### Abstract

Numerical convergence properties of a recently developed Jacobian-free Newton-Krylov (JFNK) solver are compared to the ones of the widely used EVP model when solving the sea ice momentum equation with a Viscous-Plastic (VP) formulation. To do so, very accurate reference solutions are produced with an independent Picard solver with an advective time step of 10. s and a tight nonlinear convergence criterion on 10, 20, 40, and 80-km grids. Approximate solutions with the JFNK and EVP solvers are obtained for advective time steps of 10, 20 and 30. min. Because of an artificial elastic term, the EVP model permits an explicit time-stepping scheme with a relatively large subcycling time step. The elastic waves excited during the subcycling are intended to damp out and almost entirely disappear such that the approximate solution should be close to the VP solution. Results show that residual elastic waves cause the EVP approximate solution to have notable differences with the reference solution and that these differences get more important as the grid is refined. Compared to the reference solution, additional shear lines and zones of strong convergence/divergence are seen in the EVP approximate solution. The approximate solution obtained with the JFNK solver is very close to the reference solution for all spatial resolutions tested.

Original language | English (US) |
---|---|

Pages (from-to) | 5926-5944 |

Number of pages | 19 |

Journal | Journal of Computational Physics |

Volume | 231 |

Issue number | 17 |

DOIs | |

State | Published - Jul 1 2012 |

### Fingerprint

### Keywords

- Newton-Krylov method
- Numerical convergence
- Numerical stability
- Sea ice
- Viscous-plastic rheology

### ASJC Scopus subject areas

- Computer Science Applications
- Physics and Astronomy (miscellaneous)

### Cite this

*Journal of Computational Physics*,

*231*(17), 5926-5944. https://doi.org/10.1016/j.jcp.2012.05.024

**A comparison of the Jacobian-free Newton-Krylov method and the EVP model for solving the sea ice momentum equation with a viscous-plastic formulation : A serial algorithm study.** / Lemieux, Jean François; Knoll, Dana A.; Tremblay, Bruno; Holland, David M.; Losch, Martin.

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 231, no. 17, pp. 5926-5944. https://doi.org/10.1016/j.jcp.2012.05.024

}

TY - JOUR

T1 - A comparison of the Jacobian-free Newton-Krylov method and the EVP model for solving the sea ice momentum equation with a viscous-plastic formulation

T2 - A serial algorithm study

AU - Lemieux, Jean François

AU - Knoll, Dana A.

AU - Tremblay, Bruno

AU - Holland, David M.

AU - Losch, Martin

PY - 2012/7/1

Y1 - 2012/7/1

N2 - Numerical convergence properties of a recently developed Jacobian-free Newton-Krylov (JFNK) solver are compared to the ones of the widely used EVP model when solving the sea ice momentum equation with a Viscous-Plastic (VP) formulation. To do so, very accurate reference solutions are produced with an independent Picard solver with an advective time step of 10. s and a tight nonlinear convergence criterion on 10, 20, 40, and 80-km grids. Approximate solutions with the JFNK and EVP solvers are obtained for advective time steps of 10, 20 and 30. min. Because of an artificial elastic term, the EVP model permits an explicit time-stepping scheme with a relatively large subcycling time step. The elastic waves excited during the subcycling are intended to damp out and almost entirely disappear such that the approximate solution should be close to the VP solution. Results show that residual elastic waves cause the EVP approximate solution to have notable differences with the reference solution and that these differences get more important as the grid is refined. Compared to the reference solution, additional shear lines and zones of strong convergence/divergence are seen in the EVP approximate solution. The approximate solution obtained with the JFNK solver is very close to the reference solution for all spatial resolutions tested.

AB - Numerical convergence properties of a recently developed Jacobian-free Newton-Krylov (JFNK) solver are compared to the ones of the widely used EVP model when solving the sea ice momentum equation with a Viscous-Plastic (VP) formulation. To do so, very accurate reference solutions are produced with an independent Picard solver with an advective time step of 10. s and a tight nonlinear convergence criterion on 10, 20, 40, and 80-km grids. Approximate solutions with the JFNK and EVP solvers are obtained for advective time steps of 10, 20 and 30. min. Because of an artificial elastic term, the EVP model permits an explicit time-stepping scheme with a relatively large subcycling time step. The elastic waves excited during the subcycling are intended to damp out and almost entirely disappear such that the approximate solution should be close to the VP solution. Results show that residual elastic waves cause the EVP approximate solution to have notable differences with the reference solution and that these differences get more important as the grid is refined. Compared to the reference solution, additional shear lines and zones of strong convergence/divergence are seen in the EVP approximate solution. The approximate solution obtained with the JFNK solver is very close to the reference solution for all spatial resolutions tested.

KW - Newton-Krylov method

KW - Numerical convergence

KW - Numerical stability

KW - Sea ice

KW - Viscous-plastic rheology

UR - http://www.scopus.com/inward/record.url?scp=84862871951&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862871951&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2012.05.024

DO - 10.1016/j.jcp.2012.05.024

M3 - Article

VL - 231

SP - 5926

EP - 5944

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 17

ER -