Application of Krylov subspace methods in fluid dynamics

Hrabri L. Rajic, Youcef Saad

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


A robust, fast, and powerful technique, based on Krylov subspace methods, is presented for solving large nonlinear equations of the form F(u) = O. The main methods investigated are (a) a standard Newton approach coupled with a direct or iterative sparse solver and (b) a Jacobian-free Krylov subspace Newton method. The methods are applied to fluid dynamics problems. In all tested cases, the Jacobian-free Krylov subspace methods based on a nonlinear Generalized Minimum Residual (GMRES) technique show better performance when compared with the standard Newton technique. The importance of selective preconditioners for improving the convergence is demonstrated. The two-dimensional driven cavity problem is solved for Reynolds number 3000, starting from the zero initial guess, using the nonlinear GMRES technique with the line search backtracking.

Original languageEnglish (US)
Pages (from-to)136-141
Number of pages6
JournalNuclear Science and Engineering
Issue number2
StatePublished - 1990
EventInternational Topical Meeting on Advances in Nuclear Engineering Computation and Radiation Shielding - Santa Fe, NM, USA
Duration: Apr 9 1989Apr 13 1989


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