Treatment of nonlinearities in the numerical solution of the incompressible NavierStokes equations
Abstract
The solution of the full nonlinear 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 NewtonRaphson linearization of all nonlinear 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 coupledequation line solver, which implicitly retains all the interequation couplings. This solution method was found to be competitive with the highly refined segregated solution methods that present the current stateoftheart.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 July 1986
 DOI:
 10.1002/fld.1650060702
 Bibcode:
 1986IJNMF...6..409G
 Keywords:

 Computational Fluid Dynamics;
 Incompressible Flow;
 Linearization;
 NavierStokes Equation;
 NewtonRaphson Method;
 Nonlinear Equations;
 Convergence;
 Discrete Functions;
 Iterative Solution;
 Fluid Mechanics and Heat Transfer