• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.323-351
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• 2021

The present paper addresses magnetohydrodynamic pulsating flow and heat transfer of two immiscible, incompressible, and conducting couple stress fluids between two permeable beds. The flow between the permeable beds is assumed to be governed by Stokes' [28] couple stress fluid flow equations, whereas the dynamics of permeable beds is determined by Darcy's law. In this study, matching conditions were used at the fluid-fluid interface, whereas the B-J slip boundary condition was employed at the fluid-porous interface. The governing equations were solved analytically, and the expressions for velocity, temperature, mass flux, skin friction, and rate of heat transfer were obtained. The analytical expressions were numerically evaluated, and the results are presented through graphs and tables.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.779-791
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• 2000

The nonlinear stage of the evolution of free boundary between a light fluid and a heavy fluid driven by an external force is studied by a potential flow model with a source singlarity. The potential flow model is applied to a bubble and spije evolution for constantly accelerated interface (Rayleigh-Taylor instability) and impulsively accelerated interface (Richtmyer-Meshkow instability). The numerical results of the model show that, in constantly accelerated intergace, bubble grows with constant velocity and the spike falls with gravitational acceleration at later times, while the velocity of the bubble in impulsively accelerated interface decay to zero asymp flow model for the bubble and spike for constantly accelerated interface and impulsively accelerated interface.

• Journal of computational fluids engineering
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• v.4 no.3
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• pp.28-34
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• 1999

The objective of this study is to present a numerical treatment of the pressure gradient when control volumes are sharing the interface between a homogeneous fluid and a porous medium. Two possible approaches, e.g. linear interpolation and extrapolation, are considered, and they are applied to the case of a steady and two-dimensional curved channel flow which is partially filled with a porous medium. It was found that the linear extrapolation produces a continuous velocity-field at the interface and thus is recommended. On the contrary, the linear interpolation entails a discontinuous velocity field at the interface, thereby warning its use in connection with the Brinkman-Forchheimer-extended Darcy flow model.

• Journal of Korean Port Research
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• v.13 no.1
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• pp.167-174
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• 1999

Numerical analysis of two-fluid flows for both water and air is carried out. Free-Surface flows with an arbitrary deformation have been simulated around two dimensional submerged hydrofoil. The computation is performed using a finite volume method with unstructured meshes and an interface capturing scheme to determine the shape of the free surface. The method uses control volumes with an arbitrary number of faces and allows cell-wise local mesh refinement. the integration in space is of second order based on midpoint rule integration and linear interpolation. The method is fully implicit and uses quadratic interpolation in time through three time levels The linear equation systems are solved by conjugate gradient type solvers and the non-linearity of equations is accounted for through picard iterations. The solution method is of pressure-correction type and solves sequentially the linearized momentum equations the continuity equation the conservation equation of one species and the equations or two turbulence quantities.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.1
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• pp.83-106
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• 2016

This paper reviews and compares three different methods for modeling incompressible and immiscible ternary fluid flows: the immersed boundary, level set, and phase-field methods. The immersed boundary method represents the moving interface by tracking the Lagrangian particles. In the level set method, an interface is defined implicitly by using the signed distance function, and its evolution is governed by a transport equation. In the phase-field method, the advective Cahn-Hilliard equation is used as the evolution equation, and its order parameter also implicitly defines an interface. Each method has its merits and demerits. We perform the several simulations under different conditions to examine the merits and demerits of each method. Based on the results, we determine the most suitable method depending on the specific modeling needs of different situations.

• Korea-Australia Rheology Journal
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• v.16 no.4
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• pp.219-226
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• 2004

In this study the deformation of liquid-air interface of Newtonian or Boger fluids filled between two par­allel-plates geometry was investigated when two surfaces were separated at a constant speed. The interface between the fluid and air showed either stable or unstable deformation depending on experimental con­ditions. Repeated experiments for a wide range of experimental conditions revealed that the deformation mode could be classified into three types: 'stable region', 'fingering' and 'cavitation'. The experimental condition for the mode of deformation was plotted in a capillary number vs. Deborah number phase plane. It has been found that the elasticity of Boger fluids destabilize the interface deformation. On the other hand, the elasticity suppresses the formation and growth of cavities.

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.54-57
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• 2011

In this paper we present an algorithm about how to simulate two dimensional dam breaking with lattice Boltzmann method (LBM). LBM considers a typical volume element of fluid to be composed of a collection of particles that represented by a particle velocity distribution function for each fluid component at each grid point. We use the modified Lattice Boltzmann Method for incompressible fluid. This paper will represent detailed information on single phase flow which considers only the water instead of both air and water. Interface treatment and conservation of mass are the most important things in simulating free surface where the Interface is treated by mass exchange with the water region. We consider the surface tension on the interface and also bounce back boundary condition for the treatment of solid obstacles. We will compare the results of the simulation with some methods and experimental results.

• Journal of Mechanical Science and Technology
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• v.20 no.2
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• pp.271-277
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• 2006

A numerical study is made of the spin-up from rest of a three-layer fluid in a closed, vertically-mounted cylinder. The densities in the upper layer $\rho_1$, middle layer $\rho_2$ and lower layer $\rho_3\;are\;\rho_3\;>\;\rho_2\;>\;\rho_1$, and the kinematic viscosities are left arbitrary. The representative system Ekman number is small. Numerical solutions are obtained to the time-dependent axisymmetric Navier-Stokes equations, and the treatment of the interfaces is modeled by use of the Height of Liquid method. Complete three-component velocity fields, together with the evolution of the interface deformations, are depicted. At small times, when the kinematic viscosity in the upper layer is smaller than in the middle layer, the top interface rises (sinks) in the central axis (peripheral) region. When the kinematic viscosity in the lower layer is smaller than in the middle layer, the bottom interface rises (sinks) in the periphery (axis) region. Detailed shapes of interfaces are illustrated for several cases of exemplary viscosity ratios.

• Journal of The Korean Society of Agricultural Engineers
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• v.50 no.4
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• pp.67-75
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• 2008

In construction facilities such as bridges, the fluid boundary layer(or water film) is formed at the structure-soil interface by the inflow into the system due to rainfall or/and rising ground-water. As a result, the structure-soil interaction(SSI) state changes into the structure-fluid-soil interaction(SFSI) state. In general, construction facilities may be endangered by the inflow of water into the soil foundation. Thus, it is important to predict the dynamic SFSI responses accurately so that the facilities may be properly designed against such dangers. It is desired to have the robust tools of attaining such a purpose. However, there has not been any report of a method for the SFSI analyses. The objective of this study is to propose an efficient method of finite element modelling using the new interface element named hybrid interface element capable of giving reasonable predictions of the dynamic SFSI response. This element enables the simulation of the limited normal tensile resistance and the tangential hydro-plane behaviour, which has not been preceded in the previous studies. The hybrid interface element was tested numerically for its validity and employed in the analysis of SFSI responses of the continuous bridge subjected to seismic load under rainfall or/and rising ground-water condition. It showed that dynamic responses of the continuous bridge resting on direct foundation may be amplified under rainfall condition and consequently lead to significant variation of stresses.

• Journal of the Korean Society for Marine Environment & Energy
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• v.10 no.2
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• pp.107-111
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• 2007

A two-dimensional numerical method for inviscid two-fluid flows with evolution of density interface is developed, and an initially stationary two-dimensional fluid sheet surrounded by another fluid is studied. The interface between two fluids is modeled as a vortex sheet, and the flow field with the evolution of interface is solved by using vortex-in-cell/front-tracking method. The edge of the sheet is pulled back into the sheet due to surface tension and a blob is formed at the edge. This blob and fluid sheet are connected by a thin neck. In the inviscid limit, such process of the blob and neck formation is examined in detail and their kinematic characteristics are summarized with dimensionless parameters. The edge recedes at and the capillary wave propagating into the fluid sheet must be considered for better understanding of the edge receding.