Abstract:
In this paper, we generate varied sets of exact initial and Dirichlet
boundary conditions for the 2-D Burgers’ equations from general ana-
lytical solutions via Hopf-Cole transformation and separation of vari-
ables. These conditions are then used for the numerical solutions of
this equation using finite difference methods (FDMs) and in particular
the Crank-Nicolson (C-N) 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 L 1 error. The results of the explicit
scheme are found to compare well with those of the C-N scheme for
a wide range of parameter values. The variation in the values of the
Reynolds number does not adversely affect the numerical solutions.
