• Proceedings of the KSME Conference
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• 2001.06e
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• pp.404-409
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• 2001

An account of second-order fractional-step methods and boundary conditions for the incompressible Navier-Stokes equations is presented. The present work has aimed at (i) identification and analysis of all possible splitting methods of second-order splitting accuracy; and (ii) determination of consistent boundary conditions that yield second-order accurate solutions. It has been found that only three types (D, P and M) of splitting methods called the canonical methods are non-degenerate so that all other second-order splitting schemes are either degenerate or equivalent to them. Investigation of the properties of the canonical methods indicates that a method of type D is recommended for computations in which the zero divergence is preferred, while a method of type P is better suited to the cases when highly-accurate pressure is more desirable. The consistent boundary conditions on the tentative velocity and pressure have been determined by a procedure that consists of approximation of the split equations and the boundary limit of the result. The pressure boundary condition is independent of the type of fractional-step methods. The consistent boundary conditions on the tentative velocity were determined in terms of the natural boundary condition and derivatives of quantities available at the current timestep (to be evaluated by extrapolation). Second-order fractional-step methods that admit the zero pressure-gradient boundary condition have been derived. The boundary condition on the new tentative velocity becomes greatly simplified due to improved accuracy built in the transformation.

• Journal of Advanced Research in Ocean Engineering
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• v.1 no.3
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.9
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• pp.825-834
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• 2008

Nose chine shape optimization study has been performed to maximize the directional stability at high angle of attack supersonic flow. Various chine shapes are generated using super ellipse equation. By numerically investigating the directional stability characteristics of those shapes, the baseline configuration for the shape optimization has been selected using the three-dimensional Navier-Stokes equations. The configuration is represented by the NURBS curves which can adjust the surface geometry by the control points. The response surfaces are constructed to obtain optimum shape which has high directional stability characteristics and lift-to-drag ratio. From this study, an efficient configuration design and optimization process which utilizes the parameter-based configuration generation techniques and approximation method has been established, then 29% improvement of the directional stability by strong vortexes from chine nose is accomplished.

• Journal of the Society of Naval Architects of Korea
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• v.38 no.1
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• pp.1-8
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• 2001

The computations of the turbulent flow around the ship models with the free-surface effects were carried out. Incompressible Reynolds-Averaged Navier-Stokes equations were solved by using an explicit finite-difference method with the nonstaggered grid system. The method employed second-order finite differences for the spatial discretization and a four-stage Runge-Kutta scheme for the temporal integration. For the turbulence closure, a modified Baldwin-Lomax model was exploited. The location of the free surface was determined by solving the equation of the kinematic free-surface condition using the Lax-Wendroff scheme and a free-surface conforming grid was generated at each time step so that one of the grid boundary surfaces always coincides with the free surface. An inviscid approximation of the dynamic free-surface boundary condition was applied as the boundary conditions for the velocity and pressure on the free surface. To validate the computational method developed in the present study, the computations were carried out for beth Wigley and Series 60 $C_B=0.6$ ship model and the computational results showed good agreements with the experimental data.

• Journal of Ocean Engineering and Technology
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• v.33 no.1
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• pp.76-84
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• 2019

For decades, solitary waves have commonly been used to simulate tsunami conditions in numerical studies. However, the main component of a tsunami waveform acts at completely different spatial and temporal distributions than a solitary waveform. Thus, this study applied a 2-D numerical wave tank that included a non-reflected tsunami generation system based on Navier-Stokes equations (LES-WASS-2D) to directly simulate the run-up of a tsunami-like solitary wave on a slope. First, the waveform and velocity due to the virtual depth factor were applied to the numerical wave tank to generate a tsunami, which made it possible to generate the wide waveform of a tsunami, which was not reproduced with the existing solitary wave approximation theory. Then, to validate the applied numerical model, the validity and effectiveness of the numerical wave tank were verified by comparing the results with the results of a laboratory experiment on a tsunami run-up on a smooth impermeable 1:19.85 slope. Using the numerical results, the run-up characteristics due to a tsunami-like solitary wave on an impermeable slope were also discussed in relation to the volume ratio. The maximum run-up heights increased with the ratio of the tsunami waveform. Therefore, the tsunami run-up is highly likely to be underestimated compared to a real tsunami if the solitary wave of the approximation theory is applied in a tsunami simulation in a coastal region.

• Journal of computational fluids engineering
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• v.19 no.3
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• pp.29-36
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• 2014

In the present study, an aerodynamic design optimization of UAV rotor blades was conducted using a genetic algorithm(GA) coupled with computational fluid dynamics(CFD). To reduce computational cost in making databases, a function approximation was applied using artificial neural networks(ANN) based on a radial basis function network. Three dimensional Reynolds-Averaged Navier-Stokes(RANS) solver was used to solve the flow around UAV rotor blades. Design directions were specified to maximize thrust coefficient maintaining torque coefficient and minimize torque coefficient maintaining thrust coefficient. Design variables such as twist angle, thickness and chord length were adopted to perform a planform optimization. As a result of an optimization regarding to maximizing thrust coefficient, thrust coefficient was increased about 4.5% than base configuration. In case of an optimization minimizing torque coefficient, torque coefficient was decreased about 7.4% comparing with base configuration.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.5
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• pp.1613-1623
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• 1996

In this paper, two discretization methods, hybrid and QUICK, are tested for the Navier-Stokes equations written in general nonorthogonal body fitted coordinates. Comparison is made by calculating two laminar flows at low Reynolds numbers of 10 - 100. One is a two-dimensional channel of gradually expanding cross section and the other is an axisymmetric flow through a circular tube having a circular constriction. Results show that the QUICK scheme results in a numerical solution more accurate than that of hybrid. The QUICK scheme also shows faster convergence for both test cases. As the number of grid points increases, all numerical solutions converge with more oscillation. The number of grid points in the y-direction(cross stream direction) is also shown to play a significant role in the approximation of convection term within separated flow zone.

• Journal of computational fluids engineering
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• v.11 no.1 s.32
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• pp.57-66
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• 2006

An optimal shape design approach is presented for a subsonic S-shaped intake using aerodynamic sensitivity analysis. Two-equation turbulence model is employed to capture strong counter vortices in the S-shaped duct more precisely. Sensitivity analysis is performed for the three-dimensional Navier-Stokes equations coupled with two-equation turbulence models using a discrete adjoint method For code validation, the result of the flow solver is compared with experiment data and other computational results of bench marking test. To study the influence oj turbulence models and grid refinement on the duct flow analysis, the results from several turbulence models are compared with one another and the minimum number of grid points, which can yield an accurate solution is investigated The adjoint variable code is validated by comparing the complex step derivative results. To realize a sufficient and flexible design space, NURBS equations are introduced as a geometric representation and a new grid modification technique, Least Square NURBS Grid Approximation is applied With the verified flow solver, the sensitivity analysis code and the geometric modification technique, the optimization of S-shaped intake is carried out and the enhancement of overall intake performance is achieved The designed S-shaped duct is tested in several off-design conditions to confirm the robustness of the current design approach. As a result, the capability and the efficiency of the present design tools are successfully demonstrated in three-dimensional highly turbulent internal flow design and off-design conditions.

• 한국전산유체공학회:학술대회논문집
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• 2008.03b
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• pp.568-571
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• 2008

The computation of moving interface by the level set method typically requires reinitializations of level set function. An inaccurate estimation of level set function ${\phi}$ results in incorrect free-surface capturing and thus errors such as mass gain/loss. Therefore, accurate and robust reinitialization process is essential to the free-surface flows. In the present paper, we pursue further development of the reinitialization process, which evaluates directly level set function ${\phi}$ using a normal vector in the interface without solving the re-distancing equation of hyperbolic type. The Taylor-Galerkin approximation and P1P1splitting FEM are adopted to discretize advection equation of the level set function and the Navier-Stokes equation, respectively. Advection equation of free surface and re-initialization process are validated with benchmark problems, i.e., a broken dam flow and time-reversed single vortex flow. The simulation results are in good agreement with the existing results.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.145-155
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• 1998

A computer code has been developed for the computation of the viscous flow around a ship model with the free surface. In this code, the incompressible Reynolds-averaged Navier-Stokes equations are solved numerically by a finite difference method which employes second-order finite differences for the spatial discretization and a four-stage Runge-Kutta scheme for the temporal integration of the governing equations. For the turbulence closure, a modified version of the Baldwin-Lomax model is exploited. The location of the free surface is determined by solving the equation of the kinematic free-surface condition using the Lax-Wendroff scheme and the boundary-fitted grid is generated at each time step so that one of the grid surfaces always coincides with the free surface. An inviscid approximation of the dynamic free-surface boundary condition is applied as the boundary conditions for the velocity and pressure on the free surface. To validate the computational method and the computer code developed in the present study, the numerical computations are carried out for both Wigley parabolic hull and Series 60 $C_B=0.6$ ship model and the computational results are compared with the experimental data.