An implicit, bidiagonal numerical method for solving the NavierStokes equations
Abstract
An implicit, bidiagonal numerical method is presented for solving the NavierStokes equations. The explicit predictorcorrector finite difference method developed by MacCormack (1969) is used to approximate the governing fluid flow equations to second order accuracy in space and time. The stability restriction is then removed by transforming the fluid flow equations into an implicit form. The resulting matrices are block bidiagonal and can be easily solved. The Jacobian matrices of the governing flow equations are expressed in a diagonalized form, making any matrix inversion unnecessary. The method is tested on a number of numerical examples, including an incompressible and compressible Couette flow and a supersonic diffuser with shockboundary layer interaction. The results demonstrate the method's potential for use in complex compressible viscous flow calculations.
 Publication:

AIAA Journal
 Pub Date:
 June 1983
 DOI:
 10.2514/3.8159
 Bibcode:
 1983AIAAJ..21..828V
 Keywords:

 Computational Fluid Dynamics;
 Couette Flow;
 Finite Difference Theory;
 Flow Equations;
 Jacobi Matrix Method;
 NavierStokes Equation;
 Algorithms;
 Compressible Flow;
 Incompressible Flow;
 Shock Layers;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer