The use of numerical methods in systems with chemical reaction and diffusion
Robles, Antonio Montalvo
Master of Science
In this work the application of two numerical methods to the solution of the partial differential equations of diffusion and chemical reaction is described. The following systems were considered. a) When the ends of a catalytic wire are held adiabatic, the existence of steady state temperature and composition distribution in the form of standing waves has been demonstrated. Using finite differences and Galerkin's method the development in time of perturbations of these unstable states is explored. b) In the second example analysed it is shown that with appropriate kinetics, a chemical system, originally with a steady state in which composition and temperature are uniform, might develop instabilities which eventually will produce a non homogeneous distribution of components. It is shown that this new state is probably stable and has the form of standing waves. The time behavior of these systems is investigated by integration forward in time of the full nonlinear partial differential equations using finite differences, and using Galerkin's approximation with Hermite cubic polynomials as basis functions. It was observed that for the wire problem the finite differences scheme takes considerably less computing time than the Galerkin method, and for the second problem, depending on the computational scheme used in the finite differences approximation and on the type of boundary conditions imposed on the system, the computing time can be lower than or approximately equal to that required in the Galerkin's method.