By Karlos J. Kachiashvili
The implications mentioned during this publication are fascinating and precious for a variety of experts and scientists operating within the box of utilized arithmetic, and within the modelling and tracking of pollutants of normal waters, ecology, hydrology, strength engineering and development of other constructions of water gadgets. Their value and sensible worth are submitted within the pleasant shape for comprehension and are prepared for direct software for the answer of useful projects. merits of the elaborated equipment and algorithms are proven not just via theoretical decisions and calculations, but in addition during the demonstration of result of specific calculus and modelling.
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Extra resources for Advanced Modeling and Computer Technologies for Fluvial Water Quality Research and Control
As a result for determination of these coefficients we have the following scheme: 30 Karlos J. Kachiashvili and D. Y. , N 1 by the formulae 1 u u j 1 u j 1 1 ln (u j u j 1 2arctg ). e. nodes can be the only inflection points of the given curve. For determination of each of parameters u j 1 it is necessary to solve a nonlinear equation. Therefore it is necessary correctly select the search interval of this parameter. If we write this equation in the following form f (u) 0 , the function f (u) will have two extremums ay / a ay / a , u~ u~ 1 a x / a and 1 ax / a where a is position vector conducted from the point [ x j , y j ] to the point [ x j 1 , y j 1 ] .
Geometrical characteristics of a channel of the river, on which the speed of a current depends, can strongly vary on a considered section, especially if the mountain river is investigated. From components of the vector of the current speed and their derivatives on spatial co-ordinates, in one’s turn, coefficients of turbulent diffusion depend on. It is clear, that, generally, for speed of the current it is impossible to use simple linear interpolation in which values of the speed only on the section ends are considered, except any special cases when, for example, water flows on the rectangular channel.
At h0 x, h O h 2 . 1. Review of difference schemes for one-dimensional boundary problem. X [a, b] is the interval, the operator ˆ is In the one-dimensional case, when represented in the form of ˆ A( x) B( x) C ( x) x x x A( x) 2 ~ B ( x) C ( x), 2 x x ~ where B ( x ) B ( x ) A ( x ) ; the boundary conditions are assigned in the form of pa ( x) qa ( x) a ; x x a Here pb ( x) qb ( x) b x xb .