A numerical simulation based on modified Keller Box scheme for fluid flow: The unsteady viscous Burgers’ equation

Abstract

In this paper the numerical solution of unsteady viscous Burgers’ equation is presented. A combination of Modified Keller Box difference scheme and Hopf-Cole transformation is proposed to solve the Burgers’ equation. The proposed scheme is an implicit scheme with second-order accuracy in space and time. Two test problems are considered to validate the proposed algorithm. Numerical results which are calculated for various values of kinematic viscosity and time steps are matching with the exact solution. It is also observed that, the proposed method yields satisfactory results for all the cases considered.