Shallow Water 1D Model for Pollution River Study
Pure and Applied Mathematics Journal
Volume 6, Issue 2, April 2017, Pages: 76-88
Received: Feb. 25, 2017; Accepted: Mar. 23, 2017; Published: Apr. 15, 2017
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Antoine Celestin Kengni Jotsa, Department of Fundamental Sciences, Laws and Humanities, Institute of Mines and Petroleum Industries, University of Maroua at Kaéle, Maroua, Cameroon
Vincenzo Angelo Pennati, Science and High Tecnology Department, Università Degli Studi Dell'Insubria, Via Valleggio, Como, Italy
Antonio Di Guardo, Science and High Tecnology Department, Università Degli Studi Dell'Insubria, Via Valleggio, Como, Italy
Melissa Morselli, Science and High Tecnology Department, Università Degli Studi Dell'Insubria, Via Valleggio, Como, Italy
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In this paper a finite element 1D model for shallow water flows with distribution of chemical substances is presented. The deterministic model, based on unsteady flow and convection-diffusion-decay of the pollutants, allows for evaluating in any point of the space-time domain the concentration values of the chemical compounds. The numerical approach followed is computationally cost-effectiveness respect both the stability and the accuracy, and by means of it is possible to foresee the evolution of the concentrations.
Partial Differential Equation, Finite Elements, Shallow Water Flow, River Pollution
To cite this article
Antoine Celestin Kengni Jotsa, Vincenzo Angelo Pennati, Antonio Di Guardo, Melissa Morselli, Shallow Water 1D Model for Pollution River Study, Pure and Applied Mathematics Journal. Vol. 6, No. 2, 2017, pp. 76-88. doi: 10.11648/j.pamj.20170602.13
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V. I. Agoshkov, D. Ambrosi, V. A. Pennati, A. Quarteroni and F. Saleri, “Mathematical and numerical modeling of shallow water flow”. Computational Mechanics, 11, 280-299, 1996.
D. Ambrosi, S. Corti, V. A. Pennati and F. Saleri, “Numerical simulation of unsteady flow at Po river delta”. Journal of Hydraulic Engineering, 12, 735-743, 1996.
R. Aruba, G. Negro and G. Ostacoli, “Multivariate data analysis applied to the investigation of river pollution”. Fresenoius Journal of Analytical Chemistry, 346, 10-11, 968-975, August 1993.
M. Atallah and A. Hazzad, “A Petrov-Galerkin scheme for modeling 1D channel flow with variating width and topography”. Acta Mechanica, 223, 12, 2012.
J. P. Benquè, J. A. Cunge, J. Feuillet, A. Hauguel and F. M. Holly, “New method for tidal current computation”. Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE, 108, 396-417, 1982.
D. Biasioni, “Analisi delle portate Rio Sass e Torrente Novella”. International report, Comune di Dambel, Trento, Italy, 2009-2010.
S. Bonzini, R. Verro, S. Otto, L. Lazzaro, A. Finizio, G. Zanin and M. Vighi, “Experimental validation of geographical information system based procedure for predicting pesticide exposure in surface water”. Environmental Science Technology, 40, 7561-7569, 2006.
N. Crnjaric-Zic, S. Vukovic and L. Sopta, “Balanced finite volume WENO and central WENO schemes for the shallow water and the open channel flow equations”. Journal of Computational Physics 200, 512-548, 2004.
C. Gold, A. Feurtet-Mazel, M. Coste and A. Boudou, “Impacts of Cd and Zn on the development of Periphytic Diatom communities in artificial streams located along a river pollution gradient”. Archives of Environmental Contamination and Toxicology, 44, 2, 0189-0197, February 2003.
P. Garcia-Navarro and A. Priestly, “A conservative and shape-preserving semi-Lagrangian method for the solution of the shallow water equations”. International Journal for Numerical Methods in Fluids, 18, 273-294, 1994.
D. Ghirardello, M. Morselli, M. Semplice and A. Di Guardo, “A dynamic model of the fate or organic chemicals in a multilayered air/soil system: Development and illustrative application”. Environmental Science Technology, 44, 9010-9017, 2010.
M. E. Hubbard and P. Garcia-Navarro,”Flux Difference Splitting and the Balancing of source terms and flux gradients”. Journal of Computational Physics, 165, 89-125, 2000.
IUPAC FOOTPRINT Pesticides Properties Database, Last accessed: March 26, 2013.
A. C. Kengni Jotsa, “Solution of 2D Navier-Stokes equations by a new FE fractional step method”. PhD thesis, Università degli Studi dell'Insubria sede di Como, March 2012.
A. C. Kengni Jotsa and V. A. Pennati, “A cost effective FE method for 2D Navier-Stokes equations”. Engineering Applications of Computations Fluids Mechanics, Vol. 9, N. 1, 66-83, 2015.
W. Lai and A. A. Khan, “Discontinuous Galerkin method for 1D shallow water flow in non-rectangular and non-prismatic channels”. Journal of Hydraulic Engineering, 138 (3), 285-296, 2012.
J. M. Lescot, P. Bordenave, K. Petit and O. Leccia, “A spatially-distributed cost-effectiveness analysis framework for controlling water pollution”. Environmental Modelling and Software, 41, 107-122, March 2013.
Meteotrentino webside: “” Last accessed: March 26, 2013.
P. Ortiz, O. C. Zienkiewicz and J. Szmelter, “CBS Finite element modeling of shallow water and transport problems”. ECCOMAS 2004, Jyvaskyla, 24-28, July 2004.
J. Petera and V. Nassehi, “A new-two dimensional finite element model for shallow water equations using a Lagrangian framework constructed along fluid particle trajectories”. International Journal for Numerical Methods Engineering, 39, 4159-4182, 1996.
A. Quarteroni and A. Valli, “Domain decomposition methods for partial differential equations”. Oxford Science Publications, 1999.
A. Sharma, M. Naidu and A. Sargoankar, “Development of computer automated decision support system for surface water quality assessment”. Computers and Geosciences, 51, 129-134, February 2013.
L. J. Thibodeaux and D. Mackay, “Handbook of estimation methods for chemical mass transport in the environment”. CRC Press, New York 2011.
C. D. S. Tomlin, “The Pesticide Manual: A World Compendium”. Eleventh ed. British Crop Protection Council, Farhnham, Surrey, UK 1997.
G. Vignoli, V. A. Titarev and E. F. Toro, “ADER schemes for the shallow water equations in channel with irregular bottom elevation”. Journal of Computational Physics, 227, 4, 2463-2480, 2008.
A. Walters, “Numerically induced oscillations in the finite element approximations to the shallow water equations”. International Journal for Numerical Methods in Fluids, 3, 591-604, 1983.
O. C. Zienkiewicz and P. Ortiz, “A split-characteristic based finite element model for the shallow water equations”. International Journal for Numerical Methods in Fluids, 20, 1061-1080, 1995.
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