报告题目

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

报告时间

2020年8月9日14:30-16:00

地点

腾讯会议ID：501 321 216

报告摘要

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.

报告人

简介

封利波，博士毕业于澳大利亚昆士兰科技大学，师从刘发旺教授、Ian Turner教授，现在昆士兰科技大学数学科学学院从事博后工作。曾获昆士兰科技大学High Achiever HDR Student奖，2019年度国家优秀自费留学生奖学金，参与国家自然科学基金青年项目一项，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》等国际杂志，累计发表文章20篇，其中高被引文章3篇。主要研究领域：分数阶偏微分方程的数值方法和分析。