A meshless BEM for solving transient non-homogeneous convection-diffusion problem with variable velocity and source term. (December 2020)

• Record Type: Journal Article
• Authors: Peng, Hai-Feng; Liu, Kun; Cui, Miao; Gao, Xiao-Wei
• Is Part Of: Engineering analysis with boundary elements. Volume 121(2020)
• Page Start: 65
• Page End: 75
• Publication Date: 2020-12
• Subjects: Convection-diffusion -- Non-homogeneous -- Radial integration BEM -- Space and time dependent source term -- Spatially variable velocity; 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.2020.09.009
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this paper, a meshless BEM based on the radial integration method is developed to solve transient non-homogeneous convection-diffusion problem with spatially variable velocity and time-dependent source term. The Green function served as the fundamental solution is adopted to derive the boundary domain integral equation about the normalized field quantity. The two-point backward finite difference technique is utilized to discretize the time-dependent terms in the integral equation, which results in that the final integral equation formulation is only related with the normalized field quantity at the current time and has three domain integrals. Both two domain integrals regarding the normalized field quantity at the current and previous times are transformed into boundary integrals by using radial integration method and radial basis function approximation. For domain integral about the source term being known function of time and coordinate, radial basis functions approximation is still adopted to make the transformed boundary integral be evaluated only once, not at each time level. A pure boundary element algorithm with boundary-only discretization and internal points is established and the system of equations is assembled like the corresponding steady problem. Four numerical examples are given to demonstrate the accuracy and effectiveness of the present method.