44. Water Quality of Rivers and Related Applied Mathematical Projects

Abstract

In this research we present a classical coupled differential equations mathematical model for river pollution. The development of the model is studied starting with a single water quality component C(x, t). Further, the interaction between a pollutant P(x, t) and dissolved oxygen Q(x, t) is shown, modeling the diffusion, advection and the reaction between them. Steady state solutions of simplified models as well as the general coupled system of differential equations are shown. For the latter, closed form formulas can be obtained for different components: the velocity of the stream, dissolved oxygen levels etc. They are used to compute values that are compared against results obtained by implementing other models. Lastly, changes of the model in the part of the differential equation that is responsible for the reactions between the studied components are implemented and the effect of those changes to the model and the computed results is studied.