Mathematical Sciences: Parallel Algorithms for Surface Water Flows and Transport

研究者和她的同事们研究了可扩展的并行算法来解决流体动力学流动和输运方程。数学模型是基于波高的广义波动连续性方程，速度的非保守形式的动量方程和输运的平流扩散方程。数值求解技术是基于混合有限元法和伽辽金有限元法。对于平流过程，他们研究了特征方法和高阶Godunov方法。这些算法在并行平台上实现，包括工作站集群和大规模并行系统。领域分解技术用于实现并行性。一旦这些代码被开发和验证，它们将被应用于海湾和河口的建模以及墨西哥湾沿岸风暴潮的建模。本研究的目的是制定、分析和实现准确、高效的模拟地表水环境流动和运输的并行算法。这项研究的推动力是需要州和联邦机构以及私营企业了解潮汐对沿海地区和近海结构的影响，并研究工业和市政发展对海湾和河口的影响。更具体地说，这项工作在几个领域都有应用，包括1)计算由飓风等极端风暴事件引起的潮差和潮涌，以便规划沿海地区的发展并预测洪水的潜在危害；2)为那些有兴趣为商业目的捕获潮汐能的人建立潮汐波动模型；3)海上构筑物受力估算；4)预测沿海航道疏浚或防波堤建设的影响；5)研究污染对海湾和河口的影响，包括可能的修复策略；6)为市政当局分配允许排放量，以达到特定的水质目标。在此资助下开发的算法通过有效地使用大规模并行计算机来提高分辨率并减少模拟的计算时间，从而改进了现有算法。要开发的代码可以作为新一代软件的范例，这些软件利用了高性能计算向大规模并行架构发展的趋势。

Wheeler The investigator and her colleagues study scalable parallel algorithms for the solution of the hydrodynamic flow and transport equations. The mathematical model is based on the generalized wave-continuity equation for wave height, the non-conservative form of the momentum equations for velocity, and the advection-diffusion equation for transport. The numerical solution techniques are based on mixed and Galerkin finite element methods. For advection processes they study both characteristic and higher-order Godunov methods. These algorithms are implemented on parallel platforms, including clusters of workstations and massively parallel systems. Domain decomposition techniques are used to achieve parallelism. Once the codes are developed and validated, they are applied to bay and estuarine modeling and modeling of storm surges along the Gulf of Mexico. The objective of this research is to formulate, analyze and implement accurate and efficient parallel algorithms for modeling flow and transport in surface water environments. The impetus for this research is the need for state and federal agencies and private industry to understand the effects of tides on coastal regions and offshore structures, and to study the effects of industrial and municipal development on bays and estuaries. More specifically, this work has applications in several areas, including 1) calculating tidal ranges and surges caused by extreme storm events such as hurricanes in order to plan development in coastal areas and predict potential hazards from flooding; 2) modeling tidal fluctuations for those interested in capturing tidal energy for commercial purposes; 3) estimating forces on offshore structures; 4) predicting influence of dredging of intercoastal waterways or constructing breakwaters; 5) studying effects of pollution on bays and estuaries, including possible remediation strategies; and 6) allocating allowable discharges for municipalities in order to meet spec ific water quality objectives. The algorithms developed under this grant improve upon existing algorithms by effectively using massively parallel computers to increase resolution and reduce the computational time for a simulation. The code to be developed serves as paradigm for a new generation of software that takes advantage of the trend in high-performance computing toward massively parallel architectures.