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A localized hybrid kernel meshless technique for solving the fractional Rayleigh–Stokes problem for an edge in a viscoelastic fluid
A localized hybrid kernel meshless technique for solving the fractional Rayleigh–Stokes problem for an edge in a viscoelastic fluid
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Date
2023
Authors
Zakieh Avazzadeh
Omid Nikan
Anh Tuan Nguyen
Van Tien Nguyen
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Research Projects
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Abstract
"This paper presents an efficient stabilized meshless technique with a hybrid kernel to simulate the fractional
Rayleigh–Stokes problem for an edge in a viscoelastic fluid. The proposed method approximates the unknown
solution through two phases. Firstly, the temporal discretization of the govern model is performed by
integrating both sides of it, and then the space discretization is obtained by making use of the local hybrid
Gaussian-cubic kernel meshless. The localized approach considers merely neighboring collocation nodes, while
avoiding the ill-conditioning occurring in other techniques with dense and large matrix systems. The semidiscretized
approach in terms of the convergence and stability properties is discussed theoretically in the
weighted 𝐻1-norm and confirmed numerically. Two illustrative examples are given to show the efficiency and
applicability of the proposed strategy."
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Keywords
"Fractional derivative,
Rayleigh–Stokes model,
Local hybrid kernel meshless technique,
Stability,
Convergence"