Treatment of non-linearities in the numerical solution of the incompressible Navier–Stokes equations

✍ Scribed by P. F. Galpin; G. D. Raithby

• Publisher: John Wiley and Sons
• Year: 1986
• Tongue: English
• Weight: 937 KB
• Volume: 6
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.1650060702

✦ Synopsis

The solution of the full non-linear set of discrete fluid flow equations is usually obtained by solving a sequence of linear equations. The type of linearization used can significantly affect the rate of convergence of the sequence to the final solution. The first objective of the present study was to determine the extent to which a full Newton-Raphson linearization of all non-linear terms enhances convergence relative to that obtained using the 'standard' incompressible flow linearization. A direct solution procedure was employed in this evaluation. It was found that the full linearization enhances convergence, especially when grid curvature effects are important.

The direct solution of the linear set is uneconomical. The second objective of the paper was to show how the equations can be effectively solved by an iterative scheme, based on a coupled-equation line solver, which implicitly retains all the inter-equation couplings. This solution method was found to be competitive with the highly refined segregated solution methods that represent the current state-of-the-art.