The present chapter proposes a numerical calculation for simulating the macroscopic movements of lava flows on actual topography of volcanoes and tests it for three recent Japanese eruptions. The topography of the volcanoes as shown on pre-eruption maps was digitized using a grid in which the sampling interval was smaller than the width of the main stream of lava. The flux of lava among meshes is calculated from the steady-state solution of the Navier-Stokes equation for a Bingham fluid flowing due to gravity on an inclined plane. The calculation evaluates temperature change due to cooling by radiation. Viscosity is then estimated using an empirical relationship between viscosity and magma temperature and composition. The effusion rate and the duration of extrusion were estimated from the records of the eruptions. Three lava flows with different chemical compositions were simulated to check the validity of the method: the 1983 Miyakejima lava flows (53-540/0 Si0 2 ), the 1986 Izu-Oshima lava flows (54-58%), and the 1914 Sakurajima lava flows (59-62%). The simulations match fairly well the progress of flow fronts and actual thickness of the lavas. Some discrepancies in inundation area were found at the branches of lava streams and at the margins of main streams. These are largely due to insufficient precision of maps of the pre-eruptive topography and to the size of the sampling interval in the horizontal dimension being large relative to the widths of lava streams.
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