The numerical modeling of lava dome evolution at volc'an de Colima using VOF and SPH methods

Lava flows from extrusive volcanic eruptions can have catastrophic consequences both for human life and the environment. Modeling such situations is an important scientific problem. The main driving forces in the evolution of the mentioned lava flows are gravitational forces, viscous friction forces on the surface of the spill, and the processes of crystallization of molten rocks into lava plateau, tubes, and domes. In this paper, the mathematical model of an extrusive volcanic eruption includes the Navier-Stokes equation, the incompressibility equation, the viscous phase transfer equation, as well as the corresponding initial and boundary conditions. Mathematical models of volcanic lava flows are considered and compared within the Euler (Volume Of Fluid - VOF) and Lagrange (Smooth Particle Hydrodynamic - SPH) formulations. ANSYS Fluent, OpenFOAM, and SPlisHSPlasH packages were used for computer simulation. Computer simulation algorithms for the problem are implemented in C++ language. Numerical modeling of the evolution of a real lava dome formed at the Colima volcano (Mexico) in February-March 2013 was carried out. For this experiment, information about the dynamics of lava dome growth, collected during the eruption, was used. It is shown how the computer simulation approach makes it possible to establish the dependence of the lava dome morphology on the rheology of a highly viscous fluid and the intensity of lava outflow.