• Journal of Ocean Engineering and Technology
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• v.10 no.3
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• pp.96-104
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• 1996

Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.195-199
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• 2005

Wave breaking phenomenon near the fore body of a ship is numerically simulated. The ship advance with uniform velocity in calm water. For the simulation, incompressible Navier-Stokes equations and continuity equation are adopted as governing equations. The simulation is carried out in staggered variable mesh system with finite difference method. Marker and Cell(MAC) method and Marker-Density method are employed to track the free surface. Body boundary conditions are satisfied with the adoption of porosity method and no-slip condition on the hull surface. The ship model has a wedge type fore-body, and the computational domain is an appropriate region around the fore-body. The computation results are compared with some experimental results. Also the difference of the free surface tracking methods are discussed.

• International Journal of Aeronautical and Space Sciences
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• v.7 no.2
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• pp.155-174
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• 2006

Parabolized stability equations for compressible flows in general curvilinear coordinate system are derived to deal with a broad range of transition prediction problems on complex geometry. A highly accurate finite difference PSE code has been developed using an implicit marching procedure. Compressible and incompressible flat plate flow stability under two-dimensional and three¬dimensional disturbances has been investigated to test the present code. Results of the present computation are found to be in good agreement with the multiple scale analysis and DNS data. Stability calculation results by the present PSE code for compressible boundary layer at Mach numbers ranging from 0.02 to 1.5 are also presented and are again seen to be as accurate as the spectral method.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1079-1101
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• 2020

This work is concerned with a geometric inverse problem in fluid mechanics. The aim is to reconstruct an unknown obstacle immersed in a Newtonian and incompressible fluid flow from internal data. We assume that the fluid motion is governed by the Stokes-Brinkmann equations in the two dimensional case. We propose a simple and efficient reconstruction method based on the topological sensitivity concept. The geometric inverse problem is reformulated as a topology optimization one minimizing a least-square functional. The existence and stability of the optimization problem solution are discussed. A topological sensitivity analysis is derived with the help of a straightforward approach based on a penalization technique without using the classical truncation method. The theoretical results are exploited for building a non-iterative reconstruction algorithm. The unknown obstacle is reconstructed using a levelset curve of the topological gradient. The accuracy and the robustness of the proposed method are justified by some numerical examples.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.1-23
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• 2001

This paper is concerned with an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. by introducing an artificial compressibility term to relax the incompressibility constraints, we take the penalty method. The existence of optima solutions for the penalized problem will be shown. Next, by employing Lagrange multipliers method and the material derivatives, we derive the shape gradient for the minimization problem of the shape functional which represents the viscous drag.

• Journal of Advanced Research in Ocean Engineering
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• v.2 no.2
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• pp.61-66
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• 2016

This study presents the wave run-up height and depression depth around offshore cylindrical structures according to the wave period. The present study employs the volume of fluid method with the realizable turbulence model based on a commercial computational fluid dynamics software called the "STAR-CCM+" to simulate a 3D incompressible viscous two-phase turbulent flow. The present results for the wave run-up height and depression depth with regard to the wave period are compared with those of the relevant previous experimental and numerical studies.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.28 no.2
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• pp.63-68
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• 2018

Natural convection of a two dimensional laminar steady-state incompressible fluid flow in a rectangular enclosure has been investigated numerically for low aspect ratios with the physical vapor transport crystal growth. Results show that for aspect ratio (Ar = L/H) range of $0.1{\leq}Ar{\leq}1.5$, with the increase in Grashof number by one order of magnitude, the total mass flux is much augmented, and is exponentially decayed with the aspect ratio. Velocity and temperature profiles are presented at the mid-width of the rectangular enclosure. It is found that the effect of Grashof number on mass transfer is less significant when the enclosure is shallow (Ar = 0.1) and the influence of aspect ratio is stranger when the enclosure is tall and the Grashof number is high. Therefore, the convective phenomena are greatly affected by the variation of aspect ratios.

• Journal of Ocean Engineering and Technology
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• v.5 no.1
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• pp.55-63
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• 1991

This study is to predict accurately the wave induced current accuring by the radiation stress which acts as the driving force around Nearshore structure. For the wave induced current, the depth integrated and time averaged governing equation of an unsteady nonlinear form is derived from the continuity and momentum equation of an incompressible fluid. Numerical solutions are obtained by a finite difference method for the governing equation. In the vicinity of a structure, computed flow patterns show good agreement with the hydraulic experimental data. The numerical results obtained by neglecting the convective term show a large change of alongshore and offshore current.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.291-293
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• 2003

This paper deals with a thrust generation of flapping-airfoil by dynamic stall. From many other previous research results, phase angle $ between pitching and plunging mode of flapping motion must be 90 deg. to satisfy maximum propulsive efficiency. In this case, leading edge vortex is relatively small. This phenomenon is related dynamic stall. So preventing leading edge vortex induced by dynamic stall guarantees maximum propulsive efficiency. But, in this paper we insist the leading edge vortex yields quite a positive influence on thrust generation and propulsive efficiency. In order to certify our opinion, pitching and plunging motions were calculated with the parameter of amplitude and frequency by using the unsteady, incompressible Navier-Stokes flow solver with a two-equation turbulence model. For more efficient computation, it is parallelized by MPI programming method.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.63-65
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• 2003

General classes of boundary-pressure-driven flows of incompressible Newtonian fluids in three­dimensional (3D) channels and in 3D pipes with known steady laminar realizations are investigated respectively. The characteristic physical and geometrical quantities of the flows are subsumed in the kinetic Reynolds number Re and a parameter $\psi$, which involves the energetic ratio and the directions of the boundary-driven part and the pressure-driven part of the laminar flow. The solution of non-stationary dimension-free Navier-Stokes equations is sought in the form $\underline{u}=u_{L}+U,\;where\;u_{L}$ is the scaled laminar velocity and periodical conditions are prescribed for U in the unbounded directions. The objects of our numerical investigations are autonomous systems (S) of ordinary differential equations for the time-dependent coefficients of the spatial Stokes eigenfunction, where these systems (S) were received by application of the Galerkin-method to the dimension-free Navier-Stokes equations for u.