Numerical Algorithms

, Volume 65, Issue 1, pp 43–68 | Cite as

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

  • Zhong-Zhi Bai
  • Yu-Hong Ran
  • Li Yuan
Original Paper


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.


Incompressible Navier-Stokes equations Artificial compressibility method Upwind compact finite difference scheme Preconditioning Krylov subspace method 

Mathematics Subject Classfication (2010)

65F10 65F15 76D05 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems Science, Chinese Academy of SciencesBeijingPeople’s Republic of China

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