On a deferredcorrection procedure for determination of centraldifference solutions to the NavierStokes equations
Abstract
The convergence conditions of an iterative method for determination of centraldifference solutions to the vorticitystreamfunction formulation of the NavierStokes equations subject to Dirichlet boundary conditions are studied. It is found that if the vorticity values are equal in the numerical solution, and if the starting values are sufficiently close to the solution, then the iteration converges if the streamfunction and vorticity iterations involved converge separately. This prompts consideration of the vorticity iteration for fixed values of the stream function. Analytical treatment of the problem becomes possible when the vorticity equation is replaced by a constantcoefficient model problem in a rectangle. The range of the relaxation parameters which yield convergence is investigated, and some comparisons with the standard SOR method are made.
 Publication:

Numerical Methods in Laminar and Turbulent Flow
 Pub Date:
 1981
 Bibcode:
 1981nmlt.proc.1129L
 Keywords:

 Computational Fluid Dynamics;
 Flow Theory;
 Iterative Solution;
 NavierStokes Equation;
 Stream Functions (Fluids);
 Convergence;
 Dirichlet Problem;
 Incompressible Fluids;
 Viscous Fluids;
 Vorticity;
 Fluid Mechanics and Heat Transfer