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Abstract: In this paper the numerical solution of a highly nonlinear model for the thermomechanical behavior of polythermal glaciers is presented. The modeling follows the shallow ice approximation (SIA) for glaciers introduced in Fowler (1997) . The model has been extended to incorporate additional moving boundaries and other nonlinear features. Moreover, a fixed domain formulation is proposed to avoid the computational drawbacks of a time-dependent domain in the numerical simulation with front tracking methods. In this setting, the coupled problem is decomposed into different nonlinear problems which allow one to obtain sequentially the profile evolution, the velocity field, the glacier surface and atmospheric temperatures, basal magnitudes and the temperature distribution inside the ice mass. A fixed point iteration algorithm converges to the solution of the nonlinear coupled problem. Among different numerical methods involved in the solution of the subproblems, characteristic schemes for time discretization, finite elements for spatial discretization, duality methods for the nonlinearities associated to maximal monotone operators and a Newton scheme for the nonlinear viscous term are proposed. Several numerical simulation examples illustrate the performance of the numerical methods and the behavior of the involved physical magnitudes. [Copyright &y& Elsevier]

Abstract: In this paper we develop a set of numerical techniques for the simulation of the profile evolution of a valley glacier in the framework of isothermal shallow ice approximation models. The different mathematical formulations are given in terms of a highly nonlinear parabolic equation. A first nonlinearity comes from the free boundary problem associated with the unknown basal extension of the glacier region. This feature is treated using a fixed domain complementarity formulation which is solved numerically by a duality method. The nonlinear diffusive term is explicitly treated in the time marching scheme. A convection dominated problem arises, so a characteristic scheme is proposed for the time discretization, while piecewise linear finite elements are used for the spatial discretization. The presence of infinite slopes in polar regimes motivates an alternative formulation based on a prescribed flux boundary condition at the head of the glacier instead a homogeneous Dirichlet one. Finally, several numerical examples illustrate the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract: A shallow ice thermocoupled model for the complex nonlinear polythermal ice sheet dynamics is proposed and solved by means of efficient numerical methods. A novelty is the obstacle problem formulation associated to a nonlinear integro-differential equation (with nonlocal temperature dependent coefficients) for the ice sheet profile. This formulation is motivated by the free boundary feature and the influence of the temperature on the profile (fully nonisothermal model). Concerning the temperature equation, a dynamically prescribed surface temperature, obtained from an Energy Balance model corrected by the altitude effect, is posed. As the profile and temperature equations are fully coupled, a nonlinear PDE system governing the upper ice sheet profile, the velocity field, the temperature and the basal stress is stated. In addition to the numerical difficulties associated to the new profile equation, several techniques have been considered for the numerical solution of the temperature, velocity and basal magnitudes. Discussions concerning the nonlinear dynamics of the different involved magnitudes and the improvement in their computed values with respect to previous works are also presented. [Copyright &y& Elsevier]

The here presented GLAciology NUmerical SImulation Toolbox (GLANUSIT) is a software application which provides a user friendly environment for the numerical simulation of large ice masses evolution. The graphical user interface has been developed in MATLAB while the core of GLANUSIT contains the original FORTRAN codes, which develop the specific numerical methods for the solution of the complex shallow ice model. This highly nonlinear model governs the coupled thermodynamical and hydrodynamical processes. The global algorithm mainly consists on a fixed point iteration between the different subproblems. The numerical solution of each subproblem requires specific techniques, which are not common in present software packages, as for example the part of moving boundaries solvers included in the code. Finally, a practical case study with real data is presented. [Copyright &y& Elsevier]

This work deals with the numerical solution of a complex mathematical model arising in theoretical glaciology. The global moving boundary problem governs thermomechanical processes jointly with ice sheet hydrodynamics. One major novelty is the inclusion of the ice velocity field computation in the framework of the shallow ice model so that it can be coupled with profile and temperature equations. Moreover, the proposed basal velocity and shear stress laws allow the integration of basal sliding effects in the global model. Both features were not taking into account in a previous paper (Math. Model. Methods Appl. Sci. 12 (2) (2002) 229) and provide more realistic convective terms and more complete Signorini boundary conditions for the thermal problem. In the proposed numerical algorithm, one- and two-dimensional piecewise linear Lagrange finite elements in space and a semi-implicit upwinding scheme in time are combined with duality and Newton''s methods for nonlinearities. A simulation example involving real data issued from Antarctic shows the temperature, profile and velocity qualitative behaviour as well as the free boundaries and basal effects. [Copyright &y& Elsevier]