Abstract

Ice-sheet modelling continues to be challenging because of the need to balance computational efficiency with model complexity, a trade-off that affects the accuracy of sea-level projections. A major reason for the computational efficiency bottleneck is that the system of PDEs describing ice flow is stiff, meaning that the time-step size is restricted by fast-decaying modes. Generally, restrictive time stepping can be alleviated by solving a system of PDEs implicitly rather than explicitly. However, without modification, this has not been shown to result in a marked improvement in the numerical stability and efficiency of ice-flow models.

To address these time-step restrictions, we develop numerical stabilisation schemes for ice-sheet models of varying complexity by modifying the forcing term in the momentum equations. Our methods enable larger stable time steps, including when using a fully implicit time-stepping scheme, providing a pathway towards improved computational efficiency in large-scale simulations of the Antarctic and Greenland Ice Sheets.