A local meshless method for solving multi-dimensional Galilei invariant fractional advection–diffusion equation

In this article, a local meshless technique is applied for numerical simulation of multi-dimensional Galilei invariant fractional advection–diffusion model on regular and irregular computational domains. In the suggested method, a second-order Crank–Nicolson scheme along with the second-order weight...

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Bibliographic Details
Published in:Engineering analysis with boundary elements 2022-10, Vol.143, p.283-292
Main Authors: Eslami, Samira, Ilati, Mohammad, Dehghan, Mehdi
Format: Article
Language:English
Subjects:
Galilei invariant fractional advection–diffusion model
Local meshless method
Radial point interpolation method
Regular and irregular domains
Weighted and shifted Grünwald difference (WSGD) formula
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Summary:In this article, a local meshless technique is applied for numerical simulation of multi-dimensional Galilei invariant fractional advection–diffusion model on regular and irregular computational domains. In the suggested method, a second-order Crank–Nicolson scheme along with the second-order weighted and shifted Grünwald difference (WSGD) formula, is used to discretize the time derivatives of the model. This time-discretization scheme is unconditionally stable and convergent with order O(τ2). To approximate the spatial derivatives of this model, a local radial point interpolation technique is employed. Finally, to prove and demonstrate the validity of the proposed algorithm, various one, two and three-dimensional problems are investigated on regular and irregular computational domains.
ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2022.06.013