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1 2013

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Ecological modeling and Lagrangian approach

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Arkhipov B. , Solbakov V. , Solov’ev M. , Shapochkin D.

Open Mathematics

2013

tom 11

nr 4

734-745

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.