A difference method for solving the Navier-Stokes equations

It is shown that by a suitable adaptation of an alternative to the Allen and Southwell finite difference scheme suggested by Dennis (1960), an approximation of second-order accuracy yielding difference equations with an associated matrix which is diagonally dominant can be obtained for approximate solution of the Navier-Stokes equations. The difference equations do not involve the exponential function and can be looked upon as a rather more complicated version of the central-difference formulation. Some numerical experiments are carried out which indicate that the method succeeds where the standard central-difference formulation fails.