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.
