Articles | Volume 10, issue 1
The Cryosphere, 10, 1–14, 2016
https://doi.org/10.5194/tc-10-1-2016
The Cryosphere, 10, 1–14, 2016
https://doi.org/10.5194/tc-10-1-2016

Research article 15 Jan 2016

Research article | 15 Jan 2016

A moving-point approach to model shallow ice sheets: a study case with radially symmetrical ice sheets

B. Bonan et al.

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Cited articles

Baines, M. J., Hubbard, M. E., and Jimack, P. K.: A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries, Appl. Numer. Math., 54, 450–469, https://doi.org/https://doi.org/10.1016/j.apnum.2004.09.013, 2005.
Baines, M. J., Hubbard, M. E., and Jimack, P. K.: Velocity-based moving mesh methods for nonlinear partial differential equations, Commun. Comput. Phys., 10, 509–576, https://doi.org/https://doi.org/10.4208/cicp.201010.040511a, 2011.
Blake, K. W.: Moving Mesh Methods for Non-Linear Parabolic Partial Differential Equations, PhD thesis, available at: https://doi.org/http://www.reading.ac.uk/web/FILES/maths/Kw_blake.pdf (last access: 4 August 2015), University of Reading, Reading, Berks, UK, 2001.
Budd, C. J., Huang, W., and Russell, R. D.: Adaptivity with moving grids, Acta Numerica, 18, 111–241, https://doi.org/https://doi.org/10.1017/S0962492906400015, 2009.
Bueler, E., Lingle, C. S., Kallen-Brown, J. A., Covey, D. N., and Bowman, L. N.: Exact solutions and verification of numerical models for isothermal ice sheets, J. Glaciol., 51, 291–306, https://doi.org/https://doi.org/10.3189/172756505781829449, 2005.
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Short summary
This paper introduce a moving-point approach to model the flow of ice sheets. This particular moving-grid numerical approach is based on the conservation of local masses. This allows the ice sheet margins to be tracked explicitly. A finite-difference moving-point scheme is derived and applied in a simplified context (1-D). The conservation method is also suitable for 2-D scenarios. This paper is a first step towards applications of the conservation method to realistic 2-D cases.