Study on Preconditioning of the clavier-Stokes Equations Using 3-Dimensional Unstructured Meshes

- Journal title : Transactions of the Korean Society of Mechanical Engineers B
- Volume 25, Issue 11, 2001, pp.1581-1593
- Publisher : The Korean Society of Mechanical Engineers
- DOI : 10.22634/KSME-B.2001.25.11.1581

Title & Authors

Study on Preconditioning of the clavier-Stokes Equations Using 3-Dimensional Unstructured Meshes

Nam, Young-Sok; Choi, Hyoung-Gwon; Yoo, Jung-Yul;

Nam, Young-Sok; Choi, Hyoung-Gwon; Yoo, Jung-Yul;

Abstract

An efficient variable-reordering method for finite element meshes is used and the effect of variable-reordering is investigated. For the element renumbering of unstructured meshes, Cuthill-McKee ordering is adopted. The newsy reordered global matrix has a much narrower bandwidth than the original one, making the ILU preconditioner perform bolter. The effect of variable reordering on the convergence behaviour of saddle point type matrix it studied, which results from P2/P1 element discretization of the Navier-Stokes equations. We also propose and test 'level(0) preconditioner'and 'level(2) ILU preconditioner', which are another versions of the existing 'level(1) ILU preconditioner', for the global matrix generated by P2/P1 finite element method of incompressible Navier-Stokes equations. We show that 'level(2) ILU preconditioner'performs much better than the others only with a little extra computations.

Keywords

Variable-Reordering;Navier-Stokes Equations;ILU Preconditioning;

Language

Korean

References

1.

Meijerink, J. A. and Van der Vorst H. A., 1977, 'An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix,' Mathematics of Computations. Vol. 31, pp. 148-162

2.

Kershaw, D. S., 1978, 'The Incomplete Cholesky-Conjugate Gradient Method for the Iterative Solution of Systems of Linear Equations,' Journal of Computational Physics. Vol. 26, pp. 43-65

3.

Ferziger, J. H. and Peric, M., 1996, Computational Methods for Fluid Dynamics, Springer

4.

Chung, S. T., Choi, H. G. and Yoo, J. Y., 1998, 'An Analysis of Turbulent Flow Around a NACA4421 Airfoil by Using a Segregated Finite Element Method,' KSME International Journal, Vol. 12, pp. 1194-1199

5.

Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York

6.

Chorin, A. J., 1968, 'Numerical Solution of the Navier-Stokes Equations,' Mathematics of Computations. Vol. 22, pp. 745-762

7.

Hanby, R. F., Silvester, D. J. and Chew, J. W., 1996, 'A Comparison of Coupled and Segregated Iterative Solution Techniques for Incompressible Swirling Flow,' International Journal for Numerical Methods in Fluids, Vol. 22, pp. 353-373

8.

Hu, H. H., Joseph, D. D, and Crochet, M. J., 1992, 'Direct Simulation of Flows of Fluid-Particle Motions,' Theoretical Computational Fluid Dynamics. Vol. 3, pp. 285-306

9.

Choi, H. G., 2000, 'Splitting Method for the Combined Formulation of Fluid-Particle Problem,' Computer Methods in Applied Mechanics and Engineering. Vol. 190, pp. 1367-1378

10.

Saud, Y., 1996, I terati ve Methods for Sparse Linear Systems, PWS Publishing Company, pp. 72-76

11.

Carey, G. F. and Oden, J. T., 1986, Finite Elements: Fluid Mechanics Vol. VI, PRENTICE-HALL., Englewood Cliffs, New Jersey, Section 3.3.3

12.

Hughes, T. J. R., Franca, L. P. and Balestre, M., 1986, 'A New Finite Element Formulation for Computational Fluid Dynamics: V Circumventing the Babuska-Brezzi Condition: A Stable Petrov-Galerkin Formulation of Stokes Problems Accommodating Equal Order Interpolations,' Computer Methods in Applied Mechanics and Engineering. Vol. 59, pp. 85-99

13.

Joseph, D. D. et al., 1998-2001, Direct Simulation of the Motion of Particles in Flowing Liquids, NSF KDI/New Computional Challenge

14.

van der Vorst, H. A., 1992, 'Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Non-Symmetric Linear Systems,' SIAM Journal on Scientific and Statistical Computing, Vol. 12, pp. 631-634

15.

Fornberg, B., 1988, 'Steady Viscous Flow Past a Sphere at High Reynolds Numbers,' J. Fluid Mech., Vol. 190, pp. 471-489

16.

Anonymous, 1997, 'Validation of CFD Codes for Predicting Aerodynamic Performance,' Automotive Engineer. Vol. 17, pp. 46-49