Multiphase flow modeling and numerical simulation of pyroclastic density currents

Pyroclastic density currents are hot and high-density mixtures of gas and particles of different sizes which can be originated during explosive volcanic events by the fragmentation of a viscous magma. The dynamics of these currents are not fully understood and their complexity is deeply related with their multiphase nature, since the particle concentration infuences some key aspect of current propagation (e.g, traveling speed, turbulent mixing with the atmosphere, sole erosion). Moreover, the pyroclastic density currents are among the most destructive phenomena associated with volcanic eruptions and so the problem is important not only from a pure scientic point of view, but has relevant consequences for the assessment of their related hazard. In last decades these currents have been studied adopting a continuum description. In some of the proposed models a pyroclastic density current is modeled as a single homogeneous fluid, simplifying the effects of dispersed particles. A different approach treats the particles as different fluid phases, for which the transport equations are closed with semi-empirical relations, in particular for solid stress tensor and transport coefficients. An alternative approach, which has been developed to describe particulate systems, adopts the formalism of the kinetic theory and statistical mechanics to describe the interaction between solid particles instead of molecules. Such models are widely used in dierent disciplinary fields, especially in the engineering context, but their application to geophysics is not consolidated. A relevant part of this thesis is dedicated to a review of the derivation of the equations for solid phases using the kinetic theory of granular flows. Starting from the Liouville equation, we examine the effectiveness of the assumptions necessary to obtain the transport equation and which define the range of applicability of the model. The main goal of this thesis is to investigate the effects of the particle concentration and stratification on current dynamics, by means of numerical simulations performed adopting a kinetic-theory-based model. We study the effect of a kinetic-based model for solids on the current propagation and compare them with semi-empirical models. Finally, complex modeling tools are used to test and validate simplifed simulation tools, not too computationally demanding, as requested for probabilistic studies of pyroclastic density hazard assessment in active volcanic regions. In this thesis we analyze an integral model for pyroclastic density currents, which considers the gravity current as homogeneous preudo-fluids in hydrostatic equilibrium whith external ambient and does not consider the multiphase nature of particulate flows. Since it represents an over-simplication of gravity currents, we investigate its range of applicability and calibrate it against numerical simulation obtained with the newly developed multiphase flow model, that describes the current dynamics with more accuracy and can predict non-equilibrium phenomena, such as gas-particle decoupling and current stratication, which can play a fundamental role on current propagation.