Project dates: 01/01/2017 - Ongoing
This project aims to develop a unifying theoretical framework for generalised fractional models using measure theory and a new class of distributed-order nonlocal operators to simulate anomalous transport processes in heterogeneous and anisotropic porous medium.
The project expects to generate a sound mathematical foundation for fractional modelling and unprecedented clarity on the role of, and the relationship between, the many variants of fractional operators used in modern practice and how to impose boundary conditions on finite domains or irregular domains. Expected outcomes of the project include an evaluation of dimensionality and/or complexity reduction of the governing equations in fractional transport models with a focus on groundwater applications.
Funding / Grants
- ARC Discovery (DP180103858) (2018 - 2020)
Chief Investigators
Other Team Members
Publications
- Zhang, Hui, Liu, Fawang, Jiang, Xiaoyun, Zeng, Fanhai, Turner, Ian (2018) A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space distributed-order advection-diffusion equation. Computers and Mathematics with Applications, 76 (10), pp.2460-2476.
- J. Li, F. Liu*, L. Feng and I. Turner (2017) A novel finite volume method for the Riesz space distributed-order advection-diffusion equation. Applied Mathematical Modelling
- J. Li, F. Liu*, L. Feng and I. Turner (2017) A novel finite volume method for the Riesz space distributed-order diffusion equation. Computers and Mathematics with Applications
- X. Hu, F. Liu*, I. Turner and V. Anh (2016) An implicit numerical method of a new time distributed-order and two-sided space-fractional advection-dispersion equation. Numerical Algorithms
- H. Ye, F. Liu*, V.Anh and I. Turner (2015) Numerical analysis for the time distributed order and Riesz space fractional diffusions on bounded domains. IMA Journal of Applied Mathematics
- X. Wang, F. Liu*, X. Chen (2015) Novel second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations. Advances in Mathematical Physics
- H. Ye, F. Liu* and V. Anh (2015) Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains. J. Comp Physics
- X. Hu, F. Liu*, I. Turner, and V. Anh (2014) A numerical investigation of the time distributed-order diffusion model. ANZIAM J.
- Ye, H., Liu, Fawang, Turner, Ian, Anh, Vo, Burrage, Kevin (2013) Series expansion solutions for the -term time and space fractional partial differential equations in two- and three-dimensions. European Physical Journal: Special Topics, 222 (8), pp.1901-1914.
