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報告題目

An investigation of nonlinear time-fractional anomalous diffusion models for simulating transport processes in heterogeneous binary media

報告時間

2020年8月9日14:30-16:00

地點

騰訊會議ID：501 321 216

報告摘要

In this work, we consider two of the most frequently used two-dimensional nonlinear time-fractional anomalous sub-diffusion models for simulating transport phenomena in heterogeneous binary media—a variable-order model and a generalised transport equation based on the Riemann-Liouville fractional operator. Our computational modelling framework uses a second order modified weighted shifted Grünwald-Letnikov scheme with correction terms to approximate the time-fractional derivative and nonlinear source term, together with an unstructured mesh control volume method for the spatial discretisation that accommodates the heterogeneous model properties. The resulting nonlinear system of algebraic equations is then stepped in time using an efficient Jacobian-free, Newton-Krylov solver to determine the set of discrete solution unknowns. We derive a semi-analytical solution and mass balance equation for a class of two-layered problems to evaluate the accuracy of the different computational models. Finally, a series of numerical examples are presented to verify the theoretical analysis and to highlight the capability of the generalised transport model.

報告人

簡介

封利波，博士畢業于澳大利亞昆士蘭科技大學，師從劉發旺教授、Ian Turner教授，現在昆士蘭科技大學數學科學學院從事博后工作。曾獲昆士蘭科技大學High Achiever HDR Student獎，2019年度國家優秀自費留學生獎學金，參與國家自然科學基金青年項目一項，在《Communications in Nonlinear Science and Numerical Simulation》，《International Journal of Heat and Mass Transfer》，《Numerical Algorithms》，《Computers and Mathematics with Applications》，《Applied Mathematics and Computation》等國際雜志，累計發表文章20篇，其中高被引文章3篇。主要研究領域：分數階偏微分方程的數值方法和分析。