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Licensed Unlicensed Requires Authentication Published by De Gruyter October 29, 2018

Novel numerical analysis of multi-term time fractional viscoelastic non-newtonian fluid models for simulating unsteady MHD Couette flow of a generalized Oldroyd-B fluid

Libo Feng, Fawang Liu, Ian Turner and Liancun Zheng

Abstract

In this paper, we consider the application of the finite difference method for a class of novel multi-term time fractional viscoelastic non-Newtonian fluid models. An important contribution of the work is that the new model not only has a multi-term time derivative, of which the fractional order indices range from 0 to 2, but also possesses a special time fractional operator on the spatial derivative that is challenging to approximate. There appears to be no literature reported on the numerical solution of this type of equation. We derive two new different finite difference schemes to approximate the model. Then we establish the stability and convergence analysis of these schemes based on the discrete H1 norm and prove that their accuracy is of O(τ + h2) and O(τmin{3–γs,2–αq,2–β}+h2), respectively. Finally, we verify our methods using two numerical examples and apply the schemes to simulate an unsteady magnetohydrodynamic (MHD) Couette flow of a generalized Oldroyd-B fluid model. Our methods are effective and can be extended to solve other non-Newtonian fluid models such as the generalized Maxwell fluid model, the generalized second grade fluid model and the generalized Burgers fluid model.

Acknowledgement

Author Liu wishes to acknowledge that this research was partially supported by Natural Science Foundation of China (Grant No. 11772046). Author Turner wishes to acknowledge that this research was also partially supported by the Australian Research Council (ARC) via the Discovery Project DP150103675. Authors Turner and Liu also wish to acknowledge that this research was partially supported by the Australian Research Council (ARC) via the Discovery Project (DP180103858).

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Received: 2018-01-01
Published Online: 2018-10-29
Published in Print: 2018-08-28

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