• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2007년도 학술발표회 논문집
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• pp.1392-1396
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• 2007

The governing equations in generalized curvilinear coordinates for 3D laminar flow are the Incompressible Navier-Stokes (INS) equations with the artificial dissipative terms. and continuity equation discretized using a second-order accurate, finite volume method on the nonstaggered computational grid. This method adopts a dual or pseudo time-stepping Artificial Compressibility (AC) method integrated in pseudo-time. Multigrid methods are also applied because solving the equations on the coarse grids requires much less computational effort per iteration than on the fine grid. The algorithm yields practically identical velocity profiles and secondary flows that are in excellent overall agreement with an experimental measurement (Humphrey et al., 1977).

• 대한조선학회논문집
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• 제36권4호
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• pp.28-36
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• 1999

본 연구에서는 MGM(Modified Grrabedian-McFadden)방법에 기초한 효율적인 역설계 방법을 개발하였다. 표면압력 분포를 얻기 위해 2-D Navier-Stokes 방정식을 풀었고, 역설계를 수행하기 위해 MGM방법을 사용하였다. MGM 방법은 설계 목적 압력분포와 Navier-Stokes 방정식에서 계산된 압력분포의 차인 잔여량을 보정하는 잔여-보정 기법이다. 코드 개발을 위하여 몇몇 익형과 프로펠러 형상설계에 적용하였다. 이들 모두 목표하는 형상에 잘 수렴해 갔다.

• Korean Journal of Mathematics
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• 제27권1호
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• pp.193-219
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• 2019

The Navier-Stokes equations with variable density are challenging problems in numerical analysis community. We recently built the 2nd order stabilized Gauge-Uzawa method [SGUM] to solve the Navier-Stokes equations with constant density and have estimated theoretically optimal accuracy. Also we proved that SGUM is unconditionally stable. In this paper, we apply SGUM to the Navier-Stokes equations with nonconstant variable density and find out the stability condition of the algorithms. Because the condition is rather strong to apply to real problems, we consider Allen-Cahn scheme to construct unconditionally stable scheme.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
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• pp.33-34
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• 2003

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
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• pp.15-16
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• 2003

An implicit pressure correction method on unstructured Cartesian grid is developed for the incompressible Navier-Stokes equations. An immersed boundary method is also incorporated to treat the body geometry. Tests show that with an appropriate amount of dissipation, the method is second order accurate both in time and space. The driven cavity flows with and without immersed bodies are computed to demonstrate the capability of the present scheme.

• 대한기계학회논문집
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• 제11권5호
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• pp.755-761
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• 1987

본 연구에서는 익형 위에 발생하는 박리기포 주위를 사용한 박리기포 주위 유 동해석에 목적을 두고, 원시변수(primitive variable)를 사용한 부분 포물형 Navier -Stokes 방정식을 사용하여 층류유동에 관한 간단한 기본계산을 통해 비교적 박리기포 가 큰 외부유동(external flow)에도 부분 포물형 방정식이 적용될 수 있음을 보이고자 한다.수치해법은 Galpin 등 이 이차원 관유동(channel flow)에 완전 Navier-Stokes 방정식의 해법으로 사용한 CELS(coupled equation line solver) 방법을 부분 포물형 방정식에 적합하게 수정하여 사용하였다.

• 한국전산유체공학회지
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• 제16권4호
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• pp.7-13
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• 2011

A comparative analysis of thermal models in the lattice Boltzmann method(LBM) for the simulation of laminar natural convection in a square cavity is presented. A HYBRID method, in which the thermal equation is solved by the Navier-Stokes equation method while the mass and momentum conservation are resolved by the lattice Boltzmann method, is introduced and its merits are explained. All the governing equations are discretized on a cell-centered, non-uniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with a deferred correction method to ensure stability of the solutions. The HYBRID method and the double-population method are applied to the simulation of natural convection in a square cavity and the predicted results are compared with the benchmark solutions given in the literatures. The predicted results are also compared with those by the conventional Navier-Stokes equation method. In general, the present HYBRID method is as accurate as the Navier-Stokes equation method and the double-population method. The HYBRID method shows better convergence and stability than the double-population method. These observations indicate that this HYBRID method is an efficient and economic method for the simulation of incompressible fluid flow and heat transfer problem with the LBM.

• 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.

• 대한수학회보
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• 제55권2호
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• pp.379-403
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• 2018

In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.

• 한국전산유체공학회지
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• 제1권1호
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• pp.112-122
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• 1996

A finite element scheme using the concept of PISO method has been developed to solve the Navier-Stokes viscous flows in all speed range. This scheme includes development of new pressure equation that retains both the hyperbolic term related with the density variation and the elliptic term reflecting the incompressibility constraint. The present method is applied to the incompressible two-dimensional driven cavity flow problems(Re=100, 400 and 1,000). For compressible flows, the Carter plate problem(M=3 and Re=1,000) is computed. Finally, we have simulated the shock-boundary layer interaction(M=2 and Re=2.96×10/sup 5/), a more difficult problem, and compared its results with the experiment to demonstrate the shock capturing capability of the present solution algorithm.