Ecological modeling and Lagrangian approach

Boris Arkhipov; Viacheslav Solbakov; Mikhail Solov’ev; Dmitry Shapochkin

Open Mathematics (2013)

  • Volume: 11, Issue: 4, page 734-745
  • ISSN: 2391-5455

Abstract

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A mathematical model is proposed for a quantitative estimation of the damage to biological resources resulting from a pollutant discharge into an aqueous environment. On the basis of the Lagrangian description of fluid motion a set of hydrophysical parameters is introduced with help of which hydrobiologists can estimate the damage. The computation of parameters introduced is illustrated by the example of a model problem of a pollutant spreading in a canal. For the discretization of the problem a deformable Lagrangian grid is used. A special grid reconstruction procedure with the subsequent interpolation of the parameters computed is proposed, which ensures computational stability and preserves the values of the most important hydrophysical parameters. Numerical results are presented.

How to cite

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Boris Arkhipov, et al. "Ecological modeling and Lagrangian approach." Open Mathematics 11.4 (2013): 734-745. <http://eudml.org/doc/269409>.

@article{BorisArkhipov2013,
abstract = {A mathematical model is proposed for a quantitative estimation of the damage to biological resources resulting from a pollutant discharge into an aqueous environment. On the basis of the Lagrangian description of fluid motion a set of hydrophysical parameters is introduced with help of which hydrobiologists can estimate the damage. The computation of parameters introduced is illustrated by the example of a model problem of a pollutant spreading in a canal. For the discretization of the problem a deformable Lagrangian grid is used. A special grid reconstruction procedure with the subsequent interpolation of the parameters computed is proposed, which ensures computational stability and preserves the values of the most important hydrophysical parameters. Numerical results are presented.},
author = {Boris Arkhipov, Viacheslav Solbakov, Mikhail Solov’ev, Dmitry Shapochkin},
journal = {Open Mathematics},
keywords = {Environmental impact assessment; Lagrangian approach; Pollutant transport; Transport-diffusion equation; Numerical simulation; Lagrangian grids; environmental impact assessment; pollutant transport; transport-diffusion equation; numerical simulations},
language = {eng},
number = {4},
pages = {734-745},
title = {Ecological modeling and Lagrangian approach},
url = {http://eudml.org/doc/269409},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Boris Arkhipov
AU - Viacheslav Solbakov
AU - Mikhail Solov’ev
AU - Dmitry Shapochkin
TI - Ecological modeling and Lagrangian approach
JO - Open Mathematics
PY - 2013
VL - 11
IS - 4
SP - 734
EP - 745
AB - A mathematical model is proposed for a quantitative estimation of the damage to biological resources resulting from a pollutant discharge into an aqueous environment. On the basis of the Lagrangian description of fluid motion a set of hydrophysical parameters is introduced with help of which hydrobiologists can estimate the damage. The computation of parameters introduced is illustrated by the example of a model problem of a pollutant spreading in a canal. For the discretization of the problem a deformable Lagrangian grid is used. A special grid reconstruction procedure with the subsequent interpolation of the parameters computed is proposed, which ensures computational stability and preserves the values of the most important hydrophysical parameters. Numerical results are presented.
LA - eng
KW - Environmental impact assessment; Lagrangian approach; Pollutant transport; Transport-diffusion equation; Numerical simulation; Lagrangian grids; environmental impact assessment; pollutant transport; transport-diffusion equation; numerical simulations
UR - http://eudml.org/doc/269409
ER -

References

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  1. [1] Arkhipov B.V., Koterov V.N., Solbakov V.V., Shapochkin D.A., Modeling of turbulent pollutant dispersion in sea environment, Dorodnicyn Computing Center, Russian Academy of Sciences, Moscow, 2005, preprint (in Russian) 
  2. [2] Arkhipov B.V., Solbakov V.V., Solov’ev M.B., Shapochkin D.A., Modeling of hydrodynamical processes at offshore region and ecological computations, Dorodnicyn Computing Center, Russian Academy of Sciences, Moscow, 2011, preprint (in Russian) 
  3. [3] Arkhipov B.V., Koterov V.N., Solbakov V.V., Shapochkin D.A., Yurezanskaya Yu.S., Numerical simulation of pollution and oil spill spreading by the stochastic discrete particle method, Comput. Math. Math. Phys., 2007, 47(2), 280–292 http://dx.doi.org/10.1134/S096554250702011X Zbl1210.76130
  4. [4] Arkhipov B.V., Koterov V.N., Solbakov V.V., Yurezanskaya Yu.S., Simulation of suspended substance transport on the continental shelf: computation of soil dumping in the Sea of Azov, Comput. Math. Math. Phys., 2010, 50(4), 711–720 http://dx.doi.org/10.1134/S0965542510040123 Zbl1224.86001
  5. [5] Lamb H., Hydrodynamics, 6th ed., Cambridge Math. Lib., Cambridge University Press, Cambridge, 1993 Zbl0828.01012
  6. [6] Monin A.S., Yaglom A.M., Statistical Fluid Mechanics I–II, Dover, Mineola, 2007 
  7. [7] Samarskii A.A., Vabishchevich P.N., Computational Heat Transfer II, John Wiley & Sons, New York, 1996 
  8. [8] Shavykin A.A., Sokolova S.A., Vashchenko P.S., Suspended matter in hydrotechnical works at shelf region. Impact estimation at biota in the calculation of a damage to fish stock, Protection of Environment at Oil-Gas Complex, 2011, 3, 11–17 (in Russian) 
  9. [9] Volkova R.A., Mihailova N.V., Tishkin V.F., Favorskiy A.P., An application of the variational approach to the computation of gas flows on grids with variable structure, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 1982, preprint #17 (in Russian) 

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