Numerical simulation of lava flows based on depth-averaged equations

Risks and damages associated with lava flows propagation (for instance the most recent Etna eruptions) require a quantitative description of this phenomenon and a reliable forecasting of lava flow paths. Due to the high complexity of these processes, numerical solution of the complete conservation equations for real lava flows is often practically impossible. To overcome the computational difficulties, simplified models are usually adopted, including 1-D models and cellular automata. In this work we propose a simplified 2D model based on the conservation equations for lava thickness and depth-averaged velocities and temperature which result in first order partial differential equations. The proposed approach represents a good compromise between the full 3-D description and the need to decrease the computational time. The method was satisfactorily applied to reproduce some analytical solutions and to simulate a real lava flow event occurred during the 1991-93 Etna eruption.Comment: 4 pages, 4 figure

Nonlinear phenomena in fluids with temperature-dependent viscosity: an hysteresis model for magma flow in conduits

Magma viscosity is strongly temperature-dependent. When hot magma flows in a conduit, heat is lost through the walls and the temperature decreases along the flow causing a viscosity increase. For particular values of the controlling parameters the steady-flow regime in a conduit shows two stable solutions belonging either to the slow or to the fast branch. As a consequence, this system may show an hysteresis effect, and the transition between the two branches can occur quickly when certain critical points are reached. In this paper we describe a model to study the relation between the pressure at the inlet and the volumetric magma flow rate in a conduit. We apply this model to explain an hysteric jump observed during the dome growth at Soufri\`ere Hills volcano (Montserrat), and described by Melnik and Sparks [1999] using a different model.Comment: 4 pages, 4 figures, corrected version of "Nonlinear phenomena in fluids with temperature-dependent viscosity: an hysteresis model for magma flow in conduits" GRL Vol 29, No 10,200