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Abstract.Numerical simulations of the geodynamo have successfully represented many observable characteristics of the geomagnetic field, yielding insight into the fundamental processes that generate magnetic fields in the Earth's core. Because of limited spatial resolution, however, the diffusivities in numerical dynamo models are much larger than those in the Earth's core, and consequently, questions remain about how realistic these models are. The typical strategy used to address this issue has been to continue to increase the resolution of these quasi-laminar models with increasing computational resources, thus pushing them toward more realistic parameter regimes. We assess which methods are most promising for the next generation of supercomputers, which will offer access to O(10 6 ) processor cores for large problems. Here we report performance and accuracy benchmarks from 15 dynamo codes that employ a range of numerical and parallelization methods. Computational performance is assessed on the basis of weak and strong scaling behavior up to 16,384 processor cores. Extrapolations of our weak scaling results indicate that dynamo codes that employ two-or three-dimensional domain decompositions can perform efficiently on up to ∼ 10 6 processor cores, paving the way for more realistic simulations in the next model generation.

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Convection in planetary cores can generate fluid flow and magnetic fields, and a number of sophisticated codes exist to simulate the dynamical behaviour of such systems. We report on the first community activity to compare numerical results of computer codes designed to calculate fluid flow within a whole sphere. The flows are incompressible and rapidly rotating and the forcing of the flow is either due to thermal convection or due to moving boundaries. All problems defined have solutions that allow easy comparison, since they are either steady, slowly drifting or perfectly periodic. The first two benchmarks are defined based on uniform internal heating within the sphere under the Boussinesq approximation with boundary conditions that are uniform in temperature and stress-free for the flow. Benchmark 1 is purely hydrodynamic, and has a drifting solution. Benchmark 2 is a magnetohydrodynamic benchmark that can generate oscillatory, purely periodic, flows and magnetic fields. In contrast Benchmark 3 is a hydrodynamic rotating bubble benchmark using no slip boundary conditions that has a stationary solution. Results from a variety of types of code are reported, including codes that are fully spectral (based on spherical harmonic expansions in angular coordinates and polynomial expansions in radius), mixed spectral and finite difference, finite volume, finite element and also a mixed Fourier-finite element code. There is good agreement between codes. It is found that in Benchmarks 1 and 2, the approximation of a whole sphere problem by a domain that is a spherical shell (a sphere possessing an inner core) does not represent an adequate approximation to the system, since the results differ from whole-sphere results.