RIA: Long-Term Solution of the Transport Equation for Complex Flows

该项目将研究和改进输运方程数值解的准确性和成本之间的权衡，当(a)驱动流是非定常和强烈不均匀的，(b)模拟周期比必须解决的最小时间尺度长得多（由于“物理”）。研究的重点是粒子方法和欧拉-拉格朗日方法。研究的一部分将涉及数值精度，强调(a)对粒子跟踪替代算法的精度特性的理解，作为流动复杂性的函数，以及(b)这些特性对pm和elm输运方程全局精度的影响。研究的另一部分将关注数值效率：调查选定的pm和elm在替代类型的计算机体系结构上的实现：串行和并行（具有共享和分布式内存）。不同对的数值方法和计算机体系结构将根据(a)固定精度的“成本”（CPU和用户时间）和(b)固定“成本”的精度进行比较。研究将融合(a)数值方法的理论分析，(b)算法开发（重点是并行算法）和(c)数值实验。河口和海岸潮汐输运的长期模拟提供了直接的动力，但结果也应有利于其他科学和工程领域。

This project will investigate and improve the trade-off between accuracy and cost of the numerical solution of the transport equation, when (a) the driving flow is unsteady and strongly non- uniform, and (b) the period of simulation is much longer than the smallest time scales that must be resolved (due to "physics"). The research focus is on particle methods (PMs) and on Eulerian- Lagrangian methods (ELMs). One part of the research will concern numerical accuracy, emphasizing (a) the understanding of the accuracy properties of alternative algorithms for particle tracking, as a function of the flow complexity, and (b) the influence of these properties on the global accuracy of the transport equation by PMs and ELMs. The other part of the research will concern numerical efficiency: investigation of implementations of selected PMs and ELMs on alternative types of computer architectures: serial and parallel (with shared and distributed memory). The different pairs of numerical methods and computer architectures will be compared with regard to (a) "cost" (CPU and user time) for fixed accuracy, and (b) accuracy for fixed "cost." Research will blend (a) theoretical analysis of numerical methods, (b) algorithm development (with emphasis on parallel algorithms), and (c) numerical experimentation. Direct motivation is provided by long-term simulations of tidal transport in estuaries and coasts, but results should also benefit other scientific and engineering fields.