• 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.

• Korean Journal of Mathematics
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• v.4 no.2
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• pp.179-193
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• 1996

This paper is concerned with the penalized stationary incompressible Navier-Stokes system with the inhomogeneous Dirichlet boundary condition on the part of the boundary. By taking a generalized velocity space on which the homogeneous essential boundary condition is imposed and corresponding trace space on the boundary, we pose the system to the weak form which the stress force is involved. We show the existence and convergence of the penalized system in the regular branch by extending the div-stability condition.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.2
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• pp.123-130
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• 2008

The effects of characteristic condition number on the convergence of preconditioned Navier-Stokes equations were investigated. The two-dimensional preconditioned Navier-Stokes adopting Choi and Merkle's preconditioning and the temperature preconditioning are considered. Preconditioned Roe's FDS scheme was adopted for spatial discretization and preconditioned LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of the Navier-Stokes equations are strongly affected by the characteristic condition number. Also it is shown that the optimal characteristic condition numbers for viscous flows are larger than that in inviscid flows.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.9
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• pp.1325-1334
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• 1998

The objectives of the present study are to develop a systematic method rather than a conventional trial-and-error method for an optimal shape design using a mathematical theory, and to apply it to engineering problems. In the present study, an optimal condition for a minimum pressure loss in a two-dimensional curved duct flow is derived and then an optimal shape of the curved duct is designed from the optimal condition. In the design procedure, one needs to solve the adjoint Navier-Stokes equations which are derived from the Navier-Stokes equations and the cost function. Therefore, a computer code of solving both the Navier-Stokes and adjoint Navier-Stokes equations together with an automatic grid generation is developed. In a curved duct flow, flow separation occurs due to an adverse pressure gradient, resulting in an additional pressure loss. Optimal shapes of a curved duct are obtained at three different Reynolds numbers of 100, 300 and 800, respectively. In the optimally shaped curved ducts, the separation region does not exist or is significantly reduced, and thus the pressure loss along the curved duct is significantly reduced.

• Journal of Integrative Natural Science
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• v.6 no.1
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• pp.53-56
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• 2013

We are interested in the rate of convergence of solutions of 2D Navier-Stokes equations in a smooth bounded domain as the viscosity tends to zero under Navier friction condition. If the initial velocity is smooth enough($u{\in}W^{2,p}$, p>2), it is known that the rate of convergence is linearly propotional to the viscosity. Here, we consider the rate of convergence for nonsmooth velocity fields when the gradient of the corresponding solution of the Euler equations belongs to certain Orlicz spaces. As a corollary, if the initial vorticity is bounded and small enough, we obtain a sublinear rate of convergence.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.6
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• pp.525-531
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• 2008

• Proceedings of the KSME Conference
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• 2000.11b
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• pp.597-602
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• 2000

In a MEMS(micro-electro mechanical system), the fluid may slip near the surface of a solid and have a discontinuous temperature profile. A numerical prediction in this slip flow region can provide a reasonable guide for the design and fabrication of micro devices. The compressible Navier-Stokes equation with Maxwell/smoluchowski boundary condition is solved for two simple systems; couette flow and pressure driven flow in a long channel. We found that the couette flow could be regarded as an incompressible system in low speed regions. For the pressure driven flow system, we observed nonlinear distribution of pressure in the long channel and numerical results showed a good agreement with the experimental results.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.753-760
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• 2013

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a bounded Lipschitz do-main under Dirichlet boundary condition. We present by a very simple argument that a strong solution exists globally when the product of $L^2$ norms of the initial velocity and the gradient of the initial velocity and $L^{p,2}$, $p{\geq}4$ norm of the forcing function are small enough. Our condition is scale invariant and implies many typical known global existence results for small initial data including the sharp dependence of the bound on the volumn of the domain and viscosity. We also present a similar result in the whole domain with slightly stronger condition for the forcing.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.315-324
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• 2012

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a long periodic domain. We show by a simple argument that a strong solution exists globally in time when the initial velocity in $H^1$ and the forcing function in $L^p$([0; T);$L^2$), T > 0, $2{\leq}p{\leq}+\infty$ satisfy a certain condition. This condition common appears for the global existence in thin non-periodic domains. Larger and larger initial data and forcing functions satisfy this condition as the thickness of the domain $\epsilon$ tends to zero.

• Journal of the Korean Chemical Society
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• v.40 no.6
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• pp.409-414
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• 1996

The limit of applicability of Navier-Stokes equation to stationary plane shock-waves is examined by using the principle of minimum entropy production of linear irreversible thermodynamics. In order to obtain analytic results, the equation is linearized near the equilibrium of downstream. Results show that the solution of Navier-Stokes equation which fits the boundary condition of far downstream flow is consistent with the thermodynamic requirement within the first order when the solution is expanded around the M=1, where M is the Mach number of upstream speed.