Spectral Element Modeling of the Navier-Stokes Equations in a Rapidly Rotating Reference Frame

Great progress has been made over the past years in modeling the geodynamo numerically. However, the large range of time and length scales in the geodynamo far exceeds the resolving power of spectral models even on the most powerful supercomputers currently available. As a result dynamo simulations are undertaken with parameters far from their geophysical value. Powerful and cost efficient clusters of PCs promise significant advance in our ability to resolve the geodynamo. Here we address the problem by introducing a spectral element approach for the momentum balance of the core, and a domain decomposition method well adapted for such distributed memory architectures. We have performed a number of benchmarks to verify it. For the kinematic problem of axisymmetric flow induced by a slight super rotation of the inner core, we find agreement with previously published linear results to within better than 0.1 percent for Ekman numbers as low as 10^-5. We discuss the nonlinear extension of this problem and illustrate the potential of our method. These preliminary results indicate that spectral elements provide an accurate and efficient approach to model the geodynamo on modern parallel computers.