Simplified implicit blockbidiagonal finite difference method for solving the NavierStokes equations
Abstract
The simplified implicit blockbidiagonal finite difference method is proposed in order to overcome the numerical instability problems associated with the solution of twodimensional NavierStokes equations when solved by the MacCormack (1981) algorithm. This novel method involves the use of the spectral formal form in the blockbidiagonal 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.
 Publication:

AIAA Journal
 Pub Date:
 July 1985
 DOI:
 10.2514/3.9052
 Bibcode:
 1985AIAAJ..23.1130V
 Keywords:

 Channel Flow;
 Computational Fluid Dynamics;
 Finite Difference Theory;
 NavierStokes Equation;
 Supersonic Diffusers;
 Transonic Compressors;
 Airfoils;
 Flow Distribution;
 Mach Number;
 Robustness (Mathematics);
 Run Time (Computers);
 Skin Friction;
 Viscosity;
 Fluid Mechanics and Heat Transfer