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On Direct and Semi-Direct Inverse of Stokes, Helmholtz and Laplacian Operators in View of Time-Stepper-Based Newton and Arnoldi Solvers in Incompressible CFD

Published online by Cambridge University Press:  03 June 2015

H. Vitoshkin  and
A. Yu. Gelfgat
H. Vitoshkin*
Affiliation:
School of Mechanical Engineering, Faculty of Engineering, Tel-Aviv University, Ramat Aviv 69978, Tel-Aviv, Israel
A. Yu. Gelfgat
Affiliation:
School of Mechanical Engineering, Faculty of Engineering, Tel-Aviv University, Ramat Aviv 69978, Tel-Aviv, Israel
*
Corresponding author.Email:[email protected]
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Abstract

Factorization of the incompressible Stokes operator linking pressure and velocity is revisited. The main purpose is to use the inverse of the Stokes operator with a large time step as a preconditioner for Newton and Arnoldi iterations applied to computation of steady three-dimensional flows and study of their stability. It is shown that the Stokes operator can be inversed within an acceptable computational effort. This inverse includes fast direct inverses of several Helmholtz operators and iterative inverse of the pressure matrix. It is shown, additionally, that fast direct solvers can be attractive for the inverse of the Helmholtz and Laplace operators on fine grids and at large Reynolds numbers, as well as for other problems where convergence of iterative methods slows down. Implementation of the Stokes operator inverse to time-stepping-based formulation of the Newton and Arnoldi iterations is discussed.

Keywords

76D05CFDNewton iterationArnoldi iterationStokes operator
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 4 , October 2013 , pp. 1103 - 1119
Copyright
Copyright © Global Science Press Limited 2013

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