In this paper, the 2D mathematical water pollution model describing the transport–diffusion processes of some contaminant substances in Thanh Nhan Lake in Hanoï is considered. The finite-volume method is used to solve the model equations. The Singular Evolutive Interpolated Kalman filter is applied to evaluate the pollution level at arbitrary mesh point based only on a small number of measurement points.
Dans cet article, on étudie le processus de transport–diffusion de substances contaminantes dans le lac Than Nhan de Hanoï. Cela se traduit par un modèle mathématique bimensionnel d'équations aux dérivées partielles. Une approximation numérique de la solution est obtenue par une méthode de volumes finis. Des mesures de pollution sont faites en un nombre de points faible. Pour évaluer la pollution en tout point de discrétisation, on propose d'utiliser la méthode du filtre de Kalman singulier évolutif et interpolé.
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Mots-clés : Assimilation de données, Méthode des volumes finis, Modèle hydraulique 2D, Filtre de Kalman, Pollution
Thu Ha Tran 1; Dinh Tuan Pham 2; Van Lai Hoang 1; Hong Phong Nguyen 1
@article{CRMECA_2014__342_2_106_0,
author = {Thu Ha Tran and Dinh Tuan Pham and Van Lai Hoang and Hong Phong Nguyen},
title = {Water pollution estimation based on the {2D} transport{\textendash}diffusion model and the {Singular} {Evolutive} {Interpolated} {Kalman} filter},
journal = {Comptes Rendus. M\'ecanique},
pages = {106--124},
publisher = {Elsevier},
volume = {342},
number = {2},
year = {2014},
doi = {10.1016/j.crme.2013.10.007},
language = {en},
}
TY - JOUR AU - Thu Ha Tran AU - Dinh Tuan Pham AU - Van Lai Hoang AU - Hong Phong Nguyen TI - Water pollution estimation based on the 2D transport–diffusion model and the Singular Evolutive Interpolated Kalman filter JO - Comptes Rendus. Mécanique PY - 2014 SP - 106 EP - 124 VL - 342 IS - 2 PB - Elsevier DO - 10.1016/j.crme.2013.10.007 LA - en ID - CRMECA_2014__342_2_106_0 ER -
%0 Journal Article %A Thu Ha Tran %A Dinh Tuan Pham %A Van Lai Hoang %A Hong Phong Nguyen %T Water pollution estimation based on the 2D transport–diffusion model and the Singular Evolutive Interpolated Kalman filter %J Comptes Rendus. Mécanique %D 2014 %P 106-124 %V 342 %N 2 %I Elsevier %R 10.1016/j.crme.2013.10.007 %G en %F CRMECA_2014__342_2_106_0
Thu Ha Tran; Dinh Tuan Pham; Van Lai Hoang; Hong Phong Nguyen. Water pollution estimation based on the 2D transport–diffusion model and the Singular Evolutive Interpolated Kalman filter. Comptes Rendus. Mécanique, Volume 342 (2014) no. 2, pp. 106-124. doi : 10.1016/j.crme.2013.10.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.10.007/
[1] On some linearized problems of shallow water flows, Differ. Integral Equ., Volume 22 (2009) no. 3–4, pp. 275-283
[2] 2D-Model of contaminant water transmission processes and numerical simulation on a natural lake, J. Mech., Volume 32 (2010) no. 3, pp. 157-166
[3] A simplified reduced order Kalman filtering and application to altimetric data assimilation in the Tropical Pacific, J. Mar. Syst., Volume 36 (2002) no. 1, pp. 101-127
[4] A singular evolutive extended Kalman filter for data assimilation in oceanography, J. Mar. Syst., Volume 16 (1998) no. 3–4, pp. 323-340
[5] Filtres de Kalman singuliers évolutif pour l'assimilation de données en océnographie, C. R. Acad. Sci. Paris, Ser. IIa, Volume 326 (1998), pp. 255-260
[6] Stochastic methods for sequential data assimilation in strongly nonlinear systems, Mon. Weather Rev., Volume 129 (2001) no. 5, pp. 1194-1207
[7] Sequential data assimilation with a non-linear quasi-geostrophic model using Monte-Carlo methods to forecast error statistics, J. Geophys. Res., Volume 99 (1994) no. C5, pp. 10143-10162
[8] Advanced data assimilation in strongly nonlinear dynamics, Mon. Weather Rev., Volume 125 (1997), pp. 1342-1354
[9] S.J. Julier, J.K. Uhlmann, A new extension of the Kalman filter to nonlinear systems, in: Proc. of AeroSense: The 11th Int. Symp. on Aerospace/Defence Sensing, Simulation and Controls, 1997.
[10] A new method for nonlinear transformation of means and covariances in filters and estimators, IEEE Trans. Autom. Control, Volume 45 (2000), pp. 477-482
[11] The unscented Kalman filter for nonlinear estimation, Lake Louise, Alberta, Canada (2000), pp. 153-158
[12] An unstructured finite volume algorithm for predicting flow in rivers and estuaries, Comput. Fluids, Volume 27 (1998), pp. 479-508
[13] River water quality modeling: I. State of the art, Water Sci. Technol., Volume 38 (1998) no. 11, pp. 237-244
[14] Water quality model for Quang Ninh-Haiphong area, Proceedings of the 8th National Congress on Mechanics, 2004, pp. 143-153
[15] Danish Hydraulic Institute, 2003, MIKE 21/3 WQ, Water quality module, Reference Manual.
[16] (User's Manual and Programmer's Guide) ( January 1988 ), pp. 78-83
[17] A. Lebosse, Codes de calcul d'écoulement à surface libre filaire “LIDO”, “SARA” et “REZO“ (Version 2), Note de validation HE-43/92-65, EDF, 1992.
[18] Analysis and computation of steady open Channel flow, University of Reading Dept. of Mathematics, 1996 (PhD thesis)
[19] Numerical Computation of Internal and External Flows. Vol. 2: Computation Methods for Inviscid and Viscous Flows, Wiley-Interscience, New York, 1988
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