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

  • Authors:

  • Jean-FrançOis Lemieux;Dana A. Knoll;Bruno Tremblay;David M. Holland;Martin Losch

  • Affiliations:

  • Recherche en Prévision Numérique environnementale/Environnement Canada, 2121 route Transcanadienne, Dorval, Qc, Canada H9P 1J3;Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545, USA;Department of Atmospheric and Oceanic Sciences, McGill University, 805 Sherbrooke Street West, Montréal, Qc, Canada H3A 2K6;Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185, USA;Alfred-Wegener-Institut für Polar-und Meeresforschung, Postfach 120161, 27515, Germany

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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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 10s 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 30min. 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.