Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model

O. Nikan, Z. Avazzadeh*, J. A. Tenreiro Machado

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)

Abstract

The generalized Cattaneo model describes the heat conduction system in the perspective of time-nonlocality. This paper proposes an accurate and robust meshless technique for approximating the solution of the time fractional Cattaneo model applied to the heat flow in a porous medium. The fractional derivative is formulated in the Caputo sense with order 1<α<2. First, a finite difference technique of convergence order O(δt3−α) is adopted to achieve the temporal discretization. The unconditional stability of the method and its convergence are analysed using the discrete energy technique. Then, a local meshless method based on the radial basis function partition of unity collocation is employed to obtain a full discrete algorithm. The matrices produced using this localized scheme are sparse and, therefore, they are not subject to ill-conditioning and do not pose a large computational burden. Two examples illustrate in computational terms of the accuracy and effectiveness of the proposed method.

Original languageEnglish
Pages (from-to)107-124
Number of pages18
JournalApplied Mathematical Modelling
Volume100
DOIs
Publication statusPublished - Dec 2021

Keywords

  • Caputo fractional derivative
  • Convergence
  • Finite difference
  • Fractional Cattaneo equation
  • RBF-PU
  • Stability

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