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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  nonequilibrium gas–particle jets, we consider monodisperse and  bidisperse mixtures, and we quantify nonequilibrium effects in terms  of the ratio between the particle relaxation time and  a characteristic jet timescale. 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 with 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 other hand, display significant nonequilibrium effects, which associated  with their larger relaxation time. Deviations from the equilibrium regime, with maximum  velocity and temperature differences on the order of 150 m s<sup>−1</sup>  and 80 K across shock waves,  occur especially during the rapid acceleration phases, and are able  to   modify substantially the jet dynamics with respect to the homogeneous case

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