Title: Computational study of three numerical methods for some linear and nonlinear advection-diffusion-reaction problems

Authors: A.R. Appadu; Jean M-S. Lubuma; N. Mphephu

Addresses: Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa ' Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa ' Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa

Abstract: In this paper, we use three existing schemes namely, upwind forward Euler, non-standard finite difference (NSFD) and unconditionally positive finite difference (UPFD) schemes to solve two numerical experiments described by a linear and a nonlinear advection-diffusion-reaction equation with constant coefficients. These equations model exponential travelling waves and biofilm growth on a medical implant respectively. We study the exact and numerical dissipative and dispersive properties of the three schemes for both problems. Moreover, L₁ error, dispersion and dissipation errors, at some values of temporal and spatial step sizes have been computed for the three schemes for both problems.

Keywords: advection-diffusion-reaction; ADR; stability; dispersion; dissipation; finite difference; modelling; exponential travelling waves; biofilm growth; medical implants.

DOI: 10.1504/PCFD.2017.082520

Progress in Computational Fluid Dynamics, An International Journal, 2017 Vol.17 No.2, pp.114 - 129

Received: 02 Jun 2014
Accepted: 26 Apr 2015
Published online: 28 Feb 2017 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article