Numerical stabilisation of grounding line dynamics in Stokes problems

The grounding line marks the boundary between grounded and floating ice, and is a critical region for ice-sheet stability and sea-level projections. The complex ice-flow at the grounding line, where the stress regime moves from vertical shear to horizontal extension over a relatively short distance, is prone to numerical instability in transient full-Stokes simulations. Furthermore, boundary conditions change at the grounding line, switching from a friction law in grounded ice to an ocean pressure force at the ice-ocean interface. Grounding-line full-Stokes problems have been successfully stabilised by the sea spring stabilisation scheme in Elmer/Ice (Durand et al., 2009) which mimicks an implicit time-stepping scheme by predicting the surface elevation and corresponding ocean pressure corrections in the next time step. We extend on this stabilisation approach by introducing the Free-Surface Stabilisation Approximation (FSSA) to the ice-ocean interface. FSSA has been proven successful in allowing larger stable time steps in grounded problems with an evolving ice-atmosphere interface (Löfgren et al., 2022; Löfgren et al., 2024). This stabilisation approach incorporates a boundary condition term into the weak-form of the Stokes equations representing the predicted stress adjustment between the current and next time step. Using a synthetic MISMIP set up (Pattyn et al., 2012), we investigate the applicability of FSSA to the ice-ocean interface.

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