Pure and Applied Mathematics Journal

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Shallow Water 1D Model for Pollution River Study

Received: 25 February 2017    Accepted: 23 March 2017    Published: 15 April 2017
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Abstract

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.

DOI 10.11648/j.pamj.20170602.13
Published in Pure and Applied Mathematics Journal (Volume 6, Issue 2, April 2017)
Page(s) 76-88
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Partial Differential Equation, Finite Elements, Shallow Water Flow, River Pollution

References
[1] 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.
[2] 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.
[3] 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.
[4] M. Atallah and A. Hazzad, “A Petrov-Galerkin scheme for modeling 1D channel flow with variating width and topography”. Acta Mechanica, 223, 12, 2012.
[5] 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.
[6] D. Biasioni, “Analisi delle portate Rio Sass e Torrente Novella”. International report, Comune di Dambel, Trento, Italy, 2009-2010.
[7] 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.
[8] 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.
[9] 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.
[10] 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.
[11] 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.
[12] 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.
[13] IUPAC FOOTPRINT Pesticides Properties Database, http://sitem.herts.ac.uk/aeru/iupac/ Last accessed: March 26, 2013.
[14] 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.
[15] 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.
[16] 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.
[17] 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.
[18] Meteotrentino webside: “http://www.meteotrentino.it/” Last accessed: March 26, 2013.
[19] 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.
[20] 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.
[21] A. Quarteroni and A. Valli, “Domain decomposition methods for partial differential equations”. Oxford Science Publications, 1999.
[22] 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.
[23] L. J. Thibodeaux and D. Mackay, “Handbook of estimation methods for chemical mass transport in the environment”. CRC Press, New York 2011.
[24] C. D. S. Tomlin, “The Pesticide Manual: A World Compendium”. Eleventh ed. British Crop Protection Council, Farhnham, Surrey, UK 1997.
[25] 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.
[26] 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.
[27] 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.
Author Information
  • Department of Fundamental Sciences, Laws and Humanities, Institute of Mines and Petroleum Industries, University of Maroua at Kaéle, Maroua, Cameroon

  • Science and High Tecnology Department, Università Degli Studi Dell'Insubria, Via Valleggio, Como, Italy

  • Science and High Tecnology Department, Università Degli Studi Dell'Insubria, Via Valleggio, Como, Italy

  • Science and High Tecnology Department, Università Degli Studi Dell'Insubria, Via Valleggio, Como, Italy

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  • APA Style

    Antoine Celestin Kengni Jotsa, Vincenzo Angelo Pennati, Antonio Di Guardo, Melissa Morselli. (2017). Shallow Water 1D Model for Pollution River Study. Pure and Applied Mathematics Journal, 6(2), 76-88. https://doi.org/10.11648/j.pamj.20170602.13

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    ACS Style

    Antoine Celestin Kengni Jotsa; Vincenzo Angelo Pennati; Antonio Di Guardo; Melissa Morselli. Shallow Water 1D Model for Pollution River Study. Pure Appl. Math. J. 2017, 6(2), 76-88. doi: 10.11648/j.pamj.20170602.13

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    AMA Style

    Antoine Celestin Kengni Jotsa, Vincenzo Angelo Pennati, Antonio Di Guardo, Melissa Morselli. Shallow Water 1D Model for Pollution River Study. Pure Appl Math J. 2017;6(2):76-88. doi: 10.11648/j.pamj.20170602.13

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  • @article{10.11648/j.pamj.20170602.13,
      author = {Antoine Celestin Kengni Jotsa and Vincenzo Angelo Pennati and Antonio Di Guardo and Melissa Morselli},
      title = {Shallow Water 1D Model for Pollution River Study},
      journal = {Pure and Applied Mathematics Journal},
      volume = {6},
      number = {2},
      pages = {76-88},
      doi = {10.11648/j.pamj.20170602.13},
      url = {https://doi.org/10.11648/j.pamj.20170602.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.pamj.20170602.13},
      abstract = {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.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Shallow Water 1D Model for Pollution River Study
    AU  - Antoine Celestin Kengni Jotsa
    AU  - Vincenzo Angelo Pennati
    AU  - Antonio Di Guardo
    AU  - Melissa Morselli
    Y1  - 2017/04/15
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    DO  - 10.11648/j.pamj.20170602.13
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
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    EP  - 88
    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.20170602.13
    AB  - 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.
    VL  - 6
    IS  - 2
    ER  - 

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