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 L 1 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