Journal
GEOPHYSICAL JOURNAL INTERNATIONAL
Volume 191, Issue 1, Pages 12-29Publisher
OXFORD UNIV PRESS
DOI: 10.1111/j.1365-246X.2012.05609.x
Keywords
Numerical solutions; Numerical approximations and analysis; Non-linear differential equations; Dynamics: convection currents; and mantle plumes
Categories
Funding
- Graduate School in Mathematics and Computing (FMB) at Uppsala University, Sweden
- Computational Infrastructure in Geodynamics initiative (CIG)
- National Science Foundation [EAR-0949446, OCI-0622780, TG-MCA04N026, DMS-0922866]
- University of California-Davis
- King Abdullah University of Science and Technology (KAUST) [KUS-C1-016-04]
- Alfred P. Sloan Research Fellowship
- SNIC through Uppsala Multidisciplinary Center for Advanced Computational Science (UPPMAX) [p2010002]
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Numerical simulation of the processes in the Earths mantle is a key piece in understanding its dynamics, composition, history and interaction with the lithosphere and the Earths core. However, doing so presents many practical difficulties related to the numerical methods that can accurately represent these processes at relevant scales. This paper presents an overview of the state of the art in algorithms for high-Rayleigh number flows such as those in the Earths mantle, and discusses their implementation in the Open Source code Aspect (Advanced Solver for Problems in Earths ConvecTion). Specifically, we show how an interconnected set of methods for adaptive mesh refinement (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 numbers 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.
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