A new shallow-depth approximation model for lava flow advance and cooling on a quantized topography is presented in this paper. To apply the model, lava rheology is described using a non-isothermal three-dimensional viscoplastic fluid in which the rheological properties are assumed to be temperature dependent. Asymptotic analysis allows a three-dimensional flow scenario to be reduced to a two-dimensional problem using depth-averaged equations. These equations are numerically approximated by an autoadaptive finite element method, based on the Rheolef C++ library, which allows economy of computational time. Here, the proposed approach is first evaluated by comparing numerical output with non-isothermal experimental results for a flow of silicon oil. Finally, the December 2010 eruption of Piton de la Fournaise (La Réunion Island) is numerically reproduced and compared with available data.

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Spatio-temporal evolution of temperature and fluid flow through a new "thermo-lithological" boundary; the case of a pit crater of Karthala volcano (Comoros archipelago) refilled on January 13 th 2007 by a lava flow.