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

Available online: 23 Feb 2017 *

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