Toward Computational Models of Magma Genesis and Geochemical Transport in Subduction Zones
Richard Katz, Columbia University
The chemistry of material erupted from subduction-related volcanoes records important information about the processes that lead to its formation at depth in the Earth. Self-consistent numerical simulations provide a useful tool for interpreting this data as they can explore the non-linear feedbacks between processes that control the generation and transport of magma.
To handle variable-viscosity solid-flow in the wedge, we are adapting a Patankar-based FAS multigrid scheme developed by Albers (2000, J. Comp. Phys.). The pressure field in this scheme is the solution to an elliptic equation on a staggered grid. Thus, we expect computed pressure gradient fields to be smooth and suitable for porous flow calculations. For computing thermal structure we present a novel scheme that is a hybrid of Crank-Nicholson (CN) and Semi-Lagrangian (SL) methods. We have tested the SLCN scheme on advection across a broad range of Peclet numbers and show the results. This scheme is also useful for low-diffusivity chemical transport.
We also describe our parameterization of hydrous mantle melting [Katz et al., G3, 2003, accepted]. This parameterization is designed to capture the melting behavior of peridotite-water systems over parameter ranges relevant to subduction. The parameterization incorporates data and intuition gained from laboratory experiments and thermodynamic calculations, yet it remains flexible and computationally efficient.
Given accurate solid-flow fields, a parameterization of hydrous melting and a method for calculating thermal structure (enforcing energy conservation), the final step is to integrate these components into a consistent framework for reactive-flow and chemical transport in deformable porous media. We present preliminary results for reactive flow in and 2-D static and upwelling columns and discuss possible mechanical and chemical consequences of open system reactive melting with application to arcs.
Abstract Author(s): Richard F. Katz and Marc Spiegelman