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Research Spending & Results

Award Detail

Awardee:UNIVERSITY OF DELAWARE
Doing Business As Name:University of Delaware
PD/PI:
  • Yangwen Zhang
  • (573) 202-8068
  • ywzhangf@udel.edu
Award Date:06/08/2021
Estimated Total Award Amount: $ 86,476
Funds Obligated to Date: $ 28,157
  • FY 2021=$28,157
Start Date:07/01/2021
End Date:06/30/2024
Transaction Type:Grant
Agency:NSF
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:Collaborative Research: Computational Methods for Optimal Transport via Fluid Flows
Federal Award ID Number:2111315
DUNS ID:059007500
Parent DUNS ID:059007500
Program:COMPUTATIONAL MATHEMATICS
Program Officer:
  • Malgorzata Peszynska
  • (703) 292-2811
  • mpeszyns@nsf.gov

Awardee Location

Street:210 Hullihen Hall
City:Newark
State:DE
ZIP:19716-0099
County:Newark
Country:US
Awardee Cong. District:00

Primary Place of Performance

Organization Name:University of Delaware
Street:210 Hullihen Hall
City:Newark
State:DE
ZIP:19716-2553
County:Newark
Country:US
Cong. District:00

Abstract at Time of Award

Transport and mixing in fluids is a topic of fundamental interest in engineering and natural sciences, with broad applications ranging from industrial and chemical mixing on small and large scales, to preventing the spreading of pollutants in geophysical flows. This project focuses on computational methods for control of optimal transport and mixing of some quantity of interest in fluid flows. The question of what fluid flow maximizes mixing rate, slows it down, or even steers a quantity of interest toward a desired target distribution draws great attention from a broad range of scientists and engineers in the area of complex dynamical systems. The goal of this project is to place these problems within a flexible computational framework, and to develop a solution strategy based on optimal control tools, data compression strategies, and methods to reduce the complexity of the mathematical models. This project will also help the training and development of graduate students across different disciplines to conduct collaborative research in optimal transport and mixing, flow control, and computational methods for solving these problems. The project is concerned with the development and analysis of numerical methods for optimal control for mixing in fluid flows. More precisely, the transport equation is used to describe the non-dissipative scalar field advected by the incompressible Stokes and Navier-Stokes flows. The research aims at achieving optimal mixing via an active control of the flow velocity and constructing efficient numerical schemes for solving this problem. Various control designs will be investigated to steer the fluid flows. Sparsity of the optimal boundary control will be promoted via a non-smooth penalty term in the objective functional. This essentially leads to a highly challenging nonlinear non-smooth control problem for a coupled parabolic and hyperbolic system, or a semi-dissipative system. The project will establish a novel and rigorous mathematical framework and also new accurate and efficient computational techniques for these difficult optimal control problems. Compatible discretization methods for coupled flow and transport will be employed to discretize the controlled system and implement the optimal control designs numerically. Numerical schemes for the highly complicated optimality system will be constructed and analyzed in a systematic fashion. New incremental data compression techniques will be utilized to avoid storing extremely large solution data sets in the iterative solvers, and new model order reduction techniques specifically designed for the optimal mixing problem will be developed to increase efficiency. The synthesis of optimal control and numerical approximation will enable the study of similar phenomena arising in many other complex and real-world flow dynamics. 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.

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