Avaliação de Três Formas de Soluções de Sistemas de Equações de Transporte Advectivo-difusivo com Decaimento
DOI:
https://doi.org/10.5540/tema.2007.08.03.0443Abstract
Este trabalho apresenta uma avaliação abrangente de três formas para resolver sistemas de equações de transporte advectivo-difusivo com decaimento em um meio fluido. As formas avaliadas diferenciam-se em acoplada implícita, desacoplada sequencialmente implícita e desacoplada explícita. Os modelos podem ser descritos por esquemas de reações irreversível ou reversível envolvendo tanto os processos de reações lineares quanto os não lineares. Para o caso das equações que envolvam processos não lineares pode-se utilizar a primeira ordem da expansão em série de Taylor de forma a lineariza-los, sendo então possível analisar este caso também. Avaliou-se os resultados obtidos considerando o n´umero da Peclet de malha (Pe). Se Pe > 1, a advecção é dominante, os sistemas acoplado implícito, desacoplado sequencialmente implícito e desacoplado explícito geram resultados satisfatórios. Observou-se ainda nas avaliações que nos sistemas acoplado e desacoplado sequencialmente implícito os resultados são satisfatórios para qualquer valor de Peclet. O mesmo não ocorre para o caso do desacoplamento explícito, onde se Pe < 1, difusão dominante, o método gera resultados não satisfatórios.References
[1] M. Bai, Z. Shu, J. Cao, et al., A semi-analytical solution for a two-dimensional capacitance model in solute transport, Journal of Petroleum Science and Engineering, 22 (1999), 275-295.
A.N. Brooks, T.J.R. Hughes, Streamline-upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comp. Meth. Appl. Mech. Engrg., 32 (1982), 199-259.
M.A. Célia, J.S. Kindred, Contaminant transport and biodegradation 1. A numerical model and test simulations, Water Resources Research, 25, No. 6 (1989a), 1149-1159.
M.A. Célia, J.S. Kindred, I. Herrera, Contaminant transport and biodegradation. 2. Conceptual model for reactive transport in porous media, Water Resources Research, 25, No. 6 (1989b), 1141-1148.
T.P. Clement, Generalized solution to multispecies transport equations coupled with a first-order reaction network, Water Resources Research, 37, No. 1(2001), 157-163.
A.E. Croucher, M.J. O’Sullivan, Numerical methods for contaminant transport in river and estuaries, Computers & Fluids, 27, No. 8 (1998), 861-878.
P.A. Domenico, An analytical model for multidimensional transport of a decaying contaminant species, Journal of Hydrology, 91 (1987), 49-58.
D.A. Farrell, A.D. Woodbury, Numerical modelling of mass transport in hydrogeologic environments: performance comparison of Laplace Transform Galerkin and Arnoldi modal reduction schemes, Adv. Water Resources, 21 (1998), 217-235.
J.J. Kaluarachchi, J. Morshed, Critical assessment of the operator-splitting technique in solving the advection-dispersion-reaction equation: 1. First-order reaction, Advances in Water Resources, 18, No. 2 (1995), 89-100.
K. Park, A.Y. Kuo, Multi-step computation scheme: decoupling kinetic from physical transport in water quality models, Water Research, 30, No. 10 (1996), 2255-2264.
N.M.L. Romeiro, “Simulação Numérica de Modelos de Qualidade de água usando o Método de Elementos Finitos Estabilizados”, Tese de Doutorado, COPPE/UFRJ/RJ, 2003.
N.M.L. Romeiro, R.G.S. Castro, L. Landau, “Análise comparativa de modelos de transporte de poluentes com reações cinéticas linear, linearizadas e não linear”, em 56o Seminário Brasileiro de Análise, Niterói, RJ, 917-927, 2002.
N.M.L. Romeiro, R.G.S. Castro, L. Landau, “Modelo Acoplado de Transporte de Poluentes de M´ultiplas Espécies com Reações Cinéticas Não Lineares”, em 58o Seminário Brasileiro de Análise, UNICAMP, Campinas, SP, 465-472, 2003.
N.M.L. Romeiro, R.G.S. Castro, S.M.C., Malta, L. Landau, “A Linearization Technique for Multi-species Transport Problems”, Transport in Porous Media, Publicado online, http://dx.doi.org/10.1007/s11242-006-9081-4, 2007.
Y. Sun, J.N. Petersen, T.P. Clement, et al., Development of analytical solutions for multispecies transport with serial and parallel reactions, Water Resources Research, 35, No. 1 (1999a), 185-190.
Y. Sun, J.N. Petersen, T.P. Clement, Analytical solutions for multiple species reactive transport in multiple dimensions, Journal of Contaminant Hydrology, 35 (1999b), 429- 440.
M.T. Van Genuchten, Analytical solutions for chemical transport with simultaneous adsorption, zero-order production and first-order decay, Journal of Hydrology, 49 (1981), 213-233.
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