Numerical Solvers of the p-Stokes Equations with Applications in Ice-Sheet Dynamics

Sammanfattning: In glacier dynamics – i.e. the field of research concerning the movement of ice – intricate mathematical models are used to describe its motion. Ice can be considered as a highly viscous, non-Newtonian fluid, obeying a set of equations closely related to the well-known Navier-Stokes equations describing classical fluid mechanics. These equations are called the p-Stokes equations and is to date the most precise mathematical description of the flow of ice. Using the finite element method, the non-linear p-Stokes equations are most efficiently solved numerically by a Newton solver in combination with preconditioned iterative solvers. This thesis investigate the use of such solvers when applied to glacier dynamics. To avoid singularities, the non-linear shear dependent viscosity that arise in the p-Stokes equations is modeled with a regularization term to avoid singularities. Inorder to facilitate fast convergence for glacier simulations we implement and discuss the use of an optimal expression of this regularization. The regularization term is tested fora simplified flow configuration, for well-known glaciological benchmark experiments and lastly, an Antarctic glacial geometry. We come to the conclusion that the regularization parameter implemented increase the efficiency of the numerical methods used, generally without the introduction of significant errors to the model.