Lava flows represent a challenge for physically based modeling, since the mechanical properties of lava change over time. This change is ruled by a temperature field, which needs to be modeled. MAGFLOW Cellular Automata (CA) model was developed for physically based simulations of lava flows in near real-time. We introduced an algorithm based on the Monte Carlo approach to solve the anisotropic problem. As transition rule of CA, a steady state solution of Navier-Stokes equations was adopted in the case of isothermal laminar pressure-driven Bingham fluid. For the cooling mechanism, we consider the radiative heat loss only from the surface of the flow, and the change of the temperature due to mixture of lavas between cells with different temperatures. The model was applied to reproduce a real lava flow occurred during the 2004-2005 Etna eruption. The simulations were computed using three different empirical relationships between viscosity and temperature.
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