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Research Spending & Results

Award Detail

Doing Business As Name:William Marsh Rice University
  • Jesse L Chan
  • (713) 348-6113
Award Date:01/16/2020
Estimated Total Award Amount: $ 449,907
Funds Obligated to Date: $ 271,331
  • FY 2020=$271,331
Start Date:09/01/2020
End Date:08/31/2025
Transaction Type:Grant
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:CAREER: Tailored Entropy Stable Discretizations of Nonlinear Conservation Laws
Federal Award ID Number:1943186
DUNS ID:050299031
Parent DUNS ID:050299031
Program Officer:
  • Yuliya Gorb
  • (703) 292-2113

Awardee Location

Street:6100 MAIN ST
Awardee Cong. District:02

Primary Place of Performance

Organization Name:William Marsh Rice University
Street:6100 Main Street
Cong. District:02

Abstract at Time of Award

The simulation of fluid flow is foundational to many scientific fields, ranging from environmental and aerospace engineering to solar physics. However, next-generation modeling and analysis is computationally challenging using existing tools. Tailored numerical methods have the potential to address such limitations. For example, projection-based reduced order models decrease computational costs associated with many-query scenarios (such as engineering design or uncertainty quantification) by replacing a high fidelity model with a less expensive low-dimensional surrogate. Similarly, high order accurate schemes are particularly effective at resolving fine-scale features in transient vorticular flows. Unfortunately, when applied to the equations of fluid dynamics, these numerical methods experience non-physical instabilities which can cause simulations to fail unexpectedly. The goal of this project is to enable robust and efficient simulations using discretely "entropy stable" schemes. By building fundamental energetic principles directly into a discretization, entropy stable methods retain accuracy while inheriting verifiable properties which improve "out-of-the-box" robustness. Discretely entropy stable high order discretizations for nonlinear conservation laws have seen rapid development over the last 7 years. This project will extend this methodology to three areas where existing approaches are suboptimal or unavailable: (1) high order methods on non-conforming meshes, (2) high order physical-frame discretizations for domain boundaries with fine-scale features, and (3) reduced order modeling. Additionally, the PI will integrate aspects of the proposed research with an educational program aimed at promoting computational science and improving retention among college students and K-12 teachers. Specifically, the PI will (1) design and supervise senior capstone research projects for engineering undergraduates, and (2) organize a summer research program for K-12 teachers centered around numerical modeling and discovery-based learning. The summer research program will also provide graduate students with mentoring experience, and the PI will follow up by partnering with teachers to incorporate concepts from numerical computing into reusable classroom modules. 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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