Towards a contact formulation for efficient numerical simulation of marine ice-sheet instabilities

Abstract

Marine ice sheets are characterized by a high degree of complexity. Some underlying physical processes can feedback on each other and cause the system to exhibit irreversible bifurcations known as Marine Ice Sheet Instabilities. These are mainly controlled by geometrical features of bedrock in the transition zone between the grounded ice sheet and the floating ice shelf. Efficient and accurate numerical methods are needed to make reliable predictions of such complex systems. In this work we study numerical methods based on variational formulations for the solution of essential ice sheet models. We carry out our study by applying these numerical methods to a simple marine ice sheet model. It describes the evolution of a fast sliding marine ice sheet coupled with a floating ice shelf by means of a non-linear transport equation for the ice thickness coupled to a non-linear p-Laplace equation. The vertical equilibrium of the marine ice sheet is formulated as a unilateral contact problem and reformulated as a saddle point problem. It allows to draw from efficient numerical methods originating from frictional contact mechanics. A Mortar Finite Element discretization was employed and a semi-smooth Newton algorithm was constructed. It was shown that the segment per segment integration approach was capable of taking subgrid sized rugosity of the bedrock into account up to some extend. The methods presented in this work are not restricted to marine ice sheets. They are rather general and could be employed in other domains of computational physics as well.