Simplified implicit block-bidiagonal finite difference method for solving the Navier-Stokes equations

The simplified implicit block-bidiagonal finite difference method is proposed in order to overcome the numerical instability problems associated with the solution of two-dimensional Navier-Stokes equations when solved by the MacCormack (1981) algorithm. This novel method involves the use of the spectral formal form in the block-bidiagonal system of equations, and is demonstrated, in light of application in several flow cases, to improve computational efficiency by a factor of 3. Since viscous effects are, however, overestimated, the method requires a postprocessor employing the full implicit MacCormack scheme to redefine the boundary layer part of the solution. Numerical instabilities are avoided through the use of a nearly converged solution as the initial profile.