Nonlocal and Fractional Order Methods for Near-wall Turbulence, Large-eddy Simulation, and Fluid-structure Interaction
Abstract
Fractional-order operators such as the space-fractional advection-diffusion equation, or special cases of it like the space-fractional Laplacian, have seen considerable treatment in the mathematical literature as specialized techniques for handling microstructural heterogeneity whereby the underlying processes deviate from exponential distribution statistics. As an example, a heavy tailed distribution of tracer particle mean squared distances can lead to interesting processes such as Lvy flights. Time-fractional models have also received considerable attention and have found usefulness in modeling history-dependent materials and processes, e.g. viscoelasticity. If we correctly interpret the fractional derivative operation as a nonlocal operator, we can elucidate connections with weakly nonlocal higher-order gradient-based methods, strong (i.e. integral) nonlocal diffusion, and peridynamic mechanics. While fractional order methods have a niche audience in the literature, and they provide the tools to incorporate more general physics, they have yet to find widespread adoption in engineering analysis. The reason for this may partly be due to the specialized mathematics behind them, but more practical issues arise that are associated with the solution offractional order equations. Presented in this report is a collection of mathematical formulations, engineering applications, and a description of numerical solutions to nonlocal equations involved in fluid and heat transport.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 04, 2019
- Accession Number
- AD1091247
Entities
People
- John T. Foster
Organizations
- University of Texas at Austin