Dynamic simulations of convection in the Earth’s mantle

Abstract

In this chapter, we model dynamic convection processes in the Earth’s mantle; linking the geody- namical equations, numerical implementation and Python code tightly together. The convection of material is generated by heating from below with a compositionally distinct and denser layer at the bottom. The time-dependent nonlinear partial differential equations to be solved are the quasi-static Stokes equations with depth- and temperature-dependent viscosity, and advection-diffusion equations for the composition and temperature. We present a numerical algorithm for the simulation of these equations as well as an implementation of this algorithm using the DOLFIN Python interface. The results show that the compositional heterogeneities persist, but interact strongly with the convecting system, generating upwellings and movement as material from the surface displaces them. This chapter will be of interest to those seeking to model compositional discontinuities using field methods, as well as those interested in mantle convection simulations.