Numerical Investigation of Convection-Diffusion-Reaction Systems

Abstract

Numerical Investigation of Convection Diffusion Reaction Systems This work is concerned with the numerical solution of selected convection-diffusion-reaction (CDR) type mathematical models with dominating convective and reactive terms, coupled with some algebraic equations. Five established CDR-type models are analyzed namely, the gas-solid reaction, chemotaxis, liquid chromatography, radiation hydrodynamical, and hy- perbolic heat condition models. These models are encountered in various scientific and engi- neering fields, such as chemical engineering, biological systems, astrophysics, heat transfer, and fluid dynamics. The Laplace transformation is applied as a basic tool to find the ana- lytical solutions of linear CDR models for different types of boundary conditions. However, for the nonlinear models, numerical techniques are the only tools to get physical solutions. The nonlinear transport and stiff source (reaction) terms of the governing differential equa- tions produce discontinuities and narrow peaks in the solution. It is difficult to capture steep variations in the solution through a less accurate numerical scheme. Therefore, ef- ficient and accurate numerical methods are needed to obtain physically reliable solutions in acceptable computational time. The objective of this thesis project is to develop and implement simpler, robust, and accurate numerical frameworks for the solution of one and two-dimensional CDR type systems. The space-time CE/SE-method, the discontinuous Galerkin (DG) finite element method , and different high resolution finite volume schemes (FVSs) are proposed to numerically approximate the solution of these models. Several case studies are carried out. The validity and performance of the suggested numerical techniques are revealed through test problems and by comparing their results with each other, analytical solutions, and the results of some available finite volume schemes in the literature.