A local meshless method for solving multi-dimensional Galilei invariant fractional advection–diffusion equation. (October 2022)

• Record Type: Journal Article
• Authors: Eslami, Samira; Ilati, Mohammad; Dehghan, Mehdi
• Is Part Of: Engineering analysis with boundary elements. Volume 143(2022)
• Page Start: 283
• Page End: 292
• Publication Date: 2022-10
• Subjects: 41A30 -- 65M99 -- 65N99; Local meshless method -- Galilei invariant fractional advection–diffusion model -- Weighted and shifted Grünwald difference (WSGD) formula -- Radial point interpolation method -- Regular and irregular domains; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2022.06.013
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: 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 ( τ 2 ) . 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.