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

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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.

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Authors and Affiliations

  1. State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100190, People’s Republic of China

    Zhong-Zhi Bai, Yu-Hong Ran & Li Yuan

Authors
  1. Zhong-Zhi Bai
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  2. Yu-Hong Ran
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  3. Li Yuan
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Correspondence to Zhong-Zhi Bai.

Additional information

Supported by The Hundred Talent Project of Chinese Academy of Sciences, The National Natural Science Foundation for Creative Research Groups (No. 11021101), The National Natural Science Foundation (No. 91118001, No. 10972230 and No. 11021101), and The National Basic Research Program (No. 2011CB309703 and No. 2010CB731505), P.R. China.

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Bai, ZZ., Ran, YH. & Yuan, L. On approximated ILU and UGS preconditioning methods for linearized discretized steady incompressible Navier-Stokes equations. Numer Algor 65, 43–68 (2014). https://doi.org/10.1007/s11075-013-9694-y

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  • DOI: https://doi.org/10.1007/s11075-013-9694-y

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