• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.447-452
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• 2005

Given operators X and Y on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. In this article, we investigate compact interpolation problems for vectors in a tridiagonal algebra. Let L be a subspace lattice acting on a separable complex Hilbert space H and Alg L be a tridiagonal algebra. Let X = $(x_{ij})\;and\;Y\;=\;(y_{ij})$ be operators acting on H. Then the following are equivalent: (1) There exists a compact operator A = $(x_{ij})$ in AlgL such that AX = Y. (2) There is a sequence {$\alpha_n$} in $\mathbb{C}$ such that {$\alpha_n$} converges to zero and $$y_1\;_j=\alpha_1x_1\;_j+\alpha_2x_2\;_j\;y_{2k}\;_j=\alpha_{4k-1}x_{2k\;j}\;y_{2k+1\;j}=\alpha_{4k}x_{2k\;j}+\alpha_{4k+1}x_{2k+1\;j}+\alpha_{4k+2}x_{2k+2\;j\;for\;all\;k\;\epsilon\;\mathbb{N}$$.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.459-468
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• 2011

Let T ${\in}$ L(X), S ${\in}$ L(Y), A ${\in}$ L(X, Y) and B ${\in}$ L(Y, X) such that SA = AT, TB = BS, AB = S and BA = T. Then S and T shares the same local spectral properties SVEP, Bishop's property (${\beta}$), property $({\beta})_{\epsilon}$, property (${\delta}$) and and subscalarity. Moreover, the operators ${\lambda}I$ - T and ${\lambda}I$ - S have many basic operator properties in common.

• Journal of computational fluids engineering
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• v.21 no.3
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• pp.64-70
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• 2016

Multiple solutions in natural convection of water with Pr=7 between two horizontal plates with small magnitude non-uniform temperature distribution in the upper plate is numerically investigated. The dimensionless temperature of upper plate is ${\theta}={\epsilon}sinkx$. Two upright cells are formed over one wave length in the conduction-dominated regime of small Rayleigh number. However, multicellular convection occurs above a critical Rayleigh number for small wave number. When k = 1.5, dual solutions are found and a transition of $6{\rightarrow}4$ eddy flow occurs with decrease of Rayleigh number. When k = 0.75, two, three, four and five multiple solutions are observed. Transitions of $14{\rightarrow}12$, $12{\rightarrow}10$, $10{\rightarrow}8$ and $6{\rightarrow}8$ eddy flow occur with decrease of Rayleigh number.

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.129-134
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• 2011

In this paper, the confined single slot jet impingement is investigated numerically. Although the geometry of the jet impingement is simple, the flow pattern of the jet impingement is complex and the numerical results of the jet impingement is affected much by numerical methods. The first goal of this study is to analyze the effects of Reynolds models and numerical spatial discretization schemes on the results of heat transfer performance and the flaw characteristics and to select the best method. Various versions of the low Reynolds number k-epsilon turbulence models are compared. Using the selected numerical method, the flow field and heat transfer characteristics of confined single slot jet impingement on a moving plate are analyzed.

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.494-499
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• 2011

One of the devices to prevent separated flow over a wing or a flap at high angle of attack is a vortex generator. In the present work, we numerically study the flow around a low-profile or micro vortex generator whose height is less than local boundary layer thickness which can delay separation with a minimum drag penalty owing to its very small wetted surface area. As a first step toward a parametric study to efficiently design this MVG flow control system, we simulate the flow around a single MVG on a flat plate. For the simulation, we employ OpenFOAM with Launder-Sharma ${\kappa}$-epsilon model. The analysis results are validated by comparing with experimental results of a rectangular MVG at an angle of attack of 10 degrees whose height is 20% of local boundary layer. Important results and aspects of this numerical study are discussed. We also simulate the flow around rectangular, triangular and trapezoidal MVGs and the results are compared

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.187-193
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• 2011

In this report, We compared the actual test with the result of pow calculation and Resistance/Self-propulsion of the ship using STAR-CCM+ which is the commercial Reynolds Averaged Navier-Strokes(RANs) Solver. The calculation model was the KRISO Container Ship and 205K Bulk Carrier of Sungdong shipbuilding company. For this calculation, We used Realizable K-Epsilon model for flaw analysis, VOF method for the free surface creation, Moving Reference Frame method for reducing the POW calculation time, and Sliding Mesh method for Self-Propulsion analysis. Calculation of Resistance and Self-Propulsion includes the free-surface. And all calculations in this report were based on unstructured grids.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.12
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• pp.3917-3925
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• 1996

A numerical analysis on three dimensional turbulent incompressible flows through linear cascades of turbine rotor blades with high turning angles has been performed by using a generalized k-.epsilon. model which is a high Reynolds number form and derived by RNG(renormalized group) method to account for the variation of the rate of strain. A second order upwind scheme is used to suppress numerical diffusion in approximating the convective terms. Body-fitted coordinates are adopted to represent the complex blade geometry accurately. For the case without tip clearance, velocity vectors and static pressure contours are shown to be in good agreement with previous experimental results. For the case with tip clearance, the effects of the passage vortex and tip clearance flow on the total pressure loss as well as their interactions are discussed.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1891-1895
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• 2008

Water covers 70% of the earth's surface and the human body consist of 75% of it. It is clear that water is one of the prime elements responsible for life on earth. Over the last 30 years or so, numerous studies have attempted to find out more about the water microscopically. In this paper, we investigated how the receding and advancing contact angle of the moving water droplet changes on a solid surface having various LJ epsilon parameters. To observe the dynamic contact angle history, a body force applied to all water molecules after obtained the water droplet in equilibrium with the solid surface. We obtained the density profile and receding and advancing contact angle of the moving water droplet

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.315-324
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• 2012

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a long periodic domain. We show by a simple argument that a strong solution exists globally in time when the initial velocity in $H^1$ and the forcing function in $L^p$([0; T);$L^2$), T > 0, $2{\leq}p{\leq}+\infty$ satisfy a certain condition. This condition common appears for the global existence in thin non-periodic domains. Larger and larger initial data and forcing functions satisfy this condition as the thickness of the domain $\epsilon$ tends to zero.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.491-502
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• 1994

Many problems arising in science and engineering require the numerical solution of a system of n nonlinear equations in n unknowns: (1) given F : $R^{n}$ $\rightarrow$ $R^{n}$ , find $x_{*}$ $\epsilon$ $R^{n}$ / such that F($x_{*}$) = 0. Nonlinear problems are generally solved by iteration. Davidson [3] and Broyden [1] introduced the methods which had led to a large amount of research and a class of algorithm. This work has been called by the quasi-Newton methods, secant updates, or modification methods. Newton's method is the classical method for the problem (1) and quasi-Newton methods have been proposed to circumvent computational disadvantages of Newton's method.(omitted)