Hybrid Crank-Nicolson-Du Fort and Frankel (CN-DF) Scheme for the Numerical Solution of the 2-D Coupled Burgers’ System

Abstract

The two dimensional coupled Burgers’ equations constitute an appropriate model for developing computational algorithms, for solving the incompress ible Navier-Stokes equations. Moreover, they are generally used as transport equations because they model a number of fluid flow phenomena, for example, turbulent flow, shock wave formation and boundary layer formation. In this paper, we develop a hybrid Crank-Nicolson and Du Fort and Frankel (CN DF) scheme. The hybrid CN-DF is developed by introducing the Du Fort and Frankel (DF) properties into the Crank-Nicolson scheme (CN). This is a three level scheme and is also unconditionally stable. Numerical solutions from the hybrid scheme are obtained by the use of MATLAB software. By use of L1 error, it is determined that the hybrid scheme is fifth order accurate in space and produces better results in comparison to the pure Crank-Nicolson and the pure Du Fort and Frankel schemes.