Numerical modeling of magma ascent dynamics

In the world, volcanic systems exhibit a wide range of eruption styles threatening the lives of millions of people. Relatively slow effusive eruptions generate lava flows (low viscosity magma) and lava domes (high viscosity magma) and tend to evolve over days to decades. Alternatively, explosive eruptions can inject very large volumes of fragmented magma and volcanic gas high into the atmosphere over shorter periods (minutes to weeks to months). Mitigation of the associated risk to populations, the built environment, and the cultural heritage relies upon our ability to accurately assess volcanic hazards, and this, in turn, depends on our understanding of the processes that control the style and scale of volcanic eruptions. To this end, technological developments over the last couple of decades have greatly improved our ability to characterize magmatic systems and detect precursors at high spatial and temporal resolution through the use of analytical and observational volcanology, including monitoring-derived data, and volcano geophysics. Numerical modeling of magma ascent can serve to link all of these data and processes to build effective near-real-time strategies. The complexity of the volcanic system, derived from the multiphase, multicomponent character of the magmatic mixtures and from their interaction dynamics with the surrounding host rocks, is however manifested in the complexity of its mathematical representation, and numerical models able to describe several interdependent processes, eventually at disequilibrium conditions, are required to capture the nature of volcanic systems with fidelity. In this chapter, we present the main equations governing magma ascent, highlighting the multiphase and disequilibrium nature of volcanic flows, and the presence of complex feedback mechanisms between gas exsolution, outgassing, and crystallization that are able to influence the most important characteristics of the resulting volcanic events. Then, a suite of numerical simulations is described to show the effect of some parameters and processes in controlling eruption style and scale, and thus the potential eruption hazard.