Comptes Rendus
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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2013.10.007
Keywords: Data assimilation, Finite volume method, 2D Hydraulic model, Kalman filter, Pollution
Mot 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

1 Vietnamese Aca. of Sci. and Tech. – 18 Hoang Quoc Viet, Institute of Mechanics – 264 Doi Can, and University of Engineering and Tech. – 144 Xuan Thuy, Hanoï, Vietnam
2 Jean-Kuntzmann Laboratory, INPG/UJF/CNRS, BP 53, 38041 Grenoble cedex, France
@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] C. Licht; T.H. Tran; Q.P. Vu On some linearized problems of shallow water flows, Differ. Integral Equ., Volume 22 (2009) no. 3–4, pp. 275-283

[2] T.H. Tran; H.P. Nguyen 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] I. Hoteit; D.-T. Pham; J. Blum 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] D.-T. Pham; J. Verron; M.-C. Roubaud A singular evolutive extended Kalman filter for data assimilation in oceanography, J. Mar. Syst., Volume 16 (1998) no. 3–4, pp. 323-340

[5] D.-T. Pham; J. Verron; L. Gourdeau 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] D.-T. Pham Stochastic methods for sequential data assimilation in strongly nonlinear systems, Mon. Weather Rev., Volume 129 (2001) no. 5, pp. 1194-1207

[7] G. Evensen 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] G. Evensen 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] S. Julier; J. Uhlmann; H.F. Durrant-White 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] E.A. Wan; R. van der Merwe The unscented Kalman filter for nonlinear estimation, Lake Louise, Alberta, Canada (2000), pp. 153-158

[12] P.A. Sleigh; P.H. Gaskell; M. Berzins; N.G. Wright An unstructured finite volume algorithm for predicting flow in rivers and estuaries, Comput. Fluids, Volume 27 (1998), pp. 479-508

[13] W. Rauch; M. Henze; L. Koncsos; P. Shanahan; L. Somlyody; Vanrolleghem River water quality modeling: I. State of the art, Water Sci. Technol., Volume 38 (1998) no. 11, pp. 237-244

[14] Van Manh Dinh; Minh Hanh Pham Thi 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] WASP4 (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] Ian Macdonald Analysis and computation of steady open Channel flow, University of Reading Dept. of Mathematics, 1996 (PhD thesis)

[19] C. Hirsch Numerical Computation of Internal and External Flows. Vol. 2: Computation Methods for Inviscid and Viscous Flows, Wiley-Interscience, New York, 1988

Cited by Sources:

Comments - Policy