On the convergence of the LAD, NOS, and split NOS methods for solving the steady-state Navier-Stokes equations
Abstract
Convergence characteristics of the numerical method devised by Roache (1975) for solving the Navier-Stokes equations for steady planar flow of an incompressible fluid are examined. Roache defined a method that combined features of the Laplacian driver method (LAD) and the NOS method into the split NOS method, which involved introduction of relaxation parameters into the solution procedure to speed convergence. Dirichlet boundary conditions are imposed on the stream function and the vorticity, and it is shown that under certain conditions the two can be separated during iteration. Fixed values can then be used for the stream function while the vorticity values are varied. Sample results are provided for linear and one-dimensional model problems.
- Publication:
-
Numerical Methods in Laminar and Turbulent Flow
- Pub Date:
- 1983
- Bibcode:
- 1983nmlt.proc.1151L
- Keywords:
-
- Computational Fluid Dynamics;
- Incompressible Flow;
- Laplace Transformation;
- Navier-Stokes Equation;
- Oseen Approximation;
- Steady Flow;
- Convergence;
- Iterative Solution;
- Nonlinear Equations;
- One Dimensional Flow;
- Fluid Mechanics and Heat Transfer