Commun. Comput. Phys., 16 (2014), pp. 1056-1080.


A Parallel Computational Model for Three-Dimensional, Thermo-Mechanical Stokes Flow Simulations of Glaciers and Ice Sheets

Wei Leng 1, Lili Ju 2*, Max Gunzburger 3, Stephen Price 4

1 State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing 100190, China.
2 Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA.
3 Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA.
4 Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545. USA.

Received 31 August 2013; Accepted (in revised version) 1 April 2014
Available online 12 August 2014
doi:10.4208/cicp.310813.010414a

Abstract

This paper focuses on the development of an efficient, three-dimensional, thermo-mechanical, nonlinear-Stokes flow computational model for ice sheet simulation. The model is based on the parallel finite element model developed in [14] which features high-order accurate finite element discretizations on variable resolution grids. Here, we add an improved iterative solution method for treating the nonlinearity of the Stokes problem, a new high-order accurate finite element solver for the temperature equation, and a new conservative finite volume solver for handling mass conservation. The result is an accurate and efficient numerical model for thermo-mechanical glacier and ice-sheet simulations. We demonstrate the improved efficiency of the Stokes solver using the ISMIP-HOM Benchmark experiments and a realistic test case for the Greenland ice-sheet. We also apply our model to the EISMINT-II benchmark experiments and demonstrate stable thermo-mechanical ice sheet evolution on both structured and unstructured meshes. Notably, we find no evidence for the ``cold spoke'' instabilities observed for these same experiments when using finite difference, shallow-ice approximation models on structured grids.

AMS subject classifications: 86A40, 65N30, 65M08

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Key words: Stokes-flow modeling, ice-sheet modeling, finite element approximation, finite volume approximation, parallel implementation.

*Corresponding author.
Email: wleng@lsec.cc.ac.cn (W. Leng), ju@math.sc.edu (L. Ju), mgunzburger@fsu.edu (M. Gunzburger), sprice@lanl.gov (S. Price)
 

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