On approximated ILU and UGS preconditioning methods for linearized discretized steady incompressible Navier-Stokes equations

Authors:
Zhong-Zhi Bai;Yu-Hong Ran;Li Yuan
Affiliations:
State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy o ...;State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy o ...;State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy o ...
Venue:
Numerical Algorithms
Year:
2014

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Abstract

When the artificial compressibility method in conjunction with high-order upwind compact finite difference schemes is employed to discretize the steady-state incompressible Navier-Stokes equations, in each pseudo-time step we need to solve a structured system of linear equations approximately by, for example, a Krylov subspace method such as the preconditioned GMRES. In this paper, based on the special structure and concrete property of the linear system we construct a structured preconditioner for its coefficient matrix and estimate eigenvalue bounds of the correspondingly preconditioned matrix. Numerical examples are given to illustrate the effectiveness of the proposed preconditioning methods.