By Karlos J. Kachiashvili
The consequences mentioned during this publication are fascinating and invaluable for quite a lot of experts and scientists operating within the box of utilized arithmetic, and within the modelling and tracking of pollutants of ordinary waters, ecology, hydrology, strength engineering and construction of other constructions of water gadgets. Their significance and useful worth are submitted within the pleasant shape for comprehension and are prepared for direct software for the answer of useful projects. benefits of the elaborated tools 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 info for Advanced Modeling and Computer Technologies for Fluvial Water Quality Research and Control
Reduction of the multi-dimensional diffusion equation to the one-dimensional. Described below algorithm of solution of diffusion equation is used in multi-dimensional problems and is an alternative to the considered above algorithms. In this algorithm solution of the multi-dimensional diffusion equation is presented as linear combination of solutions of some one-dimensional diffusion equations [30, 43]. This method is often called the method of splitting of operator or the method of decomposition of the multi-dimensional operator.
24) in case of the condition of full mixing. 24) the method of scrolling is used in case of boundary condition of full mixing, and the modified run method - in case of non-local boundary condition. , N 1; 1 0, 1 S 0 . ,1 . In addition, were considered one-dimensional problems of river water pollutants transfer and diffusion on straight line x and half-line x 0 , on the assumption that the river flow velocity and coefficients of turbulent diffusion are constant, and the pollutants are Calculation Schemata of Mathematical Models 43 non-conservative, in conditions when the water object is under the action of R independent pollution sources located at x xr points of the section under consideration.
Let us designate for fixed j and k x a x j ; xb x j 1 ; y a y k ; y b y k 1 ; u aa u jk ; u ab u j ,k 1 ; u ba u j 1,k ; u bb u j 1,k 1 . Linear interpolation is consisted in the following that in the rectangle x a x xb ; y a y y b , the function f ( x, y) is approximated by the function S jk ( x, y ) , which is linear in relation to any of variables x , y at fixed value of other variable: S jk x, y p 0 p1 x p 2 y p12 xy xb xa yb y a , where p 0 xb y b u aa xb y a u ab x a y b u ba x a y a u bb p1 y b u aa y a u ab y b u ba y a u bb ; p 2 xb u aa xb u ab x a u ba x a u bb ; p12 u aa u ab uba ubb ; .
Advanced Modeling and Computer Technologies for Fluvial Water Quality Research and Control by Karlos J. Kachiashvili