By Karlos J. Kachiashvili
The consequences mentioned during this e-book are attention-grabbing and valuable for quite a lot of experts and scientists operating within the box of utilized arithmetic, and within the modelling and tracking of toxins of average waters, ecology, hydrology, energy engineering and development of alternative buildings of water gadgets. Their value and functional price are submitted within the pleasant shape for comprehension and are prepared for direct software for the answer of functional projects. merits of the elaborated equipment and algorithms are proven not just via theoretical decisions and calculations, but additionally 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
H1 , y k , z m , t h1 that has accuracy O(h1 ) , x i 1 ,x i are the nearest grid nodes for . Note 2. 55), a modification of the method of scrolling or of the factorization method is used. 6. OPTIMIZATION PROBLEMS OF THE ALGORITHMS CONNECTED WITH DIFFERENCE SCHEMES Let us consider problems of optimum choice of the parameters of the algorithm at practical realization of difference schemes [38, 40]. As criterion of optimality, there is considered the necessity of maximum decreasing the computation time and error.
There is introduced the system of orthogonal curvilinear coordinates which serve for simplification analytical description of plane area, restricted by coastal lines of the river. Such Deterministic Mathematical Models of Pollutants Transfer in Rivers 23 description is necessary for numerical solution of diffusion equation, describing the change of concentrations of pollutants in river water. For analytical description of plane curve, given in the form of the sequence of not coinciding points with certain Cartesian coordinates, which, in particular, can be one of the coastal lines of the river, the interpolation by splines is used.
2. Using Spline-Interpolation for Giving a Curve The easiest way is to set a contour of the river and its bank lines by means of a sequence of points with given coordinates. , N ) , is its approximation by the polygonal line connecting the given points. Parametric equations of this polygon are as follows: x xj x j s j ( s s j ); y y j y j s j (s s j ) at s j s s j 1 , N where s is natural parameter of the curve; [ s j ]0 is the sequence of values of this parameter determined by ratios s 0 0; s j x y .
Advanced Modeling and Computer Technologies for Fluvial Water Quality Research and Control by Karlos J. Kachiashvili