• Proceedings of the Korea Water Resources Association Conference
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• 2007.05a
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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).

• Journal of the Society of Naval Architects of Korea
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• v.36 no.4
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• pp.28-36
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• 1999

An efficient inverse design method based on the MGM(Modified Garabedian-McFadden) method has been developed. The 2-D Navier-Stokes equations are solved for obtaining the surface pressure distributions and coupled with the MGM method to perform the inverse design. The MGM method is a residual-correction technique, in which the residuals are the difference between the desired and the computed pressure distribution. The developed code was applied to several airfoil shapes and the propeller. It has been found that they are well converged to their targeting shapes.

• Korean Journal of Mathematics
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• v.27 no.1
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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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• 2003.10a
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• pp.33-34
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• 2003

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.5
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• pp.755-761
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• 1987

Two-Dimensional incompressible laminar boundary layer with the reversed flow region is computed using the parially parabolized Navier-Stokes equations in primitive variables. The velocities and the pressure are explicity coupled in the difference equation and the resulting penta-diagonal matrix equations are solved by a streamwise marching technique. The test calculations for the trailing edge region of a finite flat plate and Howarth's linearly retarding flows demonstrate that the method is accurate, efficient and capable of predicting the reversed flow region.

• Journal of computational fluids engineering
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• v.16 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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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.

• Journal of computational fluids engineering
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• v.1 no.1
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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.