Fractional PDEs for Conservation Laws and Beyond: Theory, Numerics and Applications
Abstract
This MURI project is the vision of a team of researchers from Brown University, Michigan State University, Columbia University, University of South Carolina, and Rice University with overlapped interests and complementary expertise on theory, numerical methods, and applications of fractional PDEs (FPDEs). Our overarching goal is the development of a seamless integration of theory and algorithms for data-driven FPDEs,while targeting the common themes of conservation, monotonicity, adaptive refinement, and high-order accuracy in the context of simulations of multiphase flows, turbulence, fluid-structure interactions, hydrology, and solid mechanics. We envision a combined mathematical and computational framework, where the fractional operators can be constructed based on available data, hence providing model validation for the specific phenomenon but also a tailor-based simulation capability that can be scaled to real-life applications
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 31, 2022
- Accession Number
- AD1228772
Entities
People
- George Kamiadakis
Organizations
- Brown University