E.G. Phillips, E.C. Cyr and J.N. Shadid,
An Investigation of Block Preconditioners For Unsteady Navier-Stokes ,
CSRI Summer Proceedings 2010, Computer Science Research Institute, Sandia National
Laboratories, December 2010.
In this paper we investigate block upper triangular preconditioners for the saddle point system generated by discretizing the unsteady Navier-Stokes equations. We focus on Schur complement approximations used within the block structure of these preconditioners. We consider Schur complements generated by Neumann series approximations based on various approximations of the convection-diffusion operator. We also consider improvements upon these approximations using a sparse approximate inverse (SPAI) algorithm and a structured probing algorithm. The preconditioners are compared based on numerical results.
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