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Numerical solution of the advection-diffusion equation using Laplace transform finite analytical method / Mahmud Ahsan in JRBM : International journal of river basin management, Vol. 10 N° 2 (Avril 2012) 

Public ISBD [article]  in JRBM : International journal of river basin management > Vol. 10 N° 2 (Avril 2012) . - pp. 177-188 Titre : Numerical solution of the advection-diffusion equation using Laplace transform finite analytical method Type de document : texte imprimé Auteurs : Mahmud Ahsan, Auteur Année de publication : 2012 Article en page(s) : pp. 177-188 Note générale : Hydraulique Langues : Anglais (eng) Mots-clés : Advection-diffusion  Laplace  transform  Finite-difference  method  Finite  analytical  method  Water  quality Résumé : In this study, a numerical method has been investigated and developed to solve the one-dimensional advection-diffusion equation to predict the quality of water in rivers. In this method, time variable is eliminated first by the Laplace transformation, and then a finite analytical method is applied in space. Both are based on a local element of the discretized domain in a finite-volume method. Since the Laplace transformation has been used for temporal approximation, an efficient and accurate inverse Laplace transform method of De Hoog 1982 [An improved method for numerical inversion of Laplace transform. SIAM, Journal of Scientific and Statistical Computing, 3 (3), 357–366] is employed to obtain the solution in real time. The proposed method is compared against analytical solutions and two finite-difference methods. The present computations and comparisons show that the proposed method is superior to the finite-difference methods. The results of the proposed method also agree with analytical solutions without numerical oscillation or diffusion. The present method is applied to steady and unsteady flows and it also provides flexibility for uniform and non-uniform grid spacing and for a wide range of Péclet numbers. It takes less computational effort than finite-difference methods. ISSN : 1571-5124 En ligne : http://www.tandfonline.com/doi/full/10.1080/15715124.2012.679736 [article] Numerical solution of the advection-diffusion equation using Laplace transform finite analytical method [texte imprimé] / Mahmud Ahsan, Auteur . - 2012 . - pp. 177-188. Hydraulique Langues : Anglais (eng) in JRBM : International journal of river basin management > Vol. 10 N° 2 (Avril 2012) . - pp. 177-188 Mots-clés : Advection-diffusion  Laplace  transform  Finite-difference  method  Finite  analytical  method  Water  quality Résumé : In this study, a numerical method has been investigated and developed to solve the one-dimensional advection-diffusion equation to predict the quality of water in rivers. In this method, time variable is eliminated first by the Laplace transformation, and then a finite analytical method is applied in space. Both are based on a local element of the discretized domain in a finite-volume method. Since the Laplace transformation has been used for temporal approximation, an efficient and accurate inverse Laplace transform method of De Hoog 1982 [An improved method for numerical inversion of Laplace transform. SIAM, Journal of Scientific and Statistical Computing, 3 (3), 357–366] is employed to obtain the solution in real time. The proposed method is compared against analytical solutions and two finite-difference methods. The present computations and comparisons show that the proposed method is superior to the finite-difference methods. The results of the proposed method also agree with analytical solutions without numerical oscillation or diffusion. The present method is applied to steady and unsteady flows and it also provides flexibility for uniform and non-uniform grid spacing and for a wide range of Péclet numbers. It takes less computational effort than finite-difference methods. ISSN : 1571-5124 En ligne : http://www.tandfonline.com/doi/full/10.1080/15715124.2012.679736