One‐dimensional, time‐dependent, homogeneous, two‐phase flow in volcanic conduits

Abstract A one‐dimensional, time‐dependent, isothermal, homogeneous, two‐phase flow model was developed to study magma ascent in volcanic conduits. The physical modeling equations were numerically solved by means of a TVD (total variation diminishing) predictor‐corrector procedure and by means of a predictor‐corrector technique based on the method of characteristics. The results from the transient model were verified with an analytical solution for wave propagation in conduits without friction and gravitational effects. The numerical solutions were also compared with those of a steady‐state, homogeneous, two‐phase model for basaltic and rhyolitic magma ascents in the fissures and circular conduits of Vesuvius and Mt St. Helens. An application of the model to magma decompression in conduits indicates very short times for gas exsolution, fragmentation, and shock wave propagation, implying that the modelling of gas exsolution should involve non‐equilibrium kinetics effects. Future coupling of the transient magma ascent model with magma chamber and pyroclastic dispersion models should allow for more realistic simulations of the time‐dependent behavior of real volcanic eruptions.