Numerical model of multi-phase porous, mush, and suspension flows in magmatic systems

Magmatic systems in the Earth's mantle and crust can range from melt-poor partially molten rock to trans-crustal magma mushes with ephemeral lenses of melt-rich suspensions. Most process-based models of magmatic systems, however, are limited to two-phase porous flow at low melt fractions (<20%) or suspension flow at high melt fractions (>60%). A lack of formal extensions to intermediate phase fractions has long hindered investigations into the dynamics of mush flows. To address this knowledge gap and unify two-phase magma flow models, we present a two-dimensional system-scale numerical model of the fluid mechanics of an n-phase system valid at all phase fractions. The numerical implementation uses a finite-difference staggered-grid approach with a dampened pseudo-transient iterative algorithm and is verified using the Method of Manufactured Solutions. Numerical experiments replicate known limits of two-phase flow including rank-ordered porosity wave trains in 1D and porosity wave breakup in 2D in the porous flow regime, as well as particle concentration waves in 1D and mixture convection in 2D in the suspension flow regime. In the mush regime, numerical experiments show strong liquid localisation into pockets and stress-aligned bands. A tentative application to a three-phase, solid-liquid-vapour system demonstrates the broad utility of the n-phase general model and its numerical implementation. The model code is available open source at github.com/kellertobs/pantarhei.