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3D Numerical Modelling of Compressible Coupled Magma/Mantle Dynamics With Adaptive Mesh Refinement

Presented by: 
Timo Heister
Juliane Dannberg
Friday 10th June 2016 - 09:00 to 11:00
INI Seminar Room 1
Juliane Dannberg (dannberg[at]math.tamu[dot]edu), Ryan Grove, Timo Heister (heister[at]clemson[dot]edu)

Melt generation and migration are important processes for the evolution of the Earth's interior and impact the global convection of the mantle.
While they have been the subject of numerous investigations, the typical time and length-scales of melt transport are vastly different from global mantle convection, which determines where melt is generated. This makes it difficult to study mantle convection and melt migration in a unified framework. In addition, modelling magma dynamics poses the challenge of highly non-linear and spatially variable material properties, in particular the viscosity.

Here, we present our extension of the community mantle convection code ASPECT, which adds the equations of two-phase flow of melt and solid, as an example for how these challenges can be addressed. First, We will analyse well-posedness, existence, and uniqueness of the problem. Then we will discuss the correct way to do a stable higher order finite element discretization. Finally, the resulting linear system is solved with an iterated solver preconditioned by a Schur complement-based block preconditioner. We demonstrate that applying adaptive mesh refinement to this type of problem is particularly advantageous, as the resolution can be increased in mesh cells where melt is present and viscosity gradients are high, whereas a lower resolution is sufficient in regions without melt. Together with a high-performance, massively parallel implementation, this allows for high resolution, 3d, compressible, global mantle convection simulations coupled with melt migration.

We present benchmarks of our solver to confirm the theoretical results, and apply our software to large-scale 3d simulations of melting and melt transport in mantle plumes interacting with the lithosphere to show robustness and parallel scalability of the linear solver. Our model incorporates the individual compressibilities of the solid and the fluid phase in addition to compaction, and we demonstrate that including these effects can change melt volumes by more than 20%. Moreover, we show how including melting, melt migration and freezing of melt in global convection models can influence convection patterns and the distribution of chemical heterogeneities in the mantle.

Our model of magma dynamics provides a framework for modelling processes on different scales and investigating links between processes occurring in the deep mantle and melt generation and migration.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons