Preconditioned Methods for Solving the Incompressible and Low Speed Compressible Equations
Abstract
Acceleration methods are presented for solving the steady state incompressible equations. These systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state. We also consider the compressible equations in conservation form with slow flow. Two arbitrary functions α and β are introduced in the general preconditioning. An analysis of this system is presented and an optimal value for β is determined given a constant α. It is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed. Several generalizations to the compressible equations are presented which extend previous results.
 Publication:

Journal of Computational Physics
 Pub Date:
 October 1987
 DOI:
 10.1016/00219991(87)900842
 Bibcode:
 1987JCoPh..72..277T
 Keywords:

 Boundary Value Problems;
 Compressible Flow;
 Computational Fluid Dynamics;
 Incompressible Flow;
 Convergence;
 Hyperbolic Differential Equations;
 Optimization;
 RungeKutta Method;
 Time Dependence;
 Fluid Mechanics and Heat Transfer