Main content

Comparison of a Semi-Implicit and a Fully-Implicit Time Integration Method for a Highly Degenerate Diffusion-Reaction Equation Coupled with an Ordinary Differential Equation

Show full item record

Title: Comparison of a Semi-Implicit and a Fully-Implicit Time Integration Method for a Highly Degenerate Diffusion-Reaction Equation Coupled with an Ordinary Differential Equation
Author: Jalbert, Eric
Department: Department of Mathematics and Statistics
Program: Mathematics and Statistics
Advisor: Eberl, Hermann
Abstract: A certain class of highly degenerate diffusion equations arises when modelling biofilm growth and propagations. We focus on the cellulolytic Clostridium thermocellum and formulate a spatially explicit model coupled to an ODE for the non-diffusive growth promoting nutrient. A fully-implicit time integration method, using a fixed-point iteration at each time-step, is introduced to solve this problem with increased accuracy at the price of extra computational effort when compared against the semi-implicit method that it generalises. This is used to simulate C.thermocellum formation on cellulose sheets with the objective of (i) understanding formation patterns and (ii) understanding the effect of the spatial diffusion term. The results suggest (i) the existence of travelling wave solutions describing biofilm movement and (ii) if the spatial heterogeneity is important a two dimensional model that explicitly includes the diffusion should be used.
URI: http://hdl.handle.net/10214/9448
Date: 2016-01
Rights: Attribution 2.5 Canada


Files in this item

Files Size Format View Description
Jalbert_Eric_201601_Msc.pdf 17.32Mb PDF View/Open Thesis

This item appears in the following Collection(s)

Show full item record

Attribution 2.5 Canada Except where otherwise noted, this item's license is described as Attribution 2.5 Canada