@article{Mao2026, 
author = {Zhi Mao and Huafang Li and Xiaobing Bao and Leilei Wei and Libin Liu and Libo Feng},
title = {An efficient adaptive moving grid algorithm for time-fractional integrodifferential equations governing viscoelastic nanofluid dynamics},
year = {2026},
journal = {Networks and Heterogeneous Media},
volume = {21},
number = {2},
pages = {402-425},
keywords = {adaptive moving grid, fractional integrodifferential equations, viscoelastic nanofluid, fractional Maxwell model, generalized Cattaneo heat conduction relation},
url = {https://www.sciopen.com/article/10.3934/nhm.2026019},
doi = {10.3934/nhm.2026019},
abstract = {An adaptive moving grid method is developed to solve the time-fractional integrodifferential governing equations of viscoelastic nanofluid. The momentum equation is derived based on a dual-parameter fractional Maxwell constitutive relation, and the energy equation employs a generalized Cattaneo heat conduction relation. To improve solution accuracy, a monitor function based on the equidistribution principle is constructed, and an adaptive mesh redistribution strategy is developed in the spatial domain. The temporal fractional-order operators are approximated by the L1 algorithm and the weighted-shifted Grünwald difference method. Numerical experiments demonstrate that the adaptive grid achieves 77.6–88.4% higher accuracy compared to uniform grids at the same grid scale, along with enhanced stability in convergence. Parametric analysis indicates that increasing the fractional-order derivative in the energy equation results in a thickening of both the velocity and thermal boundary layers. Furthermore, the dual-fractional Maxwell model exhibits a thicker velocity boundary layer than its classical single-parameter counterpart. The proposed method offers an efficient and robust approach for simulating complex viscoelastic nanofluid systems with memory effects and multi-field coupling.}
}