A second order accurate numerical model for multiphase underexpanded volcanic jets

Abstract

An improved version of the PDAC (Pyroclastic Dispersal Analysis Code) numerical model for the simulation of multiphase volcanic flows is presented and validated for the simulation of multiphase volcanic jets in supersonic regimes. The present version of PDAC includes second-order time and space discretizations and fully multidimensional advection discretizations, in order to reduce numerical diffusion and enhance the accuracy of the original model. The resulting numerical model is tested against the problem of jet decompression in both two and three dimensions. For homogeneous jets, numerical results show a good quantitative agreement with experimental results on the laboratory scale in terms of Mach disk location (Lewis and Carlson, 1964). For multiphase jets, we consider monodisperse and polydisperse mixtures of particles with different diameter. For fine particles, for which the pseudogas limit is valid, the multiphase model correctly reproduces predictions of the pseudogas model. We obtain that particles are in mechanical and thermal equilibrium with the gas phase and the jet decompression structure is in quantitative agreement with pseudogas results (Ogden et al., 2008b). For both fine and coarse particles, we measure the importance of multiphase effects with relation to the characteristic time scales of multiphase jets and we quantify how particles affect the average jet dynamics in terms of pressure, mixture density, vertical velocity and temperature. Furthermore, time dependent vent conditions are introduced, in order to achieve numerical simulation of eruption regimes characterized by transient jet behaviour. We show how in case of rapid change in vent conditions, volcanic jet structures do not evolve through a succession of steady state configurations and the transition between different flow conditions can result in the collapse of the volcanic column.