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https://doi.org/10.5194/egusphere-2025-4359
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/egusphere-2025-4359
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
01 Oct 2025
| 01 Oct 2025
Status: this preprint is open for discussion and under review for Geoscientific Model Development (GMD).
A Fully Implicit Second Order Method for Viscous Free Surface Stokes Flow – Application to Glacier Simulations
Abstract. We present a fully implicit finite element method for viscous free surface Stokes problems which are common in glaciology and geodynamics. Standard fully implicit iterative solvers diverge for such problems when using large time steps. We address this by incorporating a stabilization term that vanishes upon convergence. This approach enables the use of large time steps, thereby significantly improving the efficiency of simulations. Furthermore, we leverage the fully implicit solver to develop second-order time-stepping schemes that mitigate the high errors associated with first-order methods for large time steps. The methods are tested and evaluated on model domains relevant to geodynamics and glaciology.
How to cite. Ahlkrona, J., Henry, A. C. J., and Löfgren, A.: A Fully Implicit Second Order Method for Viscous Free Surface Stokes Flow – Application to Glacier Simulations, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2025-4359, 2025.
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Josefin Ahlkrona
CORRESPONDING AUTHOR
Department of Mathematics, Stockholm University, Stockholm, Sweden
Bolin Centre for Climate Research, Stockholm University, Stockholm, Sweden
Swedish e-Science Research Centre, Stockholm, Sweden
A. Clara J. Henry
Department of Mathematics, Stockholm University, Stockholm, Sweden
Bolin Centre for Climate Research, Stockholm University, Stockholm, Sweden
André Löfgren
Department of Mathematics, Stockholm University, Stockholm, Sweden
Bolin Centre for Climate Research, Stockholm University, Stockholm, Sweden
Short summary
This paper leverages the Free Surface Stabilization Algorithm of Kaus et al. (2010) to construct the first fully implicit discretization of viscous free surface flows. It also presents the first second order accurate time-stepping scheme applicable to ice sheet models. We test the new method on an idealized problem and on a 2D glacier simulation. The results indicates that the method has great potential to speedup ice sheet models.
This paper leverages the Free Surface Stabilization Algorithm of Kaus et al. (2010) to construct...
Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".
https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
You have archived the Biceps code on GitHub. However, GitHub is not a suitable repository for scientific publication. GitHub itself instructs authors to use other long-term archival and publishing alternatives, such as Zenodo. Therefore, the current situation with your manuscript is irregular. Please, publish your code in one of the appropriate repositories and reply to this comment with the relevant information (link and a permanent identifier for it (e.g. DOI)) as soon as possible, as we can not accept manuscripts in Discussions that do not comply with our policy. Also, please include the relevant primary input/output data.
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Juan A. Añel
Geosci. Model Dev. Executive Editor