Generating exact solutions of the two-dimensional Burgers' equations

A procedure for computationally generating exact solutions for the two-dimensional Burger's equations for fluid flows is described. Attention is focused on the steady components of Burger's equations, and a centered second-order finite difference formulation and a finite element expression were defined using linear rectangular elements. It was found that the finite element formulation required a greater amount of computer time due to an inefficient handling of the convective terms. The finite difference method was concluded suitable for using the two-dimensional Burger's equations for testing computational algorithms for solving the incompressible Navier-Stokes equations.