A semi-implicit, second order accurate numerical model for multiphase underexpanded volcanic jets

An improved version of the PDAC (Pyroclastic Dispersal Analysis Code, Esposti Ongaro et al., 2007) 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 model is tested on the problem of jet decompression, in both two and three dimensions. For homogeneous jets, numerical results are consistent with experimental results at the laboratory scale (Lewis and Carlson, 1964). For non-equilibrium gas-particle jets, we consider monodisperse and bidisperse mixtures and we quantify non-equilibrium effects in terms of the ratio between the particle relaxation time and a characteristic jet time scale. For coarse particles and low particle load, numerical simulations well reproduce laboratory experiments and numerical simulations carried out with an Eulerian-Lagrangian model (Sommerfeld, 1993). At the volcanic scale, we consider steady-state conditions associated to the development of Vulcanian and sub-Plinian eruptions. For the finest particles produced in these regimes, we demonstrate that the solid phase is in mechanical and thermal equilibrium with the gas phase and that the jet decompression structure is well described by a pseudogas model (Ogden et al., 2008). Coarse particles, on the contrary, display significant non-equilibrium effects, associated to their larger relaxation time. Deviations from the equilibrium regime occur especially during the rapid acceleration phases and are able to appreciably modify the average jet dynamics, with maximum velocity and temperature differences of the order of 150 m s 1 and 80 K across shock waves.