SIMULATION OF SYSTEMS MODELLED BY CONVECTION DIFFUSION EQUATIONS

Abstract

In the present scenario, it has become a characteristic feature to use fast and reliable computations in almost all branches of science and engineering by the evolution of modeling and simulation techniques. Various systems, processes, scientific and engineering principles, theories are being constantly modeled to carry out design, research and application oriented works. Coming to engineering field, these model equations provide a platform for a detailed analysis of the system to provide for safe and efficient operations and devising a control theory employing the system parameters. Convection Diffusion equations are one such type of the equations that are frequently used in describing a variety of chemical engineering systems such as reactors, heat exchangers etc. The solutions to these partial differential equations many a times are not possible using the regular analytical techniques and imply the use of numerical methods in finding out the solution. The development of the numerical methods which can capably represent the system is a major area of research. Presently in literature, the method of finite differences and method of finite elements are mostly used to simulate these types of equations. In this dissertation work, a detailed study on developing finite difference equations for the so termed Convection Diffusion equations (Linear or non linear partial differential equations) is carried out. Computer programs are developed in the MATLAB 7.0 software for the drafted difference schemes. The programs written are quite user friendly and hold a capability to give error free results with minute tolerances. These programs are constantly checked and compared with the PDEPE toolbox in MATLAB software for their efficiency in calculations and convergence towards the exact solutions. Finally it is concluded that the formulated difference schemes along with the computer program codes can be used effectively to carry out the simulation of a large number of Convection Diffusion equations from the fields of chemical engineering. A brief reference is given to the future research and advancements that can be carried out in the present work to simulate even complex systems for higher dimensions.