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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 08, 2022
Accession Number
AD1203039

Entities

People

  • George Karniadakis

Organizations

  • Brown University

Tags

Communities of Interest

  • Autonomy
  • Energy and Power Technologies
  • Human Systems

DTIC Thesaurus Topics

  • Bayesian Networks
  • Boundary Layer
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Fluid Dynamics
  • Fluid Flow
  • Formulas (Mathematics)
  • Information Science
  • Materials Science
  • Mathematical Analysis
  • Mathematical Models
  • Mechanical Properties
  • Mechanics
  • Monte Carlo Method
  • Neural Networks
  • Numerical Analysis
  • Numerical Methods And Procedures
  • Physics Laboratories
  • Supervised Machine Learning
  • Turbulent Mixing

Readers

  • Computational Fluid Dynamics (CFD)
  • Mathematical Modeling and Probability Theory.
  • Research Science/Academic Research