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Computation of Aqueous Environment Contamination Parameters on the Basis of the Lagrangian Approach
Author(s) -
Arkhipov B.,
Solbakov V.,
Solov’ev M.,
Shapochkin D.
Publication year - 2012
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2012.00561.x
Subject(s) - computation , interpolation (computer graphics) , lagrangian , grid , stability (learning theory) , basis (linear algebra) , mathematics , mathematical optimization , computer science , algorithm , motion (physics) , geometry , artificial intelligence , machine learning
We present a mathematical model for a quantitative estimation of the damage to aquatic life resulting from a pollutant discharge into aqueous environment. With the use of the Lagrangian description of fluid motion, we introduce a set of hydrophysical parameters on the basis of which hydrobiologists can estimate the damage. The computation of these parameters is illustrated by the example of a problem of a pollutant spreading in a canal. The problem is solved numerically on a deformable Lagrangian grid. To ensure computational stability a special grid reconstruction procedure with the subsequent interpolation of the parameters computed is used. An original interpolation technique is proposed which ensures the preservation of the most important hydrophysical quantities.