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

Jean François Lemieux, Dana A. Knoll, Bruno Tremblay, David M. Holland, Martin Losch

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)5926-5944
Number of pages19
JournalJournal of Computational Physics
Volume231
Issue number17
DOIs
StatePublished - Jul 1 2012

Keywords

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

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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