Timedependent viscous incompressible NavierStokes equations: The finite difference Galerkin formulation and streamfunction algorithms
Abstract
The finite difference Galerkin (FDG) method is extended to time dependent incompressible NavierStokes equations. Two algorithm development examples are given that use a staggered grid and centered differencing scheme for the primitive variables. Mass balance is used to solve the essential problems associated with applying the FDG method. The use of the FDG method with this underlying discretization is shows to be the discrete analog of the continuum manipulations that lead to the fourthorder streamfunction equation. Asymptotic and time evolution results obtained with a CrankNicolson AdamsBasforth algorithm are compared with published computations for Re 400, 1000, and 3200.
 Publication:

Journal of Computational Physics
 Pub Date:
 September 1989
 DOI:
 10.1016/00219991(89)901885
 Bibcode:
 1989JCoPh..84..207G
 Keywords:

 Galerkin Method;
 Incompressible Flow;
 NavierStokes Equation;
 Stream Functions (Fluids);
 Time Dependence;
 Viscous Flow;
 Finite Difference Theory;
 Grid Generation (Mathematics);
 Mass Distribution;
 Primitive Equations;
 Vorticity;
 Fluid Mechanics and Heat Transfer