A coupled multivalued model for ice streams and its numerical simulation

• Published in: IMA Journal of Applied Mathematics
• Main Authors: Calvo, Nati, Durany, José, Muñoz, Ana I., Schiavi, Emanuele, Vázquez, Carlos
• Format: Text
• Language: English
• Published: Oxford University Press 2006
• Subjects: Articles; Ice Sheet
• Online Access: http://imamat.oxfordjournals.org/cgi/content/short/71/1/62; https://doi.org/10.1093/imamat/hxh082

This paper deals with the numerical solution of a non-linear model describing a free-boundary problem arising in modern glaciology. Considering a shallow, viscous ice sheet flow along a soft, deformable bed, a coupled non-linear system of differential equations can be obtained. Particularly, an obstacle problem is then deduced and solved in the framework of its complementarity formulation. We present the numerical solution of the resulting multivalued system modelling the ice sheet non-Newtonian dynamics driven by the underlying drainage system. Our numerical results show the existence of fast ice streams when positive wave-like initial conditions are considered. The solutions are numerically computed with a decoupling iterative method and finite-element technique. A duality algorithm and a projected Gauss–Seidel method are the alternatives used to cope with the resulting variational inequality while the explicit treatment, Newton method or a duality method are proposed to deal with the non-linear source term. Finally, the numerical solutions are physically interpreted and some comparisons among the numerical methods are then discussed.