• Membrane Journal
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• v.29 no.1
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• pp.18-29
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• 2019

The dead-end ultrafiltration (UF) of BSA protein solution was performed to investigate the defouling effects of natural convection instability flow (NCIF) induced in membrane module. The permeate fluxes were measured according to the inclined angles ($0{\sim}180^{\circ}$) of membrane module with respect to gravity, and analyzed using the blocking filtration model. NCIF are more induced as the inclined angles increased from $0^{\circ}$ to $180^{\circ}$, and the induced NCIF enhances flux. Comparing the fluxes at $0^{\circ}$ inclined angle (no NCIF induction) and $180^{\circ}$ (maximum NCIF induction), the flux enhancements by NCIF induction are increased about 5 times in the short-term UF operation (2 hours) and about 17 times in the long-term operation (20 hours). As applying the blocking filtration model, it is more suitable to analyze the flux results by using the intermediate blocking model in the early times of UF operation within 15 minutes and then thereafter times by using the cake filtration model. NCIF induced at $180^{\circ}$ inclined angle reduces the intermediate blocking fouling at about 67% in the early times operation and thereafter the cake layer fouling at about 99.9%. The main defouling mechanism of NCIF induced in the membrane module is suppress the formation of protein cake layer.

• East Asian mathematical journal
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• v.33 no.5
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• pp.511-525
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• 2017

We introduce an extrapolated higher order characteristic finite element method to construct approximate solutions of a Sobolev equation with a convection term. The higher order of convergence in both the temporal direction and the spatial direction in $L^2$ normed space is established and some computational results to support our theoretical results are presented.

• East Asian mathematical journal
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• v.34 no.5
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• pp.601-614
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• 2018

In this paper, we introduce an extrapolated higher order characteristic finite element method to approximate solutions of nonlinear Sobolev equations with a convection term and we establish the higher order of convergence in the temporal and the spatial directions with respect to $L^2$ norm.

• East Asian mathematical journal
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• v.33 no.3
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• pp.295-308
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• 2017

We introduce a Crank-Nicolson characteristic finite element method to construct approximate solutions of a nonlinear Sobolev equation with a convection term. And for the Crank-Nicolson characteristic finite element method, we obtain the higher order of convergence in the temporal direction and in the spatial direction in $L^2$ normed space.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.257-270
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• 2018

An extrapolated Crank-Nicolson characteristic finite element method is introduced for approximate solutions of nonlinear Sobolev equations with a convection term. And we obtain the higher order of convergence for approximate solutions in the temporal and the spatial directions with respect to $L^2$ norm.

• East Asian mathematical journal
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• v.32 no.5
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• pp.729-744
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• 2016

A Crank-Nicolson characteristic finite element method is introduced to construct approximate solutions of a Sobolev equation with a convection term. The higher order of convergences in the temporal direction and in the spatial direction in $L^2$ normed space are verified for the Crank-Nicolson characteristic finite element method.

• Journal of Advanced Marine Engineering and Technology
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• v.14 no.2
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• pp.48-65
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• 1990

Numerical solutions of the Navier-Stokes equations, governing 2-dimensional, time-dependent, viscous, incompressible fluid flow past a square cylinde in an infinite region, are presented for Reynolds numbers $10^2$, $10^3$and $10^4$. Finite-difference scheme, based on SOLA-VOF is adopted and a discretization of the convection term for irregular grid is newly suggested by altering the original nonconservation form into conservation one. Distribution of finer grids around the body reveals fairly reasonable consistency with the experimental variables : drag coefficient, lift coefficient, Strouhal number, fluctuating pressure coefficient, etc.

• The Journal of the Acoustical Society of Korea
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• v.37 no.5
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• pp.263-270
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• 2018

In most industry fields concerning external flow noise problems, the hybrid computational aeroacoustic techniques based on the FW-H (Ffowcs Williams and Hawkings) equation are widely used for its numerical efficiency. However, when the surface integral form of FW-H equation is used without volume quadrupole sources, it is known to generate significant non-physical noise in a certain case. Especially, in the case of a flow in which the tip vortex cavitation is formed in the distant downstream direction such as flow driven by an underwater propeller, the accuracy in noise prediction becomes poor unless it is not properly modelled. Therefore, in this study, the nonphysical acoustic waves caused by the surface integral form of FW-H equation is reduced by adding the quadrupole correction term. First, to verify the accuracy of the in-house code of FW-H equation, the noise by an axial fan used in the outdoor unit of air conditioner was calculated and compared with the results of ANSYS Fluent. In order to verify the effects of the quadrupole correction term, the noise prediction for isentropic vortex convection is performed and it is confirmed that the error is reduced by the quadrupole correction term. Finally, the noise prediction is performed for the flow field generated by the Clark-Y hydrofoil in underwater. It is confirmed that the error caused by the cavitation passing through the integral surface can be reduced by the quadrupole correction term.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.3
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• pp.173-181
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• 1993

An improved two-dimensional Eulerian-Lagrangian convection-dispersion model was established after comparing several models. To simulate long term release of discontinuous suspended solid source from coastal dike construction, source was represented by Fourier transformation. It was concluded that this model can effectively simulate long term coastal dispersion problems.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1035-1054
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• 2010

We consider a mixed type singularly perturbed one dimensional elliptic problem with discontinuous source term. The domain under consideration is partitioned into two subdomains. A convection-diffusion and a reaction-diffusion type equations are posed on the first and second subdomains respectively. Two hybrid difference schemes on Shishkin mesh are constructed and we prove that the schemes are almost second order convergence in the maximum norm independent of the diffusion parameter. Error bounds for the numerical solution and its numerical derivative are established. Numerical results are presented which support the theoretical results.