• International Journal of Aeronautical and Space Sciences
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• v.17 no.2
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• pp.149-156
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• 2016

The hypersonic flow on the stagnation streamline of a blunt body is analyzed with quasi one-dimensional (1-D) Navier-Stokes equations approximated by adopting the local similarity to the two-dimensional (2-D)/axisymmetric Navier-Stokes equations. The governing equations are solved using the implicit finite volume method. The computational domain is confined from the stagnation point to the shock wave, and the shock fitting method is used to find the shock position. We propose a boundary condition at the shock, which employs the shock wave angle in the vicinity of the stagnation streamline using the shock shape correlation. As a result of numerical computation conducted for the hypersonic flow over a sphere, the proposed boundary condition is shown to improve the accuracy of the prediction of the shock standoff distance. The quasi 1-D Navier-Stokes code is efficient in computing time and is reliable for the flow analysis along the stagnation streamline and the prediction of heat flux at the stagnation point in the hypersonic blunt body flow.

• 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.

• 유체기계공업학회:학술대회논문집
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• 1999.12a
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• pp.221-226
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• 1999

Three-dimensional flow analysis and numerical optimization methods are presented for the design of an axial-flow fan. Steady, Incompressible, three-dimensional Reynolds-averaged Wavier-Stokes equations are used as governing equations, and standard k-$\epsilon$ turbulence model is chosen as a turbulence model. Governing equations are discretized using finite volume method. Steepest descent method, conjugate gradient method and BFGS method are compared to determine the searching directions. Golden section method and quadratic fit-sectioning method are tested for one dimensional search. Objective function is defined as a ratio of generation rate of the turbulent kinetic energy to pressure head. Sweep angle distributions are used as design variables.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.3
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• pp.1015-1027
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• 1996

In this paper, a numerical procedure for the calculation of the incompressible Navier-Stokes equations in a generalized nonorthogonal body fitted coordinate system is proposed and is validated through three test problems. Present numerical procedure derives the pressure equation by using the pressure substitution method on the regular grid system, and discretized momentum equations are based on the covariant velocity components. Cavity flow, backward facing step flow, and two dimensional channel flow with a sinusoidal wavy wall are chosen as three test problems. Numerical solutions obtained by present procedure shows a good agreement with previous numerical and/or experimental results. Convergence rate is also satisfactory.

• 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.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.227-253
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• 2024

This paper studies the existence of weak solutions and the stability of stationary solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays in the phase space BCL_-∞(H). We first prove the existence and uniqueness of weak solutions by using the classical technique of Galerkin approximations. Then we study stability properties of stationary solutions by using several approach methods. In the case of proportional delays, some sufficient conditions ensuring the polynomial stability in both mean square and almost sure senses will be provided.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.599-605
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• 2003

For practical calculations, the Reynolds equation is frequently used to analyze the lubricating flow. The full Navier-Stokes Equations are used to find validity limits of Reynolds equation in a lubricating flow regime by result comparison. As the amplitude of wavy upper wall increased at a given average channel height, the difference between Navier-Stokes and lubrication theory decreased slightly : however, as the minimum distance in channel throat increased, the differences in the maximum pressure between Navier-Stokes and lubrication theory became large.

• Proceedings of the Korea Water Resources Association Conference
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• 2009.05a
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• pp.516-523
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• 2009

The artificial compressibility (AC) method for the incompressible Navier-Stokes equations in the generalized curvilinear coordinates using the primitive form is implemented. The main advantage of the AC approach is that the resulting system of equations resembles the system of compressible N-S equations and can thus be integrated in time using standard, well-established time-marching methods. The errors, which are the odd-even oscillation, for pressure field in using the artificial compressibility can be eliminated by using the $4^{th}$ order artificial dissipation term which is explicitly included. Even though this paper focuses exclusively on 2D laminar flows to validate and assess the performance of this solver, this numerical method is general enough so that it can be readily extended to carry out 3D URANS simulation of engineering flows. This algorithm yields practically identical velocity profiles and primary vortex and secondary vortices that are in excellent overall agreement with the results of the vorticity-stream function formulation (Ghia et al., 1982). However, the grid resolution have to be required to be large enough to express the various vortices.

• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.833-842
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• 1999

In this paper, we construct a fully discrete solution of the incompressible Navier Stokes equations using implicit Runge kutta method. We prove the existence of the fully discrete solution.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.4
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• pp.458-465
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• 2003

The main objective of the research is to develop a research code solving transient incompressible Navier-Stokes equation. In this research code, Adams-Bashforth method was applied to the convective terms of the navier stokes equation and the splitted equations were discretized spatially by finite element methods to solve the complex geometry problems easily. To reduce the divergence on the boundaries of pressure poisson equation due to the unsuitable pressure boundary conditions, multi step approximation pressure boundary conditions derived from the boundary linear momentum equations were used. Simulations of Lid Driven Flow and Flow over Cylinder were conducted to prove the accuracy by means of the comparison with results of the previous workers.