Monthly Weather Review, September 1st, 2001
ABSTRACT
An implicit nonlinear algorithm, the Newton-Krylov method, for the efficient and accurate simulation of the Navier-Stokes equations, is presented. This method is a combination of a nonlinear outer Newton-based iteration and a linear inner conjugate residual (Krylov) iteration but does not require the explicit formation of the Jacobian matrix. This is referred to here as Jacobian-free Newton-Krylov (JFNK). The mechanics of the method are quite simple and the method has been previously used to solve a variety of complex coupled nonlinear equations. Like most Krylov-based schemes, the k...
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