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Numerical solution of the fractional Rayleigh–Stokes model arising in a heated generalized second-grade fluid

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Abstract

This paper addresses the solution of the Rayleigh–Stokes problem for an edge in a generalized Oldroyd-B fluid using fractional derivatives and the radial basis function-generated finite difference (RBF-FD) method. The time discretization is accomplished via the finite difference approach, while the spatial derivative terms are discretized using the local RBF-FD. The main idea is to consider the distribution of the data nodes within the local support domain so that the number of nodes remains constant. In addition, the stability and convergence analysis of the proposed method are discussed. The results using the RBF-FD are compared with those of other techniques on irregular domains showing the feasibility and efficiency of the new approach.

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Acknowledgements

The authors would like to express our appreciation to the Editor-in-Chief, Professor Mark Shephard, and the anonymous reviewers for their valuable comments and suggestions leading to the improved manuscript.

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Authors and Affiliations

  1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

    O. Nikan, A. Golbabai & T. Nikazad

  2. Department of Electrical Engineering, ISEP-Institute of Engineering, Polytechnic of Porto, Porto, Portugal

    J. A. Tenreiro Machado

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  1. O. Nikan
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  2. A. Golbabai
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  4. T. Nikazad
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Correspondence to A. Golbabai.

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Nikan, O., Golbabai, A., Machado, J.A.T. et al. Numerical solution of the fractional Rayleigh–Stokes model arising in a heated generalized second-grade fluid. Engineering with Computers 37, 1751–1764 (2021). https://doi.org/10.1007/s00366-019-00913-y

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