Parallel Numerical Simulation of Rayleigh-Be'nard Convection

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This is interdisciplinary research in which applied mathematics and parallel numerical simulations will be used to investigate pattern formation, transition to turbulence, and transport for Rayleigh-Bernard convection. The limit of small reduced Raleigh numbers and large aspect ratio will be emphasized since this regime is amenable to analysis by singular perturbation methods and has been extensively studied with high-precision laboratory experiments. Model equations as well as the Boussinesq equations in two- and three-dimensional domains will be studied for normal and binary fluids. A novel and central part of the work will be the development of the convection codes on a 64-node shared-memory MIMD Butterfly- Plus parallel computer (which is to be upgraded in a year to 128- nodes of more powerful processors). Issues of parallel large- scale scientific computing in a shared-memory context-especially algorithmic efficiency, memory contention, and load balancing- will be examined for spectral-element multigrid methods, which solve nonlinear partial differential equations with high efficiency and accuracy on general domains using locally refinable meshes. Advances in numerical analysis, parallel computations, model building, and the physics of driven dissipative systems are expected.