• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1950-1963
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• 1995

A modification of the approximate-factorization method is made to accelerate the convergency rate and to take sufficiently large Courant number without loss of accuracy. And a stable implicit finite-difference scheme for solving the incompressible Navier-Stokes equations employed above modified method is developed. In the present implicit scheme, the volume fluxes with contravariant velocity components and the pressure formulation in curvilinear coordinates is adopted. In order to satisfy the continuity condition completely and to remove spurious errors for the pressure, the Navier-Stokes equations are solved by a modified SMAC scheme using a staggered gird. The upstream-difference scheme such as the QUICK scheme is also employed to the right hand side. The implicit scheme is unconditionally stable and satisfies a diagonally dominant condition for scalar diagonal linear systems of implicit operator on the left hand side. Numerical results for some test calculations of the two-dimensional flow in a square cavity and over a backward-facing step are obtained using both usual approximate-factorization method and the modified one, and compared with each other. It is shown that the present scheme allows a sufficiently large Courant number of O(10$^{2}$) and reduces the computing time.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2006.05a
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• pp.36-40
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• 2006

An analysis is made of flow and rocket motion during a supersonic separation stage of air-launching rocket(ALR) from the mother plane. Three-dimensional compressible Navier-Stokes equations is numerically solved to analyze the steady/unsteady flow field around the rocket which is being separated from the mother plane configuration(F-4E Phantom). The simulation results clearly demonstrate the effect of shock-expansion wave interaction between the rocket and the mother plane. To predict the behavior of the ALR according to the change of the C.G., three cases of numerical analysis are performed. As a result, a design-guideline of supersonic air-launching rocket for the safe separation is proposed.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.5B
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• pp.575-589
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• 2008

In the present work, we investigate the hydrodynamic behavior of a turbulent bore, such as tsunami bore and tidal bore, generated by the removal of a gate with water impounded on one side. The bore generation system is similar to that used in a general dam-break problem. In order to the numerical simulation of the formation and propagation of a bore, we consider the incompressible flows of two immiscible fluids, liquid and gas, governed by the Navier-Stokes equations. The interface tracking between two fluids is achieved by the volume-of-fluid (VOF) technique and the M-type cubic interpolated propagation (MCIP) scheme is used to solve the Navier-Stokes equations. The MCIP method is a low diffusive and stable scheme and is generally extended the original one-dimensional CIP to higher dimensions, using a fractional step technique. Further, large eddy simulation (LES) closure scheme, a cost-effective approach to turbulence simulation, is used to predict the evolution of quantities associated with turbulence. In order to verify the applicability of the developed numerical model to the bore simulation, laboratory experiments are performed in a wave tank. Comparisons are made between the numerical results by the present model and the experimental data and good agreement is achieved.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.547-567
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• 2007

We obtain spatial-temporal decay rates of weak solutions of incompressible flows in exterior domains. When a domain has a boundary, the pressure term yields difficulties since we do not have enough information on the pressure term near the boundary. For our calculations we provide an idea which does not require any pressure information. We also estimated the spatial and temporal asymptotic behavior for strong solutions.

• Journal of Ocean Engineering and Technology
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• v.13 no.3 s.33
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• pp.114-122
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• 1999

준쇄파(쇄파발생정 리플형태의 불안정파)를 수치적으로 해석하고 예측하기 위하여 수중날개를 대상으로 점성유동장의 계산을 수행하였다. Navier-Stokes 방정식을 사용하여 자유수면을 계산하였고 정도향상을 위하여 Euler 형태의 자유표면조건에 고차의 유한차문법을 적용하였다. 이산화 과정에서 자유표면 격자에 3차 풍상미분항을 적용시켜 수치계산을 수행하였고, 계산결과를 사용하여 준쇄파의 생성조건을 규명하였다.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1059-1070
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• 2000

Under the critical assumption that ▽u$\in$L(sub)loc(sup)${\alpha}$,${\beta}$, 3/${\alpha}$ + 2/${\beta}$ $\leq$ 2 with ${\alpha}$ $\geq$ 3/2, a boundary L(sup)$\infty$ estimate for the solution is derived if the pressure on the boundary is bounded. Here, our estimate is local.

• Journal of computational fluids engineering
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• v.10 no.1
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• pp.67-72
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• 2005

This research is based on the iterative space-marching method for incompressible and compressible Navier-Stokes equations[1-4]. A principle of parallel computational schemes construction for steady and unsteady problems is suggested. It is analytically proven that convergence of these schemes is unconditional for incompressible case. When the parallel scheme is used the total volume of computations is the sum of a large number of independent and equal parts. Estimation of the speed-up K shows that K > 1000 in ideal case. First results of using the parallel schemes are presented.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.127-146
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• 2016

We consider a coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two. We show temporal decay estimates of solutions with small initial data and obtain their asymptotic profiles as time tends to infinity.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.78-83
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• 1998

A finite-difference method based on conservative supra characteristic method(CSCM) type upwind flux difference splitting has been studied on the bluntness effect on the wall heat transfer rate and wall pressure over blunt-body. The results show that the stagnation heating varies inversely with the square root of the nose radius.

• 한국전산유체공학회:학술대회논문집
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• 1995.10a
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• pp.154-159
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• 1995

Numerical optimization technique with Navier-Stokes code has been used to reduce the drag of conventional ogival nose. Forebody optimizations are performed for supersonic laminar and turbulent flow conditions. To alleviate the computing time of aerodynamic drag calculation, axisymmetric boundary condition is implemented in the 3-dimensional Navier-Stokes code. The automated optimization procedure with gradient based method results in a drag reduction of $4\;\%$.