Numerical Methods for Hyperbolic Equations: Theory an Applications. An international

conference to honour Professor E.F. Toro

University of Santiago de Compostela, 4-8 july 2011, Spain

Meshless methods for lava flow modeling andsimulation†

G. Bilotta G. Russo1 A. Herault C. Del Negro A. Vicari2

Keywords: meshless methods, SPH, MLS, lava flow, fluid/solid interaction

Minisymposia: Seismology and geophysics modelling

Abstract We present an innovative approach based on mesh-free (particle) methodsfor the simulation of the fluid-dynamics and thermal aspects of lava flows, a challeng-ing task with critical importance in applications such as volcanic hazard assessment.The coupled fluid/thermal equations are solved with a Smoothed Particle Hydrody-namics (SPH) approach, with corrections based on the Moving Least Squares (MLS)method to improve the accuracy in the computation of second-order derivatives. Themodel is extended to include solid/fluid interactions within the same purely mesh-freemethod (figure 1).

Figure 1: Pure SPH simulation of water pushing a block

Our approach allows us to easily model a variety of different rheologies, and inparticular Newtonian, Bingham and Hershell-Bulkley fluids, with constant as well astemperature-dependent viscosity parameters. Complete information about all prop-erties of the flow can be easilt extracted (figure 2). Prospective applications includevolcanic hazard assessment as well as verification and advancements in the physi-cal models for lava, and for relationships, such as the one between effusion rate andthermal flux, which have important applications in monitoring and forecasting.

†Work undertaken with the financial support from the V3-LAVA project (INGV-DPC 2007-2009contract)

Figure 2: Temperature and velocity evolution during a simulated lava flow

1Dipartimento di Matematica e InformaticaUniversita di Cataniaviale A. Doria, 695125 Catania, ITALYcorresponding author: G. Bilottabilotta@dmi.unict.it

2Istituto Nazionale di Geofisica e VulcanologiaSezione di Cataniapiazza Roma, 295125 Catania, ITALY