• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.505-518
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• 2014

Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.87-118
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• 1997

This paper is concerned with a mixed Lagrangian formulation of the wiscous, stationary, incompressible Navier-Stokes equations $$ (1.1) -\nu\Delta u + (u \cdot \nabla)u + \nabla_p = f in \Omega $$ and $$ (1.2) \nubla \cdot u = 0 in \Omega $$ along with inhomogeneous Dirichlet boundary conditions on a portion of the boundary $$ (1.3) u = ^{0 on \Gamma_0 _{g on \Gamma_g, $$ where $\Omega$ is a bounded open domain in $R^d, d = 2 or 3$, or with a boundary $\Gamma = \partial\Omega$, which is composed of two disjoint parts $\Gamma_0$ and $\Gamma_g$.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.519-532
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• 2016

We consider the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations with infinite delays. We prove the existence of a pullback $\mathcal{D}$-attractor for the continuous process associated to the problem with respect to a large class of non-autonomous forcing terms.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1331-1345
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• 2010

This paper describes a numerical solution of Navier-Stokes equations. It includes algorithms for discretization by finite element methods and a posteriori error estimation of the computed solutions. In order to evaluate the performance of the method, the numerical results are compared with some previously published works or with others coming from commercial code like ADINA system.

• Journal of Power System Engineering
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• v.3 no.4
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• pp.16-21
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• 1999

Numerical simulation on two-dimensional turbine cascade flow has been performed using compressible Navier-Stokes equations. The flow equations are written in a cartesian coordinate system, then mapped into a generalized body-fitted ones. All direction of viscous terms are incoporated and turbulent effects are modeled using the extended ${\kappa}-{\epsilon}$ model. Equations are discretized using control volume SIMPLE algorithm on the nonstaggered grid sysetem. Applications are made at a VKI turbine cascade flow in atransonic wind-tunnel and compared to experimental data. Present numerical results are shown to be in good agreement with the experimental results and simulate the compressible viscous flow characteristics inside the turbine blade passage.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.125-150
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• 2013

The stabilized Gauge-Uzawa method (SGUM), which is a second order projection type algorithm to solve the time-dependent Navier-Stokes equations, has been newly constructed in 2013 Pyo's paper. The accuracy of SGUM has been proved only for time discrete scheme in the same paper, but it is crucial to study for fully discrete scheme, because the numerical errors depend on discretizations for both space and time, and because discrete spaces between velocity and pressure can not be chosen arbitrary. In this paper, we find out properties of the fully discrete SGUM and estimate its errors and stability to solve the evolution Navier-Stokes equations. The main difficulty in this estimation arises from losing some cancellation laws due to failing divergence free condition of the discrete velocity function. This result will be extended to Boussinesq equations in the continuous research (part II) and is essential in the study of part II.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1737-1751
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• 2013

An efficient and stable point collocation scheme based on a meshfree method is studied for the stationary incompressible Navier-Stokes equations. We describe the diffuse derivatives associated with the moving least square method. Using these diffuse derivatives, we propose a point collocation method to fit in solving the Navier-Stokes equations which improves the stability of the direct point collocation scheme. The convergence of the numerical solution is investigated from numerical examples. The driven cavity ow and the backward facing step ow are implemented for the reliability of the scheme. Also, the viscous ow on complicated geometry is successfully calculated such as the ow past a circular cylinder in duct.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.819-839
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• 2019

We study the stabilization of 2D g-Navier-Stokes equations in bounded domains with no-slip boundary conditions. First, we stabilize an unstable stationary solution by using finite-dimensional feedback controls, where the designed feedback control scheme is based on the finite number of determining parameters such as determining Fourier modes or volume elements. Second, we stabilize the long-time behavior of solutions to 2D g-Navier-Stokes equations under action of fast oscillating-in-time external forces by showing that in this case there exists a unique time-periodic solution and every solution tends to this periodic solution as time goes to infinity.

• Journal of computational fluids engineering
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• v.21 no.1
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• pp.10-18
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• 2016

Numerical boundary conditions are as important as the governing equations when analyzing the fluid flows numerically. An explicit boundary condition method updates the solutions at the boundaries with extrapolation from the interior of the computational domain, while the implicit boundary condition method in conjunction with an implicit time integration method solves the solutions of the entire computational domain including the boundaries simultaneously. The implicit boundary condition method, therefore, is more robust than the explicit boundary condition method. In this paper, steady compressible 2-Dimensional Navier-Stokes solver is developed. We present the implicit boundary condition method coupled with LU-SGS(Lower Upper Symmetric Gauss Seidel) method. Also, the explicit boundary condition method is implemented for comparison. The preconditioning Navier-Stokes equations are solved on unstructured meshes. The numerical computations for a number of flows show that the implicit boundary condition method can give accurate solutions.