Mathematical modelling of ice with numerical experiments in alpine, polar and extraterrestrial environment

In this talk I shall present different mathematical models aimed to describe evolving thermo-mechanics of ice in different topo-morphological and climatic conditions. Up-to-date computational glaciology address to the intensive use of the large amount of data, gathered in (alpine or polar) on-field campaigns, and to the 'brute force' adaptation of the mathematical modelling of glacier evolution based on Glen's law via phenomenological multi-parametrical functional factors and/or addenda. Although, reasonable to fully satisfactory numerical results have been being obtained with this approach adopted by the most popular open-source computational glaciology codes, with the aim to improve the comprehension of the physical mechanisms and processes, I shall discuss extensions of such models by explicit inclusion of natural phase transition occurrence (inherent and/or at a boundary interface) and by expansion of Glen's constitutive equation in order to take into account the effects of the presence of sand and rock fragments in glacier interstices. Several problems will be discussed: the description of the thermo-mechanical evolution of the icy crust of Europa, Juppiter's satellite; the check of the compatibility of the existence of a subglacial lake at Svalbard archipelago; the reproduction of the borehole measurements at the Murtel-Corvatsch glacier, Grisons Alps, Switzerland. Thus extraterrestrial, polar and alpine environments, respectively, will be considered.