Chapter 7 Global volcanic simulation: Physical modeling, numerics, and computer implementation

Abstract

Abstract Physics-based, efficient and reliable simulations of the effects of volcanic eruptions on the surrounding territories are not feasible today. This is, part, due to the difficulty of incorporating all relevant volcanic and atmospheric processes that occur in a volcanic eruption into an all-inclusive multiphase and multicomponent physical model. But, even if such a model were available, there would also be difficulties in solving the resulting mathematical equations accurately and efficiently, and with enough spatial and temporal resolution, on current computers. Global volcanic simulation requires incorporating different types of models into a simulation package or Global Volcanic Simulator. These models include those pertaining to magma chamber dynamics, opening of volcanic conduits, magma ascent, and atmospheric dispersion of pyroclasts. During the past decade, we have developed several such models which are described elsewhere. As these models have disparate time and length scales, each must be carefully verfied and validated before it can be integrated into the global simulator. This chapter presents our work on a new pyroclastic dispersion model and its numerical and computer implementation on available computers. The structural model of multiphase mixtures presented here includes mass, momentum, energy, and turbulence coupling between the gaseous and particulate phases, and its microphysics accounts for the effects of condensation and evaporation of volatiles, fragmentation and aggregation of particulates, formation of precipitation from heterogenous condensation, and gas-particle-turbulence modulation. The resulting non-equilibrium multiphase and multicomponent flow model includes separate transport equations for each Eulerian and Lagrangian phase of the mixture and an additional set of transport equations that account for the mixture's structural characteristics. This allows for both the coupling between different scales and the exchange of energy between large and small eddies in the plume. Before implementing a numerical solution methodology, we have carried out detailed studies on the simulation requirements, accuracy of different numerical solvers, and tradeoffs of different parallel computer paradigms. The adopted strategy involves domain decomposition at both the physical and algebraic levels, and second- and third-order accurate numerical discretization schemes for the advection terms, multiblock grids, and iterative Krylov subspaces methods that are suitable for implementation on multiprocessor environments. This strategy permits simulations of high rising and widely dispersing plinian columns as well as of those columns that collapse and produce pyroclastic flows and surges. Following the current verification stage, the resulting physico-mathematical-computer model will be validated with data from several well-known eruptions, including those from Vesuvius, before other models for the magma chamber dyaamics, opening of volcanic conduits, and magma ascent are incorporated into a global simulation package for the prediction of volcanic eruptions. The resulting Global Volcanic Simulator will be employed for achieving some of the key objectives of the VESUVIUS 2000 project.