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STABILIZED, MULTISCALE, AND MULTIPHYSICS METHODS IN FLUID MECHANICS

Preconditioning Techniques for Nonsymmetric Linear Systems in the Computation of Incompressible Flows

[+] Author and Article Information
Murat Manguoglu

Department of Computer Science, Purdue University, 305 North University Street, West Lafayette, IN 47907mmanguog@cs.purdue.edu

Ahmed H. Sameh

Department of Computer Science, Purdue University, 305 North University Street, West Lafayette, IN 47907sameh@cs.purdue.edu

Faisal Saied

Computing Research Institute, Purdue University, Room 202, 250 North University Street, West Lafayette, IN 47907fsaied@purdue.edu

Tayfun E. Tezduyar

Mechanical Engineering, Rice University, MS 321, 6100 Main Street, Houston, TX 77005tezduyar@rice.edu

Sunil Sathe

Mechanical Engineering, Rice University, MS 321, 6100 Main Street, Houston, TX 77005sathe@rice.edu

J. Appl. Mech 76(2), 021204 (Jan 14, 2009) (7 pages) doi:10.1115/1.3059576 History: Received February 26, 2008; Revised August 14, 2008; Published January 14, 2009

In this paper we present effective preconditioning techniques for solving the nonsymmetric systems that arise from the discretization of the Navier–Stokes equations. These linear systems are solved using either Krylov subspace methods or the Richardson scheme. We demonstrate the effectiveness of our techniques in handling time-accurate as well as steady-state solutions. We also compare our solvers with those published previously.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Flow around a parachute. The model and mesh are as given in Ref. 35. The velocity vectors are colored by magnitude.

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Figure 2

BFBT preconditioner

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Figure 3

Symmetric nested preconditioner

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Figure 4

Nonsymmetric nested preconditioner

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Figure 5

Block-diagonal preconditioner

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Figure 6

Nested preconditioner

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Figure 7

Total time for various mesh sizes and Reynold’s numbers

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Figure 8

Relative residual plots

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