• 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.

• Bulletin of the Korean Chemical Society
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• v.7 no.4
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• pp.283-288
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• 1986

A nonlinear analysis is presented for the treatment of fluctuations near the critical point in the presence of diffusion in the Schlogl models. The two time scaling method is used to obtain an evolution equation for the amplitude of fluctuations. It is shown that the fluctuations decay to zero in the stable region and they are enhanced to a finite value as time goes to infinity in the unstable region.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1259-1268
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• 2017

The alpha eigenvalue problem in multigroup neutron diffusion is studied with particular attention to the theoretical analysis of the model. Contrary to previous literature results, the existence of eigenvalue and eigenflux clustering is investigated here without the simplification of a unique fissile isotope or a single emission spectrum. A discussion about the negative decay constants of the neutron precursors concentrations as potential eigenvalues is provided. An in-hour equation is derived by a perturbation approach recurring to the steady state adjoint and direct eigenvalue problems of the effective multiplication factor and is used to suggest proper detection criteria of flux clustering. In spite of the prior work, the in-hour equation results give a necessary and sufficient condition for the existence of the eigenvalue-eigenvector pair. A simplified asymptotic analysis is used to predict bands of accumulation of eigenvalues close to the negative decay constants of the precursors concentrations. The resolution of the problem in one-dimensional heterogeneous problems shows numerical evidence of the predicted clustering occurrences and also confirms previous theoretical analysis and numerical results.

• Nuclear Engineering and Technology
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• v.54 no.4
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• pp.1195-1205
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• 2022

Recent developments on spectral diffusion algorithms, i.e., algorithms which exploit the projection of the solution on the eigenfunctions of the Laplacian operator, demonstrated their effective applicability in fast transient conditions. Nevertheless, the numerical error introduced by these algorithms, together with the uncertainties associated with model parameters, may impact the reliability of the predictions on short-lived volatile fission product release from nuclear fuel. In this work, we provide an upper bound on the numerical error introduced by the presented spectral diffusion algorithm, in both constant and time-varying conditions, depending on the number of modes and on the time discretization. The definition of this upper bound allows introducing a methodology to a priori bound the numerical error on short-lived volatile fission product retention.

• Journal of Korea Water Resources Association
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• v.32 no.6
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• pp.607-616
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• 1999

A fractional step finite difference model for the longitudinal dispersion of nonconservative contaminants is developed. It is based on splitting the longitudinal dispersion equation into a set of three equations each to be solved over a one-third time step. The fourth-order Holly-Preissmann scheme, an analytic solution, and the Crank-Nicholson scheme are used to solve the equations for the pure advection, the first-order decay, and the diffusion, respectively. To test the model, it is applied to simulate the longitudinal dispersion of continuous source released into a nonuniform flow field as well as the dispersion of an instantaneous source in a uniform flow field. The results are compared with the exact solution and those computed by an existing model. Compared to the existing model which uses Euler method for the first-order decay equation, the present model yield more accurate results as the decay coefficient increases.

• Journal of Hydrogen and New Energy
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• v.20 no.6
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• pp.479-484
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• 2009

The effect of anode gas channel height on gas diffusion and cell performance in a 100 $cm^2$ class molten carbonate single cell is investigated. Single cell separators with three different channel height are used. The effect of the gas channel height on the distribution of the reactive gas concentration is evaluated by the two-dimensional concentration diffusion equation. The overpotential caused by concentration drop with different channel height is estimated by the voltage decay related to diffusion of reactants, well known as concentration polarization, using limiting current density. The estimation could have the possibility to identify the reactant mass transfer polarization in the complicate factors of the overall electrodes.

• Environmental Sciences Bulletin of The Korean Environmental Sciences Society
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• v.10 no.S_3
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• pp.97-106
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• 2001

To improve the water quality, particularly for sea bathers, the behaviour of wastewater from sewage outfalls in water adjacent to Swansea, UK, was studied using a mathematical model. The water quality in the sewage receiving basin was determined using factors like the outfall diffuser location(distance from land boundary), sewage treatment scheme, discharge time, and bacteria decay rate, etc. With respect to these factors, an optimal strategy for sewage discharge was then investigated to minimize bacteria levels along the bathing beaches. As water quality criteria, predicted faecal coliform levels were monitored along the coast adjacent to the outfall locations. The resultant values were compared with EC Mandatory(<2000, 95 % of 20 samples) and Guideline Standards(< 100, 80 % of 20 samples). For the advective-diffusion equation, the non linear advective terms were represented using the ULTIMATE algorithm and the third-order accurate QUICKEST scheme to avoid numerical diffusion. Details of the simulation results are then presented as an optimal policy for sewage discharge in the region.

• Nuclear Engineering and Technology
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• v.54 no.8
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• pp.2771-2782
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• 2022

When assessing the radiological consequences of postulated accident scenarios, it is of primary interest to determine the amount of radioactive fission gas accumulated in the fuel rod free volume. The state-of-the-art semi-empirical approach (ANS 5.4-2010) is reviewed and compared with a mechanistic approach to evaluate the release of radioactive fission gases. At the intra-granular level, the diffusion-decay equation is handled by a spectral diffusion algorithm. At the inter-granular level, a mechanistic description of the grain boundary is considered: bubble growth and coalescence are treated as interrelated phenomena, resulting in the grain-boundary venting as the onset for the release from the fuel pellets. The outcome is a kinetic description of the release of radioactive fission gases, of interest when assessing normal and off-normal conditions. We implement the model in SCIANTIX and reproduce the release of short-lived fission gases, during the CONTACT 1 experiments. The results show a satisfactory agreement with the measurement and with the state-of-the-art methodology, demonstrating the model soundness. A second work will follow, providing integral fuel rod analysis by coupling the code SCIANTIX with the thermo-mechanical code TRANSURANUS.