The meshless local Petrov–Galerkin method based on moving Taylor polynomial approximation to investigate unsteady diffusion–convection problems of anisotropic functionally graded materials related to incompressible flow. (1st November 2021)

• Record Type: Journal Article
• Authors: Abbaszadeh, Mostafa; Dehghan, Mehdi; Azis, Mohammad Ivan
• Is Part Of: Engineering analysis with boundary elements. Volume 132(2021)
• Page Start: 469
• Page End: 480
• Publication Date: 2021-11-01
• Subjects: 35R60 -- 60H15 -- 65M60; Plane elastostatic equations -- Meshless local Petrov–Galerkin (MLPG) method -- Moving Taylor polynomial approximation -- Anisotropic functionally graded materials problems; 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.2021.06.026
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: This paper concerns to a meshless local Petrov–Galerkin (MLPG) method for studying the unsteady diffusion–convection problems of anisotropic functionally graded materials. A new version of MLPG method based on the moving Taylor polynomial approximation is developed to discrete the spatial variable. Then, we obtain a system of ODEs which depends to the time variable. A strong stability preserving (SSP) Runge–Kutta idea is provided to solve the final ODEs with enough accuracy and stability. Also, the grading function which defines the variable elastic coefficient can be any types of continuous functions. The developed numerical formulation is applied for different examples of non-rectangular domains to check its accuracy.