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Research Spending & Results

Award Detail

Awardee:WILLIAM MARSH RICE UNIVERSITY
Doing Business As Name:William Marsh Rice University
PD/PI:
  • Beatrice Riviere
  • (713) 348-4094
  • Beatrice.Riviere@rice.edu
Award Date:06/17/2021
Estimated Total Award Amount: $ 291,309
Funds Obligated to Date: $ 291,309
  • FY 2021=$291,309
Start Date:09/01/2021
End Date:08/31/2024
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: Multidimensional Couplings for Flow and Transport in Porous Media
Federal Award ID Number:2111459
DUNS ID:050299031
Parent DUNS ID:050299031
Program:COMPUTATIONAL MATHEMATICS
Program Officer:
  • Yuliya Gorb
  • (703) 292-2113
  • ygorb@nsf.gov

Awardee Location

Street:6100 MAIN ST
City:Houston
State:TX
ZIP:77005-1827
County:Houston
Country:US
Awardee Cong. District:02

Primary Place of Performance

Organization Name:William Marsh Rice University
Street:6100 Main Street
City:Houston
State:TX
ZIP:77005-1827
County:Houston
Country:US
Cong. District:02

Abstract at Time of Award

The project focuses on the study of physical phenomena coupling different spatial scales. The mathematical and numerical analysis of these coupled problems is challenging because of the lack of smoothness in the solution. Applications of these coupled problems are many; for instance the mathematical modeling of blood flow in organs is important in understanding the mechanisms of organ perfusion, embolization and drug delivery. The project will train graduate students and undergraduate students in computational and applied mathematics. Research outcomes will be published in research journals, online and presented at scientific meetings. The overall goal of the project is the formulation, analysis and application of discontinuous Galerkin methods for the solution of coupled one-dimensional and three-dimensional flow and transport processes in porous media. The numerical analysis is challenging because weak solutions exhibit a singularity on the line source. The research team will develop and analyze numerical methods for model problems with singular data. The methods will combine novel efficient time-stepping algorithms with discontinuous finite element methods. The investigators will apply the algorithms to multidimensional couplings in organ and vasculature. The development and validation of physics-based computational models will be guided by imaging of flow and transport. Neural network based image image segmentation extracts the geometry of the organ and blood vessels. Students will be involved in the research and they will be trained in numerical analysis and scientific computing. Outreach activities will engage high school students with recent developments in computational mathematics. 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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