• 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.

• 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.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.7
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• pp.3275-3284
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• 2012

This study analyzed a 3D hydrodynamic advection diffusion using the EFDC model (Environmental Fluid Dynamics Code) in the agriculture lake to prevent stratification when we install a water circulator. EFDC model was predicted the range of the water circulator and various operational parameters ware derived for minimize the impact of the internal lake. Through EFDC simulation, water circulation is started overall circulation after 30days and a lake overall circulation showed that it was possible operated the water circulator after about 100days. Also, advection diffusion concentration was low in a lake when water circulator operate intermittent condition than continuous condition. And the entire circulation was stable in this condition. The S/B (Surface/Bottom) ratio can reduce the impact of lake as the surface water mixing a lot of. When the same condition (S/B ratio(3:1)), Case 8 (50days operation: 50days stop) of condition were able to minimize the impact of lake.

• Advances in environmental research
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• v.4 no.3
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• pp.183-196
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• 2015

Migration of leachate generated through embankment of construction waste soil (CWS) in low-lying areas was studied through physical and chemical analysis. A leachate solution containing soluble cations from CWS was found to have a pH above 9.0. To determine the distribution coefficients in the alkali solution, column and migration tests were conducted in the laboratory. The physical and chemical properties of CWS satisfied environmental soil criteria; however, the pH was high. The effective diffusion coefficients for CWS ions fell within the range of $0.725-3.3{\times}10^{-6}cm^2/s$. Properties of pore water and the amount of undissolved gas in pore water influenced advection-diffusion behavior. Contaminants migrating from CWS exhibited time-dependent concentration profiles and an advective component of transport. Thus, the transport equations for CWS contaminant concentrations satisfied the differential equations in accordance with Fick's 2nd law. Therefore, the migration of the contaminant plume when the landfilling CWS reaches water table can be predicted based on pH using the effective diffusion coefficient determined in a laboratory test.

• 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.45 no.2
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• pp.179-189
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• 2012

To simulate the transport of pollutant, a numeric model for the advection-diffusion equation with the decay term is developed. This is finite-difference model using the implicit method (with the weight factor ${\alpha}$) and Gauss-Seidel SOR(successive over-relaxation). This model is compared to the analytical solutions (of simpler dimensional or boundary conditions), and in the condition of Peclet number < 5~20, the result shows stable condition, and Crank-Nicolson method (${\alpha}$=0.5) shows the more accurate results than fully-implicit method (${\alpha}$=1). The mass of advection, diffusion and decay is calculated and the error of mass balance is less than 3%. This model can evaluate the 3-D concentrations of the advection-diffusion and decay problems, but this model uses only the finite-difference method with the fixd grid system, so it can be effectively used in the problems with small Peclet numbers like the pollutant transport in groundwater.

• Journal of Korea Water Resources Association
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• v.34 no.5
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• pp.499-509
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• 2001

2-D transport model based on a discrete probability distribution for a particle displacement was developed too solve advection-diffusion problems in natural stream. In this proposed model, the probabilities expressed as an average and variance function were used to predict the mass transfer between cells in one time step. The proposed model produces solutions without numerical dispersion for constant velocity, diffusion coefficient, and cross-sectional area. When the stability and positivity restrictions were satisfied, the model produced excellent results compared to analytical solutions and other finite difference methods. The proposed model is tested against the dispersion data collected in the Grand River, Canada. The simulation results show that the proposed model can properly describe the two-dimensional mixing phenomena in the natural stream.

• Journal of Environmental Science International
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• v.7 no.4
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• pp.511-522
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• 1998

The two-stage numerical model was used to study the relation between three-dimensional local wind seal area for Korean peninsula. The first stave is three dimensional time-dependent local wind model which elves the wind field and vertical diffusion coefncient. The second stage is advection/duusion model which uses the results of the first stage as input data. First, wand fields on Korean peninsula for none synoptic scale wand showed typical land and sea breeze circulation, and the emitted particles were transported by sea breeze for daytime, emissions return to sea by land breeze for nighttime.

• 한국해양학회지
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• v.23 no.1
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• pp.13-23
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• 1988

A simple model is presented which may explain the distributions of cold surface water near Ulsan. The model considers the problem as an advection-diffusion process with cold source confined within narrow coastal areas. The natural warming due to vertical process (interaction either with the atmosphere above or with the subsurface water below) also plays an important role. A simple numerical computation reproduces the observations quite well. The localization of cold surface water occurs at the point where the local warm current separates from the coast.

• Journal of Korean Society for Atmospheric Environment
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• v.8 no.3
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• pp.162-168
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• 1992

Numerical solutions to the advection equations used for long-range transport air pollution models are calculated using three numerical methods; Antidiffusion correction method(Smolarkiewicz, 1983), Positive definite advecton scheme obtained by nonlinear renormalization of the advective fluxes(Bott, 1989), and Positive definite pseudospectral method(Bartnicki, 1989). Accuracy, numerical diffusion and computational time requirement are compared for two-dimensional transport calculations in a uniform rotational flow field. The solutions from three methods are positive definite. Bartnicki(1989)'s method is most conservative but requires approximately 10 times as much computational time as Smolarkiewicz(1983)'s method of which numerical diffusion is the largest. All three methods are more conservative for a cone shape initial condition than for a rectangular block initial condition with a steep gradient.