André Löfgren: Numerical stability of ice-sheet models

Abstract

Predicting future sea-level-rise contributions from our melting glaciers and ice sheets requires accurate description of their dynamics. Unfortunately, the most accurate model of ice dynamics, the so-called full-Stokes model, is seldom used due to its computational cost. One way of speeding up numerical simulations is to increase stable time-step sizes, and thereby reducing the number of times the expensive Stokes equations are solved. To this end, the so-called free-surface stabilization algorithm (FSSA) was introduced in the context of mantle convection, where a similar set of partial differential equations are used to model the Earth's mantle. The stabilization was later adapted to the regime of ice sheet modeling, where it showed potential to increase stable time-step sizes up to an order of magnitude. However, theoretical understanding of the stabilization remains limited. In this talk, it is shown through a linear stability analysis of the corresponding dynamical system that the enhanced stability of the FSSA follows from a reduction in the spread of the eigenvalues of the Jacobian matrix. Furthermore, it is verified that time-step-size restrictions obtained from the linear stability analysis agrees well with numerically observed restrictions. The framework presented for assessing stability is general enough to also be used to assess alternative stabilization methods, for example advection-based stabilizations.