Computing the Universe a Numerical Model of Circulation in Deep Planetary Atmospheres Development of a Parallel Version of the Tough2 Software Package the Parallel Implementation

Cosmology stands at a critical juncture. Over ve years, microwave background experiments will map in exquisite detail the properties of density uctuations three hundred thousand years after the big bang. Large-scale structure surveys will characterize both the properties of galaxies and their large scale distribution. In many ways, the outstanding problem in cosmology is understanding how the tiny variations in the early universe grew to form galaxies, clusters of galaxies and the large-scale structure. The process of the formation of galaxies and large-scale structure is inherently non-linear, involving the rich coupling between non-linear gravitational dynamics, hydrodynamics, star formation feedback and radiative transfer. Moreover, there is a very wide range of relevant length and time scales. Therefore, cosmological numerical simulations are extremely challenging, requiring large, spatially adaptive grids and spatially adaptive time-stepping techniques. We have developed various numerical techniques including Eulerian TVD and PPM hydrocodes, Lagrangian SPH hydrocodes, Moving Mesh hydrocode, smoothed Lagrangian hydrocode, Multi-level AMR data structures for the Eulerian hydrocodes, PM, P3M, Tree and Tree-PM N-body codes, and out-of-core techniques (including very large out-of-core FFT method). Experiences learned and challenges present associated with the implementation of these real application codes on various large computing platforms including SGI Origin, IBM SP2, Cray T3E as well as PC clusters will be presented. The deep atmospheres of the planets such as Jupiter and Saturn and rotating stars such as our Sun are strongly innuenced by buoyancy and Coriolis forces. In addition the giant planets also feel the eeects of diierential heating (North-South temperature gradients). The latitudinal variation of Coriolis forces is crucial to understanding large-scale motions (scales comparable to the curvature of the body) that are manifested in diverse phenomena such as the diierential rotation of the Sun, and the cloud bands on Jupiter. We describe a numerical model based on the spectral element method that we have developed to study these competing forces. This paper describes the model, its parallel implementation and its performance results and presents simulation results for a range of heating and rotation rates. The present simulations also make contact with a space-laboratory experiment. In the terrestrial laboratory gravity is aligned with the rotation vector unlike the geophysical case where these vectors move from being (anti-)parallel at the poles to orthogonal at the equator. In the Geophysical Fluid Flow Cell (GFFC) experiment which has been run twice in a microgravity environment (in 1985 and in 1995, aboard the …