A new shallow approximation for tridimensional non-isothermal viscoplastic lava flows

Noé Bernabeu (1) , Pierre Saramito (1) , Claude Smutek (2, 3)

1 EDP - Equations aux Dérivées Partielles
2 LGSR - Laboratoire GéoSciences Réunion
3 IPGP - Institut de Physique du Globe de Paris

A new shallow reduced model for the non-isothermal tridimensional viscoplastic fluid flowing on a general topography is presented in this paper. Both the consistency and yield stress are supposed temperature-dependent. An asymptotic analysis leads to reduce the 3D problem to a 2D surface one with depth-averaged equations. These equations are numerical approximated by an autoadaptive finite element method, based on the Rheolef C++ library, allowing to track accurately the front position. The proposed approach is first evaluated by comparing numerical prediction with non-isothermal experimental measurements for a silicone oil dome. Next, the December 2010 eruption of Piton de la Fournaise (La Réunion island) is numerically reproduced and compared with available data.

Mots clés: shalow water approximation; viscoplastic fluid; heat equation; volcanic lava flow

Domaines: Equations aux dérivées partielles [math.AP]; Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]

Noé Bernabeu, Pierre Saramito, Claude Smutek. A new shallow approximation for tridimensional non-isothermal viscoplastic lava flows. 2014. ⟨hal-01059334v1⟩