### Calculations of the thermal structure of subduction zones using a Crank-Nicholson Semi-Lagrangian Multigrid advection-diffusion scheme

##### Richard Katz, Columbia University

Thermal structure is a primary control on magma genesis in subduction zones, where one of the Earth's tectonic plates collides with another and plunges deep into the mantle. The chemistry of fluids generated by mantle melting is a function of pressure and temperature–thus the spatial distribution of heat has important consequences for modeling the chemistry of lava erupted from subduction-related volcanoes. The thermal structure, in turn, depends strongly on the flow geometry of solid mantle through subduction zones. As a step towards models that compute consistent melting and temperature fields, we have generated advection-diffusion simulations for temperature distribution without melting.

The computations were performed using a Crank-Nicholson Semi-Lagrangian scheme on a two dimensional finite volume regular cartesian mesh. This is a semi-implicit scheme that solves for temperature along particle characteristics. It thus avoids the Courant condition that limits the timestep size of more conventional schemes, which treat advection terms with finite differencing. At each timestep we solve a set of linear equations for the temperature on the grid points using a v-cycle multigrid algorithm. We have tested the accuracy and efficiency of this advection-diffusion scheme and report the results here.

Abstract Author(s): Katz, Richard F. and Spiegelman, Marc