On the convergence of the modified elastic-viscous-plastic method for solving the sea ice momentum equation. (English) Zbl 1352.86021

Summary: Most dynamic sea ice models for climate type simulations are based on the viscous–plastic (VP) rheology. The resulting stiff system of partial differential equations for ice velocity is either solved implicitly at great computational cost, or explicitly with added pseudo-elasticity (elastic–viscous–plastic, EVP). A recent modification of the EVP approach seeks to improve the convergence of the EVP method by re-interpreting it as a pseudotime VP solver. The question of convergence of this modified EVP method is revisited here and it is shown that convergence is reached provided the stability requirements are satisfied and the number of pseudotime iterations is sufficiently high. Only in this limit, the VP and the modified EVP solvers converge to the same solution. Related questions of the impact of mesh resolution and incomplete convergence are also addressed.


86A40 Glaciology
65T60 Numerical methods for wavelets
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
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[1] Hibler, W. D., A dynamic thermodynamic sea ice model, J. Phys. Oceanogr., 9, 815-846, (1979)
[2] Zhang, J.; Hibler, W., On an efficient numerical method for modeling sea ice dynamics, J. Geophys. Res., 102, C4, 8691-8702, (1997)
[3] Lemieux, J.-F.; Tremblay, B., Numerical convergence of viscous-plastic sea ice models, J. Geophys. Res., 114, C5, (2009)
[4] Lemieux, J.-F.; Tremblay, B.; Sedlacek, J.; Tupper, P.; Thomas, S.; Huard, D.; Auclair, J.-P., Improving the numerical convergence of viscous-plastic sea ice models with the Jacobian-free Newton-Krylov method, J. Comput. Phys., 229, 8, 2840-2852, (2010) · Zbl 1184.86004
[5] Lemieux, J.-F.; Knoll, D.; Tremblay, B.; Holland, D.; Losch, M., 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, J. Comput. Phys., 231, 5926-5944, (2012)
[6] Losch, M.; Fuchs, A.; Lemieux, J.-F.; Vanselow, A., A parallel jacobian-free Newton-Krylov solver for a coupled sea ice-Ocean model, J. Comput. Phys., 257, Part A, 901-911, (2014) · Zbl 1349.86008
[7] Hunke, E.; Dukowicz, J., An elastic-viscous-plastic model for sea ice dynamics, J. Phys. Oceanogr., 27, 1849-1867, (1997)
[8] Hunke, E., Viscous-plastic sea ice dynamics with the EVP model: linearization issues, J. Comput. Phys., 170, 1, 18-38, (2001) · Zbl 1030.74032
[9] Losch, M.; Menemenlis, D.; Campin, J.-M.; Heimbach, P.; Hill, C., On the formulation of sea-ice models. part 1: effects of different solver implementations and parameterizations, Ocean Model., 33, 12, 129-144, (2009)
[10] Losch, M.; Danilov, S., On solving the momentum equations of dynamic sea ice models with implicit solvers and the elastic-viscous-plastic technique, Ocean Model., 41, 42-52, (2012)
[11] Bouillon, S.; Fichefet, T.; Legat, V.; Madec, G., The elastic-viscous-plastic method revisited, Ocean Model., 71, 2-12, (2013)
[12] Danilov, S.; Wang, Q.; Timmermann, R.; Iakovlev, N.; Sidorenko, D.; Kimmritz, M.; Jung, T.; Schröter, J., Finite-element sea ice model (FESIM), version 2, Geosci. Model Dev. Discuss., 8, 2, 855-896, (2015)
[13] Wang, Q.; Danilov, S.; Sidorenko, D.; Timmermann, R.; Wekerle, C.; Wang, X.; Jung, T.; Schröter, J., The finite element sea ice-ocean model (FESOM) v. 1.4: formulation of an Ocean general circulation model, Geosci. Model Dev., 7, 2, 663-693, (2014)
[14] Hibler, W. D.; Ip, C. F., The effect of sea ice rheology on arctic buoy drift, (Dempsey, J. P.; Rajapakse, Y. D.S., Ice Mechanics, ASME AMD, vol. 207, (1995)), 255-263
[15] Hunke, E.; Lipscomb, W., CICE: the los alamos sea ice model documentation and software users manual, (2008), T-3 Fluid Dynamics Group Los Alamos National Laboratory, Los Alamos, NM 87545, Tech. rep.
[16] Timmermann, R.; Danilov, S.; Schröter, J.; Böning, C.; Sidorenko, D.; Rollenhagen, K., Ocean circulation and sea ice distribution in a finite element global sea ice-Ocean model, Ocean Model., 27, 3-4, 114-129, (2009)
[17] Löhner, R.; Morgan, K.; Peraire, J.; Vahdati, M., Finite-element flux-corrected transport (FEM-FCT) for the Euler and Navier-Stokes equations, Int. J. Numer. Methods Fluids, 7, 10, 1093-1109, (1987) · Zbl 0633.76070
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