High accuracy mantle convection simulation through modern numerical methods

Numerical simulation of the processes in the Earth mantle is a key piece in under-standing its dynamics, composition, history, and interaction with the lithosphere and the earth core. However, doing so presents many practical difficulties related to the numerical methods that can accurately represent these processes at relevant scales. This article presents an overview of the state of the art in algorithms for high-Rayleigh number flows such as those in the earth mantle, and discusses their implementation in the Open Source code Aspect (Advanced Solver for Problems in Earth’s ConvecTion). Specifically, we show how an interconnected set of methods for adaptive mesh refine-ment (AMR), higher order spatial and temporal discretizations, advection stabilization and efficient linear solvers can provide high accuracy at a numerical cost unachievable with traditional methods, and how these methods can be designed in a way so that they scale to large number of processors on compute clusters. Aspect relies on the numerical software packages deal.II and Trilinos, enabling us to focus on high level code and keeping our implementation compact. We present results from validation tests using widely used benchmarks for our code, as well as scaling results from parallel runs. Key words: Mantle convection, numerical methods, adaptive mesh refinement, finite element method, higher order discretizations, preconditioners 1