# 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

## Access Full Article

top## Abstract

top## How to cite

topBoris 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

top- [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] 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] 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] 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] Lamb H., Hydrodynamics, 6th ed., Cambridge Math. Lib., Cambridge University Press, Cambridge, 1993 Zbl0828.01012
- [6] Monin A.S., Yaglom A.M., Statistical Fluid Mechanics I–II, Dover, Mineola, 2007
- [7] Samarskii A.A., Vabishchevich P.N., Computational Heat Transfer II, John Wiley & Sons, New York, 1996
- [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] 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)

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.