• Honam Mathematical Journal
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• v.36 no.4
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• pp.755-766
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• 2014

In the discrete formulation of the bubble stabilized Legendre Galerkin methods, the system of equations includes the artificial viscosity term as the parameter. We investigate the estimation of this parameter to get the optimal solution which minimizes the maximum error. Some numerical results are reported.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.3
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• pp.859-871
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• 2014

In order to analyze the density current due to salt and temperature difference, this study develops new numerical model (LES-WASS-3D ver. 2.0) by introducing state equation for salt and temperature and 3D advection-diffusion equation to existing 3D numerical wave tank (LES-WASS-3D ver. 1.0). To verify the applicability, the newly-developed numerical model is analyzed comparing to the experimental result of existing numerical model. In the result, it well implement the behavior and vertical salt concentration of advected and diffused seawater as well as flow velocity and temperature of the discharged warm water. This confirms the validity and effectiveness of the developed numerical model.

• Proceedings of the KSME Conference
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• 2008.11b
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• pp.2460-2464
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• 2008

The present paper suggests new method to know the effects of molecular diffusion and the helicity of microchannel flows on mixing in passive micromixers, which are essential components of a microfluidic chip. In this study, 'Helix Index' is newly defined as the magnitude of chaotic advection. Relationship between Helix Index and Mixing Index is analyzed numerically such as the wide range of Peclet and Reynolds numbers in three dimensional serpentine microchannel when using soluble solutions (water/glycerol). As a result, a simple algebraic equation is derived by this relationship based on a regression analysis. The algebraic equation is found to be able to accurately predict the mixing performance without solving the coupled, complex momentum and mass transfer equations.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.2
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• pp.495-506
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• 2013

This study developed the Time-split Mixing Model (TMM) which can represent the pollutant mixing process on a three-dimensional open channel through constructing the conceptual model based on Taylor's assumption (1954) that the shear flow dispersion is the result of combination of shear advection and diffusion by turbulence. The developed model splits the 2-D mixing process into longitudinal mixing and transverse mixing, and it represents the 2-D advection-dispersion by the repetitive calculation of concentration separation by the vertical non-uniformity of flow velocity and then vertical mixing by turbulent diffusion sequentially. The simulation results indicated that the proposed model explains the effect of concentration overlapping by boundary walls, and the simulated concentration was in good agreement with the analytical solution of the 2-D advection-dispersion equation in Taylor period (Chatwin, 1970). The proposed model could explain the correlation between hydraulic factors and the dispersion coefficient to provide the physical insight about the dispersion behavior. The longitudinal dispersion coefficient calculated by the TMM varied with the mixing time unlike the constant value suggested by Elder (1959), whereas the transverse dispersion coefficient was similar with the coefficient evaluated by experiments of Sayre and Chang (1968), Fischer et al. (1979).

• Transactions of the Korean Society of Mechanical Engineers B
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• v.32 no.6
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• pp.429-445
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• 2008

Two-phase compressible flow fields of air-water are investigated numerically in the fixed Eulerian grid framework. The phase interface is captured via volume fractions of each phase. A way to model two phase compressible flows as a single phase one is found based on an equivalent equation of states of Tait's type for a multiphase cell. The equivalent single phase field is discretized using the Roe‘s approximate Riemann solver. Two approaches are tried to suppress the pressure oscillation phenomena at the phase interface, a passive advection of volume fraction and a direct pressure relaxation with the compressible form of volume fraction equation. The direct pressure equalizing method suppresses pressure oscillation successfully and generates sharp discontinuities, transmitting and reflecting acoustic waves naturally at the phase interface. In discretizing the compressible form of volume fraction equation, phase interfaces are geometrically reconstructed to minimize the numerical diffusion of volume fraction and relevant variables. The motion of a projectile in a water-filled tube which is fired by the release of highly pressurized air is simulated presuming the flow field as a two dimensional one, and several design factors affecting the projectile movement are investigated.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.6C
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• pp.267-274
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• 2012

The conventional approach to evaluate the contaminant transport in soils adopts the macro-scale implementation while the pore configuration and network is a dominant factor to determine the fate of contaminant. However, the observation of fate and transport at pore scale may not be readily approachable because of the computational expenses to solve Navier-Stokes equation. We herein present the 2D Lattice-Boltzmann method that enables to assess the local fluid velocity and density efficiently for the case of single phase and multi-components. The solute fate spatio-temperal space is explicitly determined by the advection of fluid flow. Two different types of idealized pore space provides the path of fluid. Also, solute transport, the velocity field and average concentration of solute are computed in steady state. Results show that the pore geometry such as tortuosity mainly affect the solute fate. It highlights the significance of the pore configuration and shape in granular soils and rock discontinuity in spite of the equivalent porosity.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.4B
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• pp.335-344
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• 2006

In this study, sequential mixing model (SMM) was proposed based on the Taylor's theory which can be summarized as the fact that longitudinal advection and transverse diffusion occur independently and then the balance between the longitudinal shear and transverse mixing maintains. The numerical simulation of the model were performed for cases of different mixing time and transverse velocity distribution, and the results were compared with the solutions of 1-D longitudinal dispersion model (1-D LDM) and 2-D advection-dispersion model (2-D ADM). As a result it was confirmed that SMM embodies the Taylor's theory well. By the comparison between SMM and 2-D ADM, the relationship between the mixing time and the transverse diffusion coefficient was evaluated, and thus SMM can integrate 2-D ADM model as well as 1-D LDM model and be an explanatory model which can represents the shear flow dispersion in a visible way. In this study, the predicting equation of the longitudinal dispersion coefficient was developed by fitting the simulation results of SMM to the solution of 1-D LDM. The verification of the proposed equation was performed by the application to the 38 sets of field data. The proposed equation can predict the longitudinal dispersion coefficient within reliable accuracy, especially for the river with small width-to-depth ratio.

• Water for future
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• v.29 no.4
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• pp.187-198
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• 1996

A numerical model for unsteady dispersion of horizontal line source in turbulent shear flow is developed. A fractional step finite difference method is used which splits the unsteady two-dimensional advective diffusion equation into the longitudinal advection and the vertical diffusion equations, and solves them alternately for half time intervals by the Holly-Preissmann scheme and the Crank-Nicholson scheme, respectively. The developed numerical model is verified using a semi-analytic solution for steady dispersion in turbulent shear flow. Dispersion of an instantaneous plane source in turbulent shear flow is analyzed using the model. The degree of mixing at the same dimensionless time is almost the same regardless of the friction factor, and the travel distance required to reach a certain degree of mixing is inversely proportional to the square root of the friction factor.

• Honam Mathematical Journal
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• v.38 no.1
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• pp.47-57
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• 2016

In the discrete formulation of the bubble stabilized Legendre Galerkin methods, the system of equations includes the artificial viscosity term as the parameter. We investigate the estimation of this parameter to get the least-squares solution which minimizes the sum of the squares of errors at each node points. Some numerical results are reported.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.22 no.3
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• pp.133-142
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• 2010

We calculated using siltation model to know the influnce of the tidal current, the tidal level, the sediment transport of seabed around sea area due to the construction of the Song do New city. We calculated the tidal current and based on this we estimated scour, sedimentation using the advection-diffusion equation and accessed the sediment transport of seabed before and after the construction of the New city. Sedimentation was increased in the east coast of Young jong Do, and Scour was increased according to the direction from the front route of north harbor to Ho do. Tidal level was increased overall.