Abstract
This chapter investigates the most advanced numerical algorithm, the finite volume method with an efficient multigrid scheme, and discusses the design and implementation of a general and efficient parallel version of state-of-the-art software in various computer environments. The finite volume method with an efficient and fast multigrid scheme to solve for three-dimensional, time-dependent, incompressible thermal convection flows on parallel systems has been successfully implemented. The parallel software is numerically robust, computationally efficient, and portable to any architecture, which support message-passing interface (MPI) for communications. It also has a very flexible partition structure, which can be used for any rectangular geometry by applying a 1D, 2D, or 3D partition to achieve load balance. In spite of the difficulties associated with the large Rayleigh number simulation, the results clearly demonstrate the great potential for applying this approach to solve high resolution, large Rayleigh number flow in realistic, 3D geometries using parallel systems. Thermal convective motions driven by temperature gradients often play an essential role in the behavior of geophysical and astrophysical systems, and obtaining a detailed understanding of their role is often at the core of many important problems in the Planetary sciences. Applications include the dynamics of atmospheres, stellar convection, and convection in gaseous protostellar disks.
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