Abstract GPUSPH is a fully three-dimensional model for the simulation of the thermal and rheological evolution of lava flows that relies on the Smoothed Particle Hydrodynamics (SPH) numerical method. Thanks to the Lagrangian, meshless nature of SPH, the model incorporates a more complete physical description of the emplacement process and rheology of lava that considers the free surface, the irregular boundaries represented by the topography, the solidification fronts and the non-Newtonian rheology with temperature-dependent parameters. GPUSPH follows the very general Herschel–Bulkley rheological model, which encompasses Newtonian, power-law and Bingham flow behaviours, with both constant and temperature-dependent parameters, and can thus be used to explore in detail the impact of rheology on the behaviour of lava flows and on their emplacement. To illustrate this possibility, we present some preliminary applications of the model for studying the rheology of lava flows with different constitutive relationships and thermal regimes using the real topography of the Mt Etna volcano.

Contents Page Table 8 1. Figure of the Earth’s surface 104 2. Gravity at the surface; mass, mean density, moment of inertia 104 3. Pressure, density, acceleration of gravity and ellipticity of layers of equal density in the Earth 105 4. The Earth’s core 106 1. Benfield, Z. f. Geophys. 13, 157, 1937. 2. Birch, Bull. Seism. Soc. Amer. 29, 463, 1939. 3. Bullen, M. N. R. A. S. Geophys. Supp. 3, 395, 1936. 4. Bullen, Trans. Roy. Soc. New Zealand, 67, 122, 1937. 5. Bullen, idem, 69, 188, 1939. 6. Bullen, Bull. Seism. Soc. Amer. 30, 235, 1940. 7. Gutenberg and Richter, Beitr. z. Geophys. 54, 94, 1939. 8. Gutenberg and Richter, M. N. R. A. S. Geophys. Supp. 4, 363, 1938. 9. Jeffreys, M. N. R. A. S. Geophys. Supp. 4, 537, 548 and 594, 1939. 10. Lambert, The Internal Constitution of the Earth, Chap. 13, McGraw-Hill, New York, 1939. 11. Olczak, Acta Astron. 3, 81, 1938. 12. Williamson and Adams, J. Washington Acad. Sci. 13, 413, 1923. T able 8–1.—F igure of the E arth’s S urface (Ref. 10) Semi-axes of International Ellipsoid of Reference (1924): Equatorial, a = 6378.388 km. Polar, c = 6356.912 km. Radius of sphere of equal volume, α 0 = 6371 km. Ellipticity of surface, ( a – c )/ a = 1/297 = 0.00337. (For ellipticity of internal levels, see Table 8–3.) Quadrant of a meridian = 10,002.288 km. Quadrant of the equator = 10,019.148 km. Area of surface = 5.101 × 10 18 cm. 2 Volume = 1.083 2