Fractional PDEs for Conservation Laws and Beyond: Theory, Numerics and Applications
Abstract
This proposal will develop a new rigorous theoretical and computational framework enabling end-to-end fractional modeling of physical problems governed by conservation laws in large-scale simulations, This will involve new results in theory of well-posedness of fractional PDEs (FPDEs), Petlov-Galerkin methods for variable-order tempered FPDEs, numerical solvers for FPDEs, data-driven construction of fractional operators, benchmark examples, new models for turbulence and multiphase systems, and open source code limited to 4000 characters The technical approach will address fundamental issues associated with the construction of fractional operators for conservation laws and related applications. An integrated framework will be developed that proceeds from the initial data-driven problem to ultimate engineering applications. This general methodology will allow the development of new factional physical models, test existing models, and assess numerical methods in terms of accuracy and efficiency, the latter being very important in this early stage of fractional order modeling The integrated frame work is based on a dynamic integration of five areas: (1) Mathematical analysis of FPDEs; (2) Numerical approximation of FPDEs; (3) Development of fast solvers; Fractional PDEs for Conservation Laws and Beyond: Theory, Numerics and Applications 4) Fractional order estimation and validation, from data; and (5) Prototype application problems.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 12, 2017
- Source ID
- W911NF1510562
Entities
People
- George Karniadakis
Organizations
- Army Contracting Command
- Brown University
- United States Army