• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.567-584
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• 2014

In this paper, we consider approximation of eigenelements of a two dimensional compact integral operator with a smooth kernel by discrete collocation and iterated discrete collocation methods. By choosing numerical quadrature appropriately, we obtain convergence rates for gap between the spectral subspaces, and also we obtain superconvergence rates for eigenvalues and iterated eigenvectors. We then apply Richardson extrapolation to obtain further improved error bounds for the eigenvalues. Numerical examples are presented to illustrate theoretical estimates.

• Journal of Korea Water Resources Association
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• v.47 no.8
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• pp.703-715
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• 2014

This study aims to investigating the effect of Schmidt number (${\sigma}_c$) on sediment suspension and hydrodynamics calculation. The range of ${\sigma}_c$ is also studied based on the flux Richardson number ($Ri_f$) and gradient Richardson number ($Ri_g$). Numerical experiments are carried out by 1 dimensional vertical model. Both cohesive and non-cohesive sediments are tested under the conditions of pure current and oscillatory flow. The turbulence damping effect due to sediment suspension is examined considering ${\sigma}_c$ as a constant for the damping effect. The results of this study show the consistent effect of ${\sigma}_c$ on sediment suspension regardless of hydrodynamic condition. It is also found that the model overestimates the flow velocity and turbulent kinetic energy when the damping effect is not considered. Under the conditions of $Ri_f$ and $Ri_g$ causing density stratification, it is known that the vertical mixing of sediment is reasonably calculated in the range of ${\sigma}_c$ from 0.3 to 0.5.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.6B
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• pp.499-505
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• 2011

The mixing behavior of turbidity currents in a reservoir is closely related with the annual temperature change of the reservoir. In the summer, the reservoir has a well defined structure: one or two thermoclines and some layers of different densities. This density stratification inhibits vertical mixing and affects various hydrodynamic processes within the reservoir. Therefore, many reservoirs can be operated to release water of the specific quality with the selective withdrawal. In this study, the hydraulic experiments were performed to analyze the efficiency of selective withdrawal. The velocity distributions are measured with PIV in the stratified tank with the "two-tank" method. The relationship between the Richardson number and the selective withdrawal efficiency are provided using the measured velocity distributions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.6
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• pp.767-776
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• 1985

Unsteady thermally stratified flow caused by two-dimensional surface discharge of warm water into a oblong channel was investigated. Experimental study was focused on the rapidly developing thermal diffusion at small Richardson number. The basic objective were to study the interfacial mixing between a flowing layer of warm water and an underlying body of cold water and to accumulate experimental data to test computational turbulence models. Mean velocity field measurements were carried out by using NMR-CT (Nuclear Magnetic Resonance-Computerized Tomography). It detects quantitative flow image of any desired section in any direction of flow in short time. Results show that at small Richardson number warm layer rapidly penetrates into the cold layer because of strong turbulent mixing and instability between the two layers. It is found that the transfer ofheat across the interface is more vigorous than that of momentum. It is also proved that the NMR-CT technique is a very valuable tool to measure unsteady three dimensional flow field.

• The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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• v.15 no.3
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• pp.97-109
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• 2010

This study analyzed stratification and destratification processes in the Kangjin Bay (KB), South Sea, Korea, driven by the Nam Gang Dam water discharge based on numerical modeling experiments. Model performances were evaluated in terms of skill scores for elevation, velocity, temperature and salinity, with scores mostly exceeding 90%. The models reproduced the tidal current, density-driven and wind-driven current. The stratification by fresh water input and destratification by the wind mixing was assessed in terms of the characteristic Richardson number (Ri) in that Ri increased from 0 to 7~20 during the Dam water discharge period, while vertical mixing and destratification followed by the typhoon passage showed Ri, 0 to 2.

• Solar Energy
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• v.5 no.2
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• pp.11-19
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• 1985

In this paper, the interface stability not to occur mixing and entrainment between the adjacent layers has been studied in the case of the selective withdrawal of a stratum and the injection in stratified fluid formed by the density difference in a small solar pond. There are stability parameter, Richardson number, Rayleigh number and Froude number as the parameters governing stability in order to measure the interface stability on the stratified fluid. The model which could measure the interface stability on the stratified fluid was the small solar pond composed by 1 meters wide, 2 meters high, and 5 meters long. In order to measure the interface stability on the stratified fluid at the inlet port, the middle section and the outlet port, Richardson number, Rayleigh number, and Froude number involved in the parameters governing the stability were calculated by means of the data resulted from the test of the study on hydrodynamic stability between the convective and nonconvective layers in that solar pond. Richardson number written by the ratio of inertia force to buoyancy force can be used in order to measure the stability on the stratified fluid related to the buoyancy force generated from the injection of fluid. Rayleigh number written by the product of Grashof number by Prandtl number can be used in order to measure the stability of the fluid related to the heat flux and diffusivity of viscosity. Froude number written by the ratio of gravity force to inertia force can be used in order to measure the stability of the nonhomogeneous fluid related to the density difference. As the result of calculating the parameters governing stability, the interface stability on the stratified fluid couldn't be identified below the 70cm height from the bottom of the solar pond, but it could be identified above the 70cm height from it at the inlet port, the middle section and the outlet port. When compared with such the three parameters as Richardson number, Rayleigh number, Froude number, the calculated result was in accord with them at inlet port, the middle section and the outlet port. Henceforth, it is learned that even though any of the three parameters is used for the purpose of measuring the interface stability on the stratified fluid, the result will be the same with them. It is concluded that all the use of Richardson number, Rayleigh number, and Froude number, is desirable and infallible to measure the interface stability on the stratified fluid in the case of considering the exist of the fluid flow and the heat flux like the model of the solar pond.

• Journal of Convergence for Information Technology
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• v.9 no.8
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• pp.155-163
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• 2019

Laminar mixed convection of a nanofluid consists of water and $Al_2O_3$ in a horizontal circular tube has been studied numerically. Two-phase mixture model has been used to investigate hydrodynamic and thermal behaviors of the nanofluid with variables physical properties. Three dimensional Navier-Stokes, energy and volume fraction equations have been discretized using the finite volume method. The Brownian motions of nanoparticles have been considered to determine the thermal conductivity and dynamic viscosity of $Al_2O_3$-Water nanofluid, which depend on temperature. The calculated results show good agreement with the previous numerical data. Results show that in a given Reynolds number (Re), increasing solid nanoparticles volume fraction and Richardson number (Ri) increases the convective heat transfer coefficient and wall shear stress.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.6 s.249
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• pp.578-586
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• 2006

Numerical simulations are carried out to investigate the thermal effects of the gravitational potential on the centrifugal instability of a Taylor-Couette flow, and to further study the detailed flow fields and flow bifurcations to spiral vortices. The effects of centrifugal potential on the centrifugal instability are also investigated in the current study. Spiral vortices have various types of mode depending on Grashof number and Reynolds number. The correlation of Richardson number with the spiral angle of the spiral vortices shows that the structure of the spiral vortices strongly depends on the Richardson number. The heat transfer rate of the inner cylinder increases with increasing Grashof number. It is also confirmed that the torque required to rotate the inner cylinder increases as Grashof number increases.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.2 no.1
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• pp.1-10
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• 1990

Experimental studies oil the density currents were made in order to investigate their hydraulic conditions in the estuary. Interfacial forms in the flow direction became sharply with increasing densimetric Froude number in the estuary which arrested saline wedge exists. Interfacial thicknesses were almost constant in the open channel, while they abruptly increased out of channel and they also decreased as overall Richardson number increases. Densimetric Froude number of river mouth showed that it was not necessarily 1.0 and varies with the upper layer thickness. On the other hand, water level there tended to increase with increasing relative densities. It is observed in the Sumjin River Estuary that a strong density front has been formed between freshwater and ocean waters.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.11-24
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• 2001

We introduce an assumption about smoothing operator for mixed formulations and show that convergence of Multigrid method for the mixed finite element formulation for the Linear Elasticity. And we show that Richardson and Kaczmarz smoothing satisfy this assumption.