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

Mauritsson, Gustav LU (2013) In Master's Theses in Mathematical Sciences FMA820 20131
Mathematics (Faculty of Engineering)
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
Mauritsson, Gustav LU
supervisor
organization
course
FMA820 20131
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFMA-3255-2013
ISSN
1404-6342
other publication id
2013:E62
language
English
id
4175559
date added to LUP
2014-02-14 16:24:33
date last changed
2014-02-14 16:24:33
@misc{4175559,
  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.},
  author       = {Mauritsson, Gustav},
  issn         = {1404-6342},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master's Theses in Mathematical Sciences},
  title        = {Simulation of Wastewater Treatment Plants Modeled by a System of Nonlinear Ordinary and Partial Differential Equations},
  year         = {2013},
}