A fully implicit second order method for viscous free surface  Stokes flow – application to glacier simulations

Ahlkrona, Josefin; Henry, A. Clara J.; Löfgren, André

doi:10.5194/gmd-19-2333-2026

Articles | Volume 19, issue 6

https://doi.org/10.5194/gmd-19-2333-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/gmd-19-2333-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 19, issue 6

Development and technical paper

|

23 Mar 2026

Development and technical paper |

| 23 Mar 2026

A fully implicit second order method for viscous free surface Stokes flow – application to glacier simulations

Josefin Ahlkrona, A. Clara J. Henry, and André Löfgren

Model code and software

andrelofgrenSU/biceps: v1.0-implicit-higher-order André Löfgren https://doi.org/10.5281/zenodo.17371013

ElmerCSC/elmerfem: Elmer 9.0 J. Ruokolainen et al. https://doi.org/10.5281/zenodo.7892181

Code for the publication "A Fully Implicit Second Order Method for Viscous Free Surface Stokes Flow – Application to Glacier Simulations" by Josefin Ahlkrona, André Löfgren and A. Clara J. Henry Josefin Ahlkrona et al. https://doi.org/10.5281/zenodo.17475634

Biceps: A prognostic two-dimensional full-Stokes ice-sheet solver André Löfgren https://github.com/andrelofgrenSU/biceps

Short summary

This paper leverages the Free Surface Stabilization Algorithm of Kaus et al. (2010) to construct a 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.