• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.339-345
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• 2020

This note deals with the question of the regularity of (Leray) weak solutions of the Navier-Stokes equations in terms of the pressure. This criterion improves on the existing results.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.1
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• pp.1-7
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• 2017

To predict the transonic buffet onset for a supercritical airfoil with shock-boundary layer interactions, a practical steady approach has been proposed. In this study, it is assumed that the airfoil flow is steady even when buffet onset occurs. Steady Navier-Stokes computations are performed on the supercritical airfoil. Using the aerodynamic parameters calculated from Navier-Stokes solver, various steady approaches for predicting buffet onset are discussed. Among the various steady approaches considered in this study, Thomas' criterion based on Navier-Stokes computation has shown to be the most appropriate indicator of identifying the buffet onset for a supercritical airfoil with shock-boundary layer interactions. Good agreements have been obtained compared with the results of unsteady transonic wind tunnel tests. The present method is shown to be reliable and useful for transonic buffet onset for a supercritical airfoil with shock-boundary layer interactions in terms of practical engineering viewpoint.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.537-558
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• 2008

Consider a weak solution u of the Navier-Stokes equations in the class $L^2((0,T);X_1(\mathbb{R}^d)^d)$. We establish a new approach to treat the regularity problem for the Navier-Stokes equation in term of the multiplier space $X_1(\mathbb{R}^d)$.

• 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.

• Korean Journal of Optics and Photonics
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• v.4 no.4
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• pp.434-441
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• 1993

Focusing geometry dependence of output Stokes energy in single pass methane Raman shifter is investigated. The experimental result shows that the threshold energy decreases as confocal parameter increases. This result can be explained by gain suppression caused by Stokes - anti-Stokes coupling. In this paper, we give simple analysis for the focusing geometry dependence of Stokes - anti-Stokes coupling and present the criterion of confocal parameter to reduce the gain suppression. Focusing geometry dependence of stimulated Brillouin scattering is measured and the result is in good agreement with theoretical prediction.

• Journal of Advanced Research in Ocean Engineering
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• v.2 no.1
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• pp.1-11
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• 2016

The objective of this paper is to present an analytical solution in deep water waves and verify the validity of the theory (Shin, 2015). Hence this is a follow-up to Shin (2015). Instead of a variational approach, another approach was considered for a more accurate assessment in this study. The products of two coefficients were not neglected in this study. The two wave profiles from the KFSBC and DFSBC were evaluated at N discrete points on the free-surface, and the combination coefficients were determined for when the two curves pass the discrete points. Thus, the solution satisfies the differential equation (DE), bottom boundary condition (BBC), and the kinematic free surface boundary condition (KFSBC) exactly. The error in the dynamic free surface boundary condition (DFSBC) is less than 0.003%. The wave theory was simplified based on the assumption tanh $D{\approx}1$ in this paper. Unlike the perturbation method, the results are possible for steep waves and can be calculated without iteration. The result is very simple compared to the 5th Stokes' theory. Stokes' breaking-wave criterion has been checked in this study.

• Journal of Ocean Engineering and Technology
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• v.36 no.2
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• pp.101-107
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• 2022

Dean (1965) proposed the use of the root mean square error (RMSE) in the dynamic free surface boundary condition (DFSBC) and kinematic free-surface boundary condition (KFSBC) as an error evaluation criterion for wave theories. There are well known wave theories with RMSE more than 1%, such as Airy theory, Stokes theory, Dean's stream function theory, Fenton's theory, and trochodial theory for deep-water waves. However, none of them can be applied for deep-water breaking waves. The purpose of this study is to provide a closed-form solution for deep-water waves with RMSE less than 1% even for breaking waves. This study is based on a previous study (Shin, 2016), and all flow fields were simplified for deep-water waves. For a closed-form solution, all Fourier series coefficients and all related parameters are presented with Newton's polynomials, which were determined by curve fitting data (Shin, 2016). For verification, a wave in Miche's limit was calculated, and, the profiles, velocities, and the accelerations were compared with those of 5^th-order Stokes theory. The results give greater velocities and acceleration than 5^th-order Stokes theory, and the wavelength depends on the wave height. The results satisfy the Laplace equation, bottom boundary condition (BBC), and KFSBC, while Stokes theory satisfies only the Laplace equation and BBC. RMSE in DFSBC less than 7.25×10^-2% was obtained. The series order of the proposed method is three, but the series order of 5^th-order Stokes theory is five. Nevertheless, this study provides less RMSE than 5^th-order Stokes theory. As a result, the method is suitable for offshore structural design.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.8
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• pp.37-46
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• 2004

Several notes on ground effects drawn from Navier-Stokes analyses and their aerodynamic interpretations were addressed here; For two-dimensional ground effect, the change of surface pressure due to image vortex, the venturi effect due to thickness and the primary inviscid flow phenomena of ground effect, and for three-dimensional ground effect, strengthened wing tip vortices, increased effective span and the outward drift of trailing vortices. Irodov's criteria were evaluated to investigate the static longitudinal stability of conventional NACA 6409 and DHMTU 8-30 airfoils. The analysis results demonstrated superior static longitudinal stability of DHMTU 8-30 airfoil. The DHMTU airfoil has quite lower value of lrodov's criterion than the conventional NACA airfoil, which require much smaller tail volume to stabilize the whole WIG-craft at its design stage.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.127-132
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• 1998

The present study is aimed to investigate flow characteristics of Two dimensional backward-facing step by numerical approach. A convection conservative difference scheme based upon SOLA algorithm is used for the solution of the two-dimensional incompressible Navier-Stokes equations to simulate the laminar, transitional and turbulent flow conditions at which the experimental data can be available for the backward-facing step. The twenty kinds of Reynolds number are used for the calculations. In an effort to demonstrate that the reported solutions are dependent on the mesh refinement, computations are performed on seven different meshes of uniformly increasing refinement. Also to investigate the result of inflow dependence, two kinds of the inflow profile are chosen for the laminar flow. As criterion of benchmarking the result of numerical simulation, reattachment length is used for the selected Reynolds numbers.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.235-242
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• 2003

This paper deals with numerical analysis of static and dynamic wind effects on civil engineering structures. Aeroelastic analysis becomes a prime criterion to be confirmed during the structural design because the long-span suspension bridges are prone to the aerodynamic instabilities caused by wind. If the wind velocity exceeds the critical velocity that the bridge can withstand, then the bridge fails due to the phenomenon of flutter. The aeroelastic simulation is carried out using both Computational Fluid Dynamic(CFD) and Computational Structural Dynamic(SCD) schemes.