Three-dimensional numerical models of a multi-phase lava flow due to gravity have been developed for specified - no-slip and frictional - conditions at the model’s bottom and for various spatial discretization of lava crust into breccias. A lava flow around barriers and on a complicated surface topography has been analyzed. It has been shown that the rate of lava flow changes with boundary conditions and is higher in the case of frictional conditions. This is in a good agreement with the results obtained from analytical and two-dimensional models on the flow rates, which we have also developed in this study. We have showed that the distribution of breccias significantly varies with the boundary conditions at the model’s bottom and with the size of the breccias. We have developed three-dimensional numerical models of lava flow with breccias on two connected inclined channels allowing for various geometry of the channels and different rates of lava flow from a volcanic orifice. It is shown that the thickness of lava flow depends on the shape of channels and flow rates, and the distribution of breccias varies with boundary conditions and flow intensity along the channels.

We have proposed a new approach to assess temperature and flow velocity within lava flow in two-dimensional models of a stationary thermal and convective flow in a lava channel, when measurements of temperature and heat flow are available at the channel’s surface only, but unknown at the lava’s bottom. We have developed a numerical approach and algorithm to solve this problem for the thermal conductivity of lava depending on temperature, and the lava viscosity on the temperature- and volume fraction of crystals. The conditions at the lava surface have varied from conductive to radiative and convective heat flux with the atmosphere. We have analyzed various scenarios for reconstruction of flow properties: a flow with almost no crust, a flow with a thin or partly covered crust, and a flow with immobile crust as well as for different effusion rates. The studied models have shown the efficiency of the proposed numerical approach to assessment of temperature and the flow velocity inside a lava flow.

(Photo and figures by Tsepelev et al., 2016)