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Engineering with Computers
Erschienen in: Engineering with Computers 1/2018

06.05.2017 | Original Article

Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives: a stable scheme based on spectral meshless radial point interpolation

verfasst von: Elyas Shivanian, Ahmad Jafarabadi

Erschienen in: Engineering with Computers | Ausgabe 1/2018

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Abstract

In the present paper, a spectral meshless radial point interpolation (SMRPI) technique is applied to solve the Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative in two dimensional case. The time fractional derivative is described in the Riemann–Liouville sense. The applied approach is based on combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which act as basis functions in the frame of SMRPI. It is proved the scheme is unconditionally stable with respect to the time variable in \(H^1\) and convergent with the order of convergence \(\mathcal {O}(\delta t^{1+\beta })\), \(0<\beta <1\). In the current work, the thin plate splines (TPS) are used as the basis functions. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme. Two numerical examples show that the SMRPI has reliable accuracy in general shape domains.
Vorheriger Artikel A parallel log barrier-based mesh warping algorithm for distributed memory machines
Nächster Artikel Enhanced IGMM optimization algorithm based on vibration for numerical and engineering problems

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Metadaten
Titel
Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives: a stable scheme based on spectral meshless radial point interpolation
verfasst von
Elyas Shivanian
Ahmad Jafarabadi
Publikationsdatum
06.05.2017
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 1/2018
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-017-0522-1

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