论文信息 - Predictor-Corrector Preconditioned Newton-Krylov Method For Cavity Flow

Predictor-Corrector Preconditioned Newton-Krylov Method For Cavity Flow

The Newton-Krylov method is used to solve the incompressible Navier-Stokes equations. In the present study, two numerical schemes are considered for the method: employing the predictor-corrector method as preconditioner, and solving the equations without the preconditioner. The standard driven cavity flow is selected as the test problem to demonstrate the efficiency and the reliability of the present preconditioned method. It is found that the Newton-Krylov method becomes more efficient if combined with the preconditioner.

Giovanni Lapenta | Jianwei Ju | G. Lapenta | Jianwei Ju

[1] Homer F. Walker,et al. Globally Convergent Inexact Newton Methods , 1994, SIAM J. Optim..

[2] C. Kelley. Solving Nonlinear Equations with Newton's Method , 1987 .

[3] U. Ghia,et al. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[4] Michael Pernice,et al. A Multigrid-Preconditioned Newton-Krylov Method for the Incompressible Navier-Stokes Equations , 2001, SIAM J. Sci. Comput..

[5] Yong Hyup Kim,et al. A predictor–corrector method for structural nonlinear analysis , 2001 .

[6] D. A. Knoll,et al. On Newton-Krylov Multigrid Methods for the Incompressible Navier-Stokes Equations , 2000 .

[7] P. Roache. Fundamentals of computational fluid dynamics , 1998 .

[8] R. Dembo,et al. INEXACT NEWTON METHODS , 1982 .

[9] C. Kelley. Iterative Methods for Linear and Nonlinear Equations , 1987 .

[10] Homer F. Walker,et al. Choosing the Forcing Terms in an Inexact Newton Method , 1996, SIAM J. Sci. Comput..

[11] D. Keyes,et al. Jacobian-free Newton-Krylov methods: a survey of approaches and applications , 2004 .