Data-Driven Computation of Lagrangian Transport Structure in Realistic Flows

Virginia Polytechnic Institute And State University, Blacksburg VA

Investigators

Abstract

Forecasting the spread of contaminants in the ocean, floodwaters, or atmosphere in a timely manner is of critical importance. Accurate prediction of the contaminant location at a later time requires a realistic model of the underlying fluid flow, as well as knowledge of where the contaminant was initially located. Furthermore, to aid decision-makers, the fluid simulations must proceed sufficiently rapidly. The movement of the ocean and atmosphere, like that of other fluids, creates certain patterns whose shape is influenced by special regions, known collectively as the Lagrangian transport structure, or LTS (named after the mathematician and fluid mechanist Joseph-Louis Lagrange). LTS is a template that organizes how the fluid moves: some structures are surfaces that attract nearby fluid, some repel nearby fluid, and some form meandering jet pathways or vortex-like structures. Focusing on the LTS helps alleviate the dependence of contaminant forecast on its initial location, as contaminants tend to follow these key organizing features. Furthermore, incorporating these structures into a faster, approximate model, the fluid simulation itself can be sped up. However, despite its potential usefulness -- to predict the spread of hazardous material, debris, or missing individuals in a search-and-rescue scenario -- LTS is not currently used because of the high computational cost. This project aims to develop a new framework to make possible real-time, robust LTS computation on mobile platforms, to inform real-time decision-making (for instance, directly onboard the manned or autonomous vehicles doing reconnaissance and sensing). Such effective, timely computations for realistic aquatic and atmospheric environments can provide information to prevent the loss of lives, mitigate environmental damage, and avoid enormous financial cost. This project studies a novel Lagrangian data-driven reduced-order modeling and spatial filtering framework for fluid transport simulation. This new framework in intended to decrease the computational cost of current algorithms by orders of magnitude and yield LTS approximations that are accurate and robust with respect to the numerical inaccuracies that are inherent in realistic flows. Progress will be made by developing several intertwined approaches in computational fluid mechanics and nonlinear dynamics -- the mathematical theory underlying chaos theory. The main novelty of the project is bridging Eulerian algorithms (used in the velocity field computation) and Lagrangian algorithms (used in the LTS computation). This makes possible the development of novel Lagrangian data-driven reduced-order models (ROMs) and spatial filters. The new Lagrangian data-driven ROM is based on a novel Lagrangian inner product that makes possible the accurate and efficient approximation of average LTS. In contrast, standard Eulerian ROMs produce inaccurate LTS results. A novel Lagrangian data-driven spatial filter for LTS computation on coarse realistic meshes is also studied. This new filter is stable, accurate, efficient, and robust with respect to the numerical inaccuracies that are inherent in realistic flows. While the work will focus on environmental flows, the results are expected to apply to a wide variety of fluid applications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.