• 터널과지하공간
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• 제13권5호
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• pp.389-396
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• 2003

본 연구는 정상류 Navier-Stokes 방정식에 섭동(perturbation) 이론을 적용하여 주기함수 간극에 대한 삼승법칙의 수정에 대해 논하였다. 이를 위해, 주기함수를 진폭과 파장에 대한 무차원 함수로 전환한 뒤 미소 계수에 대한 무차원 유동함수와 연속 방정식을 적용하였다. 이러한 과정을 통해 정상류 Navier-Stokes 방정식의 섭동 근사해를 구하였으며 이를 유한 차분법에 적용하였다. 단일 절리 모델에 대한유한 차분 수치해석을 통해, 수정된 삼승 법칙이 주기함수 간극의 유체 유동에 대한 정상류 Navier-Stokes 방정식의 섭동 근사해와 잘 일치하는 것으로 나타났다. 이를 통해 본 연구에서 제시된 삼승 법칙이 간극 분포에 따른 유체 유동의 평가에 있어 유용하게 적용될 수 있는 것으로 나타났다.

• 충청수학회지
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• 제22권3호
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• pp.557-569
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• 2009

We present a new regularity criterion for suitable weak solutions of the steady-state Navier-Stokes equations near boundary in dimension five. We show that suitable weak solutions are regular up to the boundary if the scaled $L^{\frac{5}{2}}$-norm of the solution is small near the boundary. Our result is also valid in the interior.

• 한국전산유체공학회지
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• 제10권1호
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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.

• 한국항공우주학회지
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• 제33권9호
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• pp.34-40
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• 2005

본 연구에서는 비정상 유동해석을 위한 CFD 코드의 개발을 위해 대각화 ADI 기법을 적용한 정상 해석기법과 내재적 이중시간 전진기법을 도입하였다. 정상상태 Navier-Stokes 방정식의 Jacobian 행렬은 비점성항에 대해서만 적용하였고 여기에 내재적 인공점성 연산자를 첨가하여 블록 5대각 행렬을 유도하였다. 시간단축을 위해 스칼라 5대각 행렬로 대체하였다. 가상시간에 대한 정상상태기법에 실시간에 대한 미분항이 포함된 새로운 잔류항을 정의하였다. 가상시간에 대해 수렴된 해로부터 실시간 해를 구하고 시간에 대해 적분을 수행하는 내재적 이중시간 전진기법을 이용한 비정상 Navier-Stokes 코드를 개발하였다. 이에 대한 검증으로 정지한 유체속에 진동하는 평판문제, 원기둥 후방의 주기적인 Karman 와류생성, 이중원호 익형주위의 충격파 진동문제등을 수치해석하여 이론치, 실험치, 타연구자의 계산결과와 비교, 분석하였다.

• 대한수학회지
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• 제36권1호
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• pp.159-171
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• 1999

We formulate and study a finite element method for a linearized steady state, compressible, viscous Navier-Stokes equations in 2D, based on the discontinuous Galerkin method. Dislike the standard discontinuous galerkin method, we do not assume that the triangle sides be bounded away from the characteristic direction. the unique stability follows from the inf-sup condition established on the finite dimensional spaces for the (incompressible) Stokes problem. An error analysis having a jump discontinuity for pressure is shown.

• 대한수학회보
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• 제55권3호
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• pp.881-898
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• 2018

This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible Navier-Stokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudo-time derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.

• 한국전산유체공학회지
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• 제19권1호
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• pp.27-33
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• 2014

A new and efficient implicit scheme is proposed to obtain a steady-state solution in time integration and the comparison of characteristics with the approximation ways for the implicit method to solve the incompressible Navier-Stokes equations is provided. The conservative, finite-volume cell-vertex upwind scheme and artificial compressibility method using dual time stepping for time accuracy is applied in this paper. The numerical results obtained indicate that the direct application of Jacobian matrix to the Lower and upper sweeps of implicit LU-SGS leads to better performance as well as convergence regardless of CFL number and true time step than explicit scheme and approximation of Jacobian matrix. The flow simulation around box in uniform flow with unstructured meshes is demonstrated to check the validity of the current formulation.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2000년도 춘계 학술대회논문집
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• pp.178-183
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• 2000

An efficient Newton-GMRES algorithm is presented for computing two-dimensional steady compressible viscous flows on unstructured hybrid meshes. The scheme is designed on cell-centered finite volume method which accepts general polygonal meshes. Steady-state solution is obtained with pseudo-transient continuation strategy. The preconditioned, restarted general minimum residual(GMRES) method is employed in matrix-free form to solve the linear system arising at each Newton iteration. The incomplete LU fartorization is employed for the preconditioning of linear system. The Spalart-Allmars one equation turbulence model is fully coupled with the flow equations to simulate turbulence effect. The accuracy, efficiency and robustness of the presently developed method are demonstrated on various test problems including laminar and turbulent flows over flat plate and airfoils.

• 대한기계학회논문집
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• 제13권4호
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• pp.764-770
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• 1989

This paper analyze the steady state performance of a self-acting air lubricated slider bearing in hard disk/head system. Modified Reynolds' equation is derived from the steady state compressible Navier-Stokes equation, under slip-flow conditions. Finite difference technique and numerical procedure are described by using Newton-Raphson iteration method to slove the non-linear equations. These techniques are applied to conventional slider bearings and the effects of molecular mean free path(MMFP) for a recording surface of hard disk are shown. The calculation procedure developed here, wide applicabilities in practical head design procedures, and converges rapidly.

• 대한기계학회논문집
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• 제17권7호
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• pp.1805-1812
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• 1993

Two-dimensional spin-up in a rectangular domain is analysed by the numerical computation of the Navier-Stokes equations. The cells are in most cases generated by the vorticity developed near the uper and lower surfaces. Moreover, the movement and interaction of those vortices play a key role in establishing the quasi-steady state. The critical phenomena observed in the previous experiment turns out to be caused by the critical movement of the vortices.