Parallel Numerical Simulation of Rayleigh-Be'nard Convection

这是一项跨学科的研究， 并行数值模拟将用于调查 模式的形成，过渡到湍流，和运输 瑞利-伯纳德对流 小约化罗利的极限 数字和大的纵横比将被强调， 政权是服从奇异摄动法分析 并在高精度实验室进行了广泛的研究 实验 模型方程以及Boussinesq方程 在二维和三维域将研究正常的 和二元流体。 这项工作的一个新颖和核心部分将是发展 64节点共享内存MIMD蝴蝶上的对流代码， 加上并行计算机（将在一年内升级到128- 更强大的处理器节点）。 大规模并行问题- 在共享内存环境中扩展科学计算， 算法效率、内存争用和负载平衡- 将检查谱元素多重网格方法， 求解非线性偏微分方程 在一般域上使用局部 可细化网格。 并行数值分析进展 计算，模型构建，以及驱动的物理学 期望耗散系统。

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.