MATHEMATICS

On a modification of the Streater-Phelps model and its numerical implementation by means of multiprocessor computer systems

M. D. Mikhailov

Tomsk State University, Faculty of Mechanics and Mathematics

Abstract: A system consisting of water, oxygen dissolved in it, and organic substances is considered in the classical Streater-Phelps model. Mathematically, it is described by a system of two ordinary differential equations (ODEs) with appropriate initial conditions [1]. We used a modification of the classical Streater-Phelps model constructed by insertion of a biological filter in it with allowance for convection and diffusion terms. Parallel implementation of the algorithm for numerical calculation of the model is performed by use of the explicit difference scheme on the cluster of Tomsk State University.

Keywords: self-purification, biological filter, numerical method, finite difference scheme.

UDC: 519.6


Accepted: February 13, 2010