Numerical simulation of the eruption of the volcano ETNA using a depth-averaged lava flow model

Volcanic eruptions and accompanied lava flows pose a significant threat to population, buildings and regional infrastructure. Lava may occupy large spatial domains, for which a detailed three-dimensional modeling of its flow is reduced to solving discrete problems of high dimensionality and is not always effective. For sufficiently small ratio of the vertical dimension of the flow to its horizontal dimension, the mathematical models which are based on the depth-averaged equations of motion of a viscous medium are used. In this study, such a model consists of equations for lava thickness, two-dimensional equations of its motion, crystal growth kinetic equations and a heat balance equation that takes into account nonlinear convective and radiative energy exchange with the external environment, dissipation energy and latent heat of crystallization. The mathematical model was implemented numerically in the open-source package OpenFOAM. This package makes it possible to use modern high-performance computing clusters for conducting numerical experiments and to adapt the problem to specific physical aspects of the simulated natural process. The codes were verified by comparing the analytical solution of the problem and the solution obtained in terms of the model involving equations of motion of a two-phase incompressible fluid in spatial domain. The effect of the rheological characteristics of the flow represented by the Newtonian model was studied in comparison with the flow simulated using the Bingham model and the nonlinear Herschel-Bulkley model. The nonlinear rheology of the fluid of interest accounts for the dependence of the actual viscosity of a lava flow on temperature, shear rate, and yield stress (the yield stress and the flow behavior index are the functions of temperature). Parallel computer codes were implemented on the basis of OpenMPI for the computing clusters with shared and distributed memory running in Linux OS. Profiling of codes for multi-core CPUs with shared memory was carried out.