Modelling of magma dynamics from the mantle to the surface
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Abstract
Commonly, melt migration in the Earth is modelled by a coupled system of Stokes and Darcy equations governing slowly creeping deformation of highly- viscous (geo)materials and flow in porous media, respectively.
In this work we derive and investigate a discontinuous Galerkin method for the stationary Stokes system using divergence-conforming approximation spaces. Testing it in geodynamically relevant benchmark setups we find that this yields a stable and robust method. However, for fixed computational expenses it was in most cases not superior to a second order (continuous) finite element method using discontinuous pressures (Q2P1) which is often used in geodynamic modelling softwares.
Then, we focus on the coupled system. We introduce the equations governing the system including constitutive equations for visco-elasto-plastic rheologies relevant on the lithospheric scale, and we derive a stable numerical method using continuous finite elements of Taylor-Hood type. We investigate the experimental order of convergence and show validity of the method and its implementation in benchmark setups relevant for lithosphere dynamics and melt migration.
Applying this method, firstly, we perform a broad parameter study systematically varying physical parameters such as, e.g., the rheology, the tectonic deformational regime, and the geothermal gradient, and examining the corresponding effects. As the study is the first of this type, we learn about interactions of the various parameters in a numerical experiment. Furthermore, we identify physical regimes of efficient melt transport.
Secondly, we focus on multiple subsequent melt pulses and multiple simultaneous pulses. For the latter we employ an unstructured triangular mesh that is adaptively refined in regions of increased porosity for every time step. Again, it is the first application of adaptive meshes in lithospheric scale melt migration modelling using visco-elasto-plastic rheologies.