• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.869-880
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• 1998

In this paper, we show that the weak solutions of the time-dependent Magnetohydrodynamics equations in 3 dimensional periodic domain belong to L(equation omitted)(0, T; V$_{r}$) following the method of Foias-Guillope-Temam for Navier-Stokes equations.s.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.1
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• pp.81-96
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• 2007

Nonlinear shoaling characteristics over surf zone are numerically investigated based on spatially averaged NavierStokes equation. We also test the validity of gradient model for turbulent stresses due to wave breaking using the data acquainted during SUPERTANK LABORATORY DATA COLLECTION PROJECT(Krauss et al., 1992). It turns out that the characteristics length scale of breaking induced current is not negligible, which firmly stands against ever popular gradient model, ${\kappa}-{\varepsilon}$ model, but favors Large Eddy Simulation with finer grid. Based on these observations, we model the residual stress of spatially averaged NavierStokes equation after Lagrangian Dynamic Smagorinsky(Meneveau et al., 1996). We numerically integrate newly proposed wave equations using SPH with Gaussian kernel function. Severely deformed water surface profile, free falling water particle, queuing splash after landing of water particle on the free surface and wave finger due to structured vortex on rear side of wave crest(Narayanaswamy and Dalrymple, 2002) are successfully duplicated in the numerical simulation of wave propagation over uniform slope beach, which so far have been regarded very difficult features to mimic in the computational fluid mechanics.

• Journal of Korea Water Resources Association
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• v.48 no.4
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• pp.291-298
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• 2015

The aim of this study is that a theoretical formula for estimating the one-dimensional longitudinal dispersion coefficient is derived based on a transverse distribution equation for the depth averaged stream-wise velocity in open channel. In "Part I. Theoretical equation for stream-wise velocity" which is the former volume of this article, the velocity distribution equation is derived analytically based on the Shiono-Knight Model (SKM). And then incorporating the velocity distribution equation into a triple integral formula which was proposed by Fischer (1968), the one-dimensional longitudinal dispersion coefficient can be derived theoretically in "Part II. Longitudinal dispersion coefficient" which is the latter volume of this article. SKM has presented an analytical solution to the Navier-Stokes equation to describe the transverse variations, and originally been applied to straight and nearly straight compound channel. In order to use SKM in modeling non-prismatic and meandering channels, the shape of cross-section is regarded as a triangle in this study. The analytical solution for the velocity distribution is verified using Manning's equation and applied to velocity data measured at natural streams. Although the velocity equation developed in this study do not agree well with measured data case by case, the equation has a merit that the velocity distribution can be calculated only using geometric data including Manning's roughness coefficient without any measured velocity data.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.410-415
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• 2001

An analytical and numerical examination of second-order fractional-step methods and boundary condition for the incompressible Navier-Stokes equations is presented. In this study, the compatibility condition for pressure Poisson equation and its boundary conditions, stability, and numerical accuracy of canonical fractional-step methods has been investigated. It has been found that satisfaction of compatibility condition depends on tentative velocity and pressure boundary condition, and that the compatible boundary conditions for type D method and approximately compatible boundary conditions for type P method are proper for divergence-free velocity for type D and approximately divergence-free for type P method. Instability of canonical fractional-step methods is induced by approximation of implicit viscous term with explicit terms, and the stability criteria have been founded with simple model problems and numerical experiments of cavity flow and Taylor vortex flow. The numerical accuracy of canonical fractional-step methods with its consistent boundary conditions shows second-order accuracy except $D_{MM}$ condition, which make approximately first-order accuracy due to weak coupling of boundary conditions.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.1
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• pp.49-56
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• 1997

Heat-transfer enhancement is seeked through modifications of fin surface. Real life plate-fin heat exchangers have complex three-dimensional geometries. Fins can have arrays of dimples and are attached to rows of penetrating tubes. To isolate the effect of surface modification, we model the real flow by a two-dimensional channel flow with a dimple on one side. The flow is analysed by solving the incompressible Navier-Stokes equation by a finite volume method on a generalized boundary-fitted coordinate. Results show a trapped vortex inside the dimple for all cases computed. Local maximum of Nusselt number occurs near the downstream end of the dimple, due to such a vortex. Location of the vortex does not change with respect to the wall temperature change, but moved downstream when Reynolds number increases. This, together with the results that in all cases vortex core is somewhat downstream of the dimple center, suggests that the mean flow above continuously feeds the kinetic energy to the recirculating flow. Heat transfer enhancement and pressure losses are studied through analysing the relevant dimensionless parameters like, Nusselt number and friction factor. In all cases computed, dimpled channel flow experiences less pressure loss than two-dimensional Poiseuille flow.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.4
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• pp.44-52
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• 2002

Aerodynamic characteristics of a flapping airfoil in low Reynolds number flows are numerically studied using the unsteady, incompressible Navier-Stokes flow solver with a two-equation turbulence model. For more efficient computation of unsteady flows over flapping airfoil, the flow solver is parallel-implemented by MPI programming method Unsteady computations are performed for low Reynolds number flows over a NACA four-digit series airfoils. Effects of pitching, plunging, and flapping motion with different reduced frequency, amplitude, thickness and camber on aerodynamic characteristics are investigated. Present computational results yield a better agreement in thrust at various reduced frequency with experimental data.

• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.189-194
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• 2001

In this paper, non-reacting and reacting flowfields were computed using a preconditioned Navier-Stokes solver. The preconditioning technique of Merkle et al. and TVD scheme or Chakravarthy and Osher was employed and the results obtained using developed code have a good agreement with the previous results and experimental data. The preconditioned Wavier-Stokes equation set with low Reynolds number $\kappa-\epsilon$ equation and species continuity equations, are discretized with strongly implicit manner and time integrated with LU-SSOR scheme. For the purpose of treating unsteady problem the duel-time stepping scheme was employed. For the validation of the code in incompressible flow regime, steady driven square cavity flow was considered and calculation result shows reasonably good agreement with the result of incompressible code. Shock wave/boundary layer interaction problem was considered to show the shock capturing performance of preconditioned-TVD scheme. To validate unsteady flow, acoustic oscillation problem was calculated, and supersonic premix flame of $H_2$-air reaction problem which is calculated with turbulence model, 9-species/18-reaction step reaction model, shows reasonable agreement with the previous results. As a result, the preconditioning method has an advantage to calculate incompressible and compressible flow through one code and preconditioned solver easily developed from standard compressible code with minor efforts. But additional computational time and computer memory is required due to preconditioning matrix.

• Journal of the Korean Society for Marine Environment & Energy
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• v.16 no.4
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• pp.255-262
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• 2013

The boltzmann equation is based on the particle distribution function while the Navire-Stokes equation based on the continuum theory. In order to simulate free surface flow, this paper used the Lattice Boltzmann Method of which is the discretized form. The detail study on the characteristics of the Lattice Boltzmann Method for the free surface simulation was investigated. The developed code was validated with the traditional dam breaking problem by tracking the front position of the water. A basic roles of density functions in the Lattice Boltzmann Method is discussed. To have an engineering applications, the simulation is also conducted the free surface behavior with an arbitrary wall geometry.

• Journal of the Korean Society for Railway
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• v.12 no.1
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• pp.65-71
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• 2009

The pressure transient inside the passenger cabin of high-speed train has been assessed using computational fluid dynamics (CFD) based on the axi-symmetric Navier-Stokes equation. The pressure change inside a train have been calculated using first order difference approximation based on a linear equation between the pressure change ratio inside a train and the pressure difference of inside and outside of the train. The numerical results show that the pressure change inside the new Korean high-seed train passing through a tunnel of Seoul-Busan high-speed line at the speed of 330km/h satisfied well the Korean regulation for pressure change inside a passenger cabin if the train is satisfying the train specification for airtightness required by the regulation.

• Journal of computational fluids engineering
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• v.2 no.1
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• pp.46-53
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• 1997

The flow field around a three dimensional minivan-like body has been simulated. This study solves 3-D unsteady incompressible Navier-Stokes equations on a non-orthogonal curvilinear coordinate system using second-order accurate schemes for the time derivatives, and third/second-order scheme for the spatial derivatives. The Marker-and-Cell concept is applied to efficiently solve continuity equation. A H-H type of multi-block grid system is generated around a three dimensional minivan-like body. Turbulent flows have been modeled by the Baldwin-Lomax turbulent model. To validate present procedure, the flows around the Ahmed body with 12.5° of slant angle are simulated. A good agreement with other numerical results is achived. After code validation, the flows around a mimivan-like body are simulated. The simulation shows three dimensional vortex-pair just behind body. The flow separation is also observed on the rear of the body. It has concluded that the results of present study properly agreed with physical flow phenomena.