Numerical stabilization methods for level-set-based ice front migration

Numerical modeling of ice sheet dynamics is a critical tool for projecting future sea level rise. Among all the processes responsible for the loss of mass of the ice sheets, enhanced ice discharge triggered by the retreat of marine-terminating glaciers is one of the key drivers. Numerical models of ice sheet flow are therefore required to include ice front migration in order to reproduce today's mass loss and to be able to predict their future. However, the discontinuous nature of calving poses a significant numerical challenge for accurately capturing the motion of the ice front. In this study, we explore different stabilization techniques combined with varying reinitialization strategies to enhance the numerical stability and accuracy of solving the level-set function, which tracks the position of the ice front. Through rigorous testing on an idealized domain with a semicircular and a straight-line ice front, including scenarios with diverse front velocities, we assess the performance of these techniques. The findings contribute to advancing our ability to model ice sheet dynamics, specifically calving processes, and provide valuable insights into the most effective strategies for simulating and tracking the motion of the ice front.