A Stable and High Accurate Numerical Simulator for Convection- Diffusion Equation

Abstract

This study presents a simulator to obtain numerical solution of convection-diffusion equa- tion. It includes explicit, fully implicit and semi-implicit time discretization techniques. In addition to time discretization techniques, this simulator contains several space discretization methods such as first-order upstream and UMIST (University of Manchester Institute of Science and Technology) techniques. It is observed that the use of UMIST or semi-implicit techniques in the different numer- ical simulator decreases numerical errors. However, the combination of UMIST and semi-implicit methods is not available in literature. The proposed numerical simulator is suitable for easily using the different combinations of time and space discretization methods. Second objective of this study is to present a novel combination that includes both semi-implicit time discretization technique and UMIST space discretization method to minimize numerical errors namely numerical dispersion and unphysical oscillation. Alt-hough UMIST method suppresses unphysical oscillation, it causes a small and undesired oscillation at flood front for very large Courant number. Thirdly, this study proposes a minor modification on the UMIST method to elimi-nate this unphysical oscillation. The novel com- bination of modified UMIST method and semi-implicit technique decreases numerical dispersion sig- nificantly and suppress unphysical oscillation effectively. Moreover, the numeri-cal result of proposed model is very close to analytical solution.