Simulation of Wastewater Treatment Plants Modeled by a System of Nonlinear Ordinary and Partial Differential Equations

Abstract: Wastewater treatment consists of mechanical, chemical and biological purification. This master thesis concerns the biological part of the wastewater treatment called the activated sludge process (ASP). Two different mathematical models, one simplified and one complete, of the ASP are investigated. The models contain systems of nonlinear partial and ordinary differential equations. The nonlinearities in the equations give rise to discontinuous solutions, known as shock waves, which complicate the numerical analysis of the equations. The aim of the thesis is to implement the models in MATLAB and investigate how to solve these equations most efficiently with respect to accuracy and speed. Several time discretization schemes including built-in routines in MATLAB will be compared. The results show that a certain semi-implicit method seems to be the most efficient way to solve these equations numerically. Higher order fixed time step methods such as Runge-Kutta methods of order 2 and 4 are not suitable and perform even worse than the very simple Euler method of order 1.