• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.423-440
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• 2016

The bubble stabilization technique of Chebyshev-Legendre high-order element methods for one dimensional advection-diffusion equation is analyzed for the proposed scheme by Canuto and Puppo in [8]. We also analyze the finite element lower-order preconditioner for the proposed stabilized linear system. Further, the numerical results are provided to support the developed theories for the convergence and preconditioning.

• Journal of the Korean Society of Visualization
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• v.20 no.3
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• pp.74-85
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• 2022

We propose a Cubic-Interpolated Pseudo-Particle Lattice Boltzmann method (CIP-LBM) for the convection-diffusion equation (CDE) based on the Bhatnagar-Gross-Krook (BGK) scheme equation. The CIP-LBM relies on an accurate numerical lattice equilibrium particle distribution function on the advection term and the use of a splitting technique to solve the Lattice Boltzmann equation. Different schemes of lattice spaces such as D1Q3, D2Q5, and D2Q9 have been used for simulating a variety of problems described by the CDE. All simulations were carried out using the BGK model, although another LB scheme based on a collision term like two-relation time or multi-relaxation time can be easily applied. To show quantitative agreement, the results of the proposed model are compared with an analytical solution.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1841-1844
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• 2004

'Mixing Index($D_I$)'s generally used to measure the degree of mixing. A new method to calculate $D_I$ was proposed, when insoluble solution flows in micromixer. 'Vortex Index (${\Omega}_I$)'which indicate the degree of chaotic advection, is defined and formulated. A lots of arbitrary shaped microchannels were tested to calculate the $D_I$ and ${\Omega}_I$. And then a simple algebraic equation, $D_I=A{\Omega}_I+B$, was obtained. This equation may be used instead of partial differential equation, concentration equation.

• Water for future
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• v.23 no.1
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• pp.119-127
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• 1990

The concentration of cohesive suspended sediment is determined by the circulation of water and the material dispersion. The equations of the two-dimensional, depth-integrated dispersive transport are the Reynolds equation, continuity equation, and advection-dispersion equation based on the Fick's law. A finite difference method has been applied to two models of circulation and dispersion transport. The circulation model is solved by the explicit scheme and the dispersion transport model is solved by multi-operational scheme. It is investigated wheter advective terms are included when the equation of circulation is applied to the model. For advection-dispersion equation, it was also investigated about variations of suspended sediment concentration with respect to the critical shear stresses.

• Proceedings of the Korean Society of Computer Information Conference
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• 2023.07a
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• pp.585-586
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• 2023

본 논문에서는 바람의 이류(Advection)를 고려하여 사운드의 전파를 변형하는 방법을 제시한다. 사운드는 공기와 같은 매질의 진동을 통해 전파되는 파동이며, 이런 바람의 이동 방향은 사운드 에너지 전파에 직접적인 영향을 주며, 본 논문에서는 이를 광선추적법(Raytracing) 기반으로 모델링한다. 기존의 사운드 전파는 물리기반, 기하처리(Geometry processing), 혼합기법(Hybrid method) 등의 방법이 제안됐으며, 다양한 장면에서 좋은 결과를 만들어냈다. 하지만 바람의 움직임은 유체역학을 기반으로 한 나비에-스토크스 방정식(Navier-Stokes equation)에 의해 표현되기 때문에 사운드 전파만으로는 바람의 영향을 고려한 전파 형태를 모델링할 수 없다. 본 논문에서는 바람의 유동 중 이류를 고려하여 사운드 맵을 효율적으로 변형할 수 있는 방법을 제시한다.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.2 s.233
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• pp.232-238
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• 2005

The 'Mixing Index($D_I$)' is used as a conventional guidance measuring the degree of mixing for multiphase flows. For the case when insoluble solutions flow in a passive micromixer, a new method to calculate $D_I$ is proposed. The 'Vortex Index(${\Omega}_I$)' is suggested and formulated. We infer that ${\Omega}_I$ relates to the degree of chaotic advection. Various arbitrary shaped microchannels were tested to calculate the $D_I\;and\;{\Omega}_I$, and then a simple algebraic equation, $D_I=Aexp(B{\Omega}_I)$, is obtained. This equation may be used instead of the conventional partial differential equation, concentration equation, to estimate the degree of mixing.

• Nuclear Engineering and Technology
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• v.52 no.4
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• pp.819-826
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• 2020

The method of the Laplace transform has been used to obtain an analytical solution of the three-dimensional steady state advection diffusion equation for the airborne radionuclide release from any nuclear installation such as the power reactor in an area source. The present treatment takes into account the removal of the pollutants through the nuclear reaction. We assume that the pollutants are emitted as a constant rate from the area source. This physical consideration is achieved by assuming that the vertical eddy diffusivity coefficient should be a constant. The prevailing wind speed is a constant in 𝑥- direction and a linear function of the vertical height z. The present model calculations are compared with the other models and the available data of the atmospheric dispersion experiments that were carried out in the nuclear power plant of Angra dos Reis (Brazil). The results show that the present treatment performs well as the analytical dispersion model and there is a good agreement between the values computed by our model and the observed data.

• Journal of Korea Water Resources Association
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• v.37 no.11
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• pp.889-896
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• 2004

The fractal advection-diffusion equation (ADE) is a generalization of the classical AdE in which the second-order derivative is replaced with a fractal order derivative. While the fractal ADE have been analyzed with a stochastic process In the Fourier and Laplace space so far, in this study a fractal ADE for describing solute transport in rivers is derived with a finite difference scheme in the real space. This derivation with a finite difference scheme gives the hint how the fractal derivative order and fractal diffusion coefficient can be estimated physically In contrast to the classical ADE, the fractal ADE is expected to be able to provide solutions that resemble the highly skewed and heavy-tailed time-concentration distribution curves of contaminant plumes observed in rivers.

• Water for future
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• v.28 no.5
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• pp.151-162
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• 1995

A two-dimensional stream tube dispersion model is developed to simulate accurately transverse dispersion processes of pollutants in natural channels. Two distinct features of the stream tube dispersion model derived herein are that it employs the transverse cumulative discharge as an independent variable replacing the transverse distance and that it is developed in a natural coordinate system which follows the general direction of the channel flow. In the model studied, Eulerian-Lagrangian method is used to solve the stream tube dispersion equation. The stream tube dispersion equation is decoupled into two components by the operator-splitting approach; one is governing advection and the other is governing dispersion. The advection equation has been solved using the method of characteristics and the results are interpolated onto Eulerian grid on which the dispersion equation is solved by centered difference method. In solving the advection equation, cubic spline interpolating polynomials is used. In the present study, the results of the application of this model to a natural channel are compared with a steady-state flow measurements. Simulation results are in good accordance with measured data.

• Water for future
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• v.27 no.2
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• pp.155-166
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• 1994

Various Eulerian-Lagrangian numerical models for the one-dimensional longitudinal dispersion equation are studied comparatively. In the model studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing adveciton and the other dispersion. The advection equation has been solved using the method of characteristics following fluid particles along the characteristic line and the results are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpolation polynomials are superior to Lagrange interpolation polynomials in reducing dissipation and dispersion errors in the simulation.