Numerical solutions of the Burgers’ system in two dimensions under varied initial and boundary conditions

Abstract

In this paper, we generate varied sets of exact initial and Dirichlet boundary conditions for the 2-D Burgers’ equations from general analytical solutions via Hopf-Cole transformation and separation of variables. These conditions are then used for the numerical solutions of this equation using finite difference methods (FDMs) and in particular the Crank-Nicolson (CN) and the explicit schemes. The effects of the variation in the Reynolds number are investigated and the accuracy of these schemes is determined by the L1 error. The results of the explicit scheme are found to compare well with those of the CN scheme for a wide range of parameter values. The variation in the values of the Reynolds number does not adversely affect the numerical solutions.