Numerical modeling of magmatic transport processes, using the pseudo-transient method

One of the continuing trends in geodynamics is to develop codes that are suitable to model magmatic processes with an increasing level of self-consistency. Developing such models is particularly challenging as most magmatic processes are multiphysics problems, and require coupling between thermal, porous, mechanical and chemical processes.

Here we consider reactive flow in a deformable porous medium coupled to thermo-mechanical processes. We present a thermodynamically self-consistent set of governing equations, describing such processes. The governing equations consists of the conservation of mass, momentum, and energy in two phases. One phase represents the solid skeleton, which deforms in a poro-visco-elasto-plastic manner. The second phase represent low viscosity melts, percolating through the solid skeleton, that is described by Darcy’s law. As melt migrates through the rock skeleton we can quantify the chemical evolution of melts due to partial melting and crystallization. The system of equations is solved numerically, using the pseudo transient method, that is well suited to solve highly non-linear problems. We are going to discuss a few key end-member results, such as melt migration along dykes and fractures, along self-localized channels or by magmatic diapirism. We will discuss how the coupling between thermo-mechanical processes and melt migration might affect the chemical evolution of percolating melts.

All the codes presented here are written within a modular Julia framework, developed within the MAGMA ERC project, that permits easy future integration of the currently stand-alone software.