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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.

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