed. Constant temperature and convection temperature conditions are used as the thermal boundary conditions. Notably, the conditions around the bearing pad, rather than the temperature boundary conditions around the shaft, have a greater influence on the performance changes of the bearing.

• East Asian mathematical journal
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• v.38 no.5
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• pp.593-601
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• 2022

In this paper, we consider singular 𝜑-Laplacian problems with nonlocal boundary conditions. Using a fixed point index theorem on a suitable cone, the existence results for one or two positive solutions are established under the assumption that the nonlinearity may not satisfy the L¹-Carathéodory condition.

• Journal of the Korean Society for Nondestructive Testing
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• v.27 no.6
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• pp.582-590
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• 2007

Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness.