Numerical simulation of lava flows in models of isothermal viscous multiphase incompressible fluid

A lava flow begins to form when molten rock erupts onto the surface of the Earth and slowly spreads to the surface from a fissure vent. Eruptions create different lava flows (for example, flows of a different structure and flow velocity) under the influence of gravity, depending on the chemical composition, temperature of igneous rocks, and the topography of the surface over which the lava flows. Despite the fact that volcanic lava flows do not have a significant impact on people's lives, their danger is considerable, since hot lava kills vegetation, destroys infrastructure, and can cause flooding due to melting snow/ice. Following the development of computing resources, numerical modeling of lava flows over the past few decades has moved from modeling one-dimensional flows to modeling three-dimensional flows, which is most adequately able to reflect real natural processes. In order to investigate the dynamics and interaction of lava flows, the current article develops three-dimensional numerical models of flows of an isothermal viscous Newtonian multiphase fluid on various surfaces under the influence of gravity. A complete simulation of a lava flow is a challenging task from a physical, mathematical, and numerical point of view. The mathematical model includes the Navier-Stokes equation, the incompressibility equation, and the phase transfer equations with corresponding initial and boundary conditions. The finite volume method is used for numerical approximation of the mathematical model. The program codes are implemented in the ANSYS Fluent package in C. When conducting numerical experiments, a parallel-acting computer was used. The article demonstrates the results of calculations of the model experiment. Lava flow reconstruction models can provide significant assistance in the design of barriers reflecting lava flows. The availability of technological and scientific data (such as satellite monitoring data, high-speed calculation algorithms, and realistic models) will allow for integrating data into models with traditional methods of studying volcanic activity, which will allow more efficient use of the results.