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Application of Krylov Subspace Methods in Fluid Dynamics

Hrabri L. Rajic, Youcef Saad

Nuclear Science and Engineering

Volume 105 / Number 2 / June 1990 / Pages 136-141


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A robust, fast, and powerful technique, based on Krylov subspace methods, is presented for solving large nonlinear equations of the form F(u) = 0. 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.

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