Abstract A new shallow-depth approximation model for lava flow advance and cooling on a quantized topography is presented in this paper. To apply the model, lava rheology is described using a non-isothermal three-dimensional viscoplastic fluid in which the rheological properties are assumed to be temperature dependent. Asymptotic analysis allows a three-dimensional flow scenario to be reduced to a two-dimensional problem using depth-averaged equations. These equations are numerically approximated by an autoadaptive finite element method, based on the Rheolef C++ library, which allows economy of computational time. Here, the proposed approach is first evaluated by comparing numerical output with non-isothermal experimental results for a flow of silicon oil. Finally, the December 2010 eruption of Piton de la Fournaise (La Réunion Island) is numerically reproduced and compared with available data.

Abstract Prediction of the emplacement of volcanic mass flows (lava flows, pyroclastic density currents, debris avalanches and debris flows) is required for hazard and risk assessment, and for the planning of risk-mitigation measures. Numerical computer-based models now exist that are capable of approximating the motion of a given volume of volcanic material from its source to the deposition area. With these advances in technology, it is useful to compare the various codes in order to evaluate their respective suitability for real-time forecasting, risk preparedness and post-eruptive response. A ‘benchmark’ compares codes or methods, all aimed at simulating the same physical process using common initial and boundary conditions and outputs, but using different physical formulations, mathematical approaches and numerical techniques. We set up the basis for a future general benchmarking exercise on volcanic mass-flow models and, more specifically, establish a benchmark series for computational lava-flow modelling. We describe a set of benchmarks in this paper, and present a few sample results to demonstrate output analysis and code evaluation methodologies. The associated web-based communal facility for sharing test scenarios and results is also described.