The dual reciprocity boundary element formulation for convection-diffusion-reaction problems with variable velocity field using different radial basis functions

Abstract

This paper presents a dual reciprocity boundary element method (DRBEM) formulation for the solution of steady-state convection-diffusion-reaction problems with variable velocity field at moderately high Péclet number. This scheme is based on utilising the fundamental solution of the convection-diffusion-reaction equation with constant coefficients. In this case, we decompose the velocity field into an average and a perturbation, with the latter being treated using a dual reciprocity approximation to convert the domain integrals arising in the boundary element formulation into equivalent boundary integrals. A proposed approach is implemented to treat the convective terms with variable velocity, for which the concentration is expanded as a series of functions. Four numerical experiments are included with available analytical solutions, to establish the validity of the approach and to demonstrate the efficiency of the proposed method.

Numerical modelling of convection-diffusion problems with first-order chemical reaction using the dual reciprocity boundary element method

“…Therefore, in this study, it is shown Dual reciprocity boundary element method that the boundary element formulation developed precluded the need for 'upwind' or other algorithms which are common to the FEM and FVM, and they also made a decision to implement robust schemes for solving equations ( 3) and ( 4) in this research. The authors' have shown, in previous works on the subject, the solution of the corresponding problem with variable velocity fields (Al-Bayati and Wrobel, 2017Wrobel, , 2018aWrobel, , 2019. In fact, the key part of the paper falls on the development of a BEM and DRBEM formulations.…”

“…However, the functions ψ and η do not need to be numerically approximated as they are known functions for a specific set F . As seen in our previous work (Al-Bayati and Wrobel, 2018a), every node i will generate an equation like the above. It is also assumed that the number of points M exceeds the number of boundary nodes N by L units.…”

“…In dealing with the problem of numerically solving the convection–diffusion equation, several techniques have been applied such as finite differences, finite elements, boundary elements and meshless methods. Comprehensive studies and extensive lists of works using finite differences and finite elements can be found in references (Lewis et al , 2004; Nithiarasu et al , 2016; Yu and Heinrich, 1987) and Li (1990), while for boundary elements, the papers (Taigbenu and Liggett, 1986; Tanaka et al , 1987; Al-Bayati and Wrobel, 2018b; Al-Bayati and Wrobel, 2018a; Tanaka and Honma, 1989; Al-Bayati and Wrobel, 2019; Al-Bayati, 2018; Al-Bayati and Wrobel, 2020; Azis, 2019; Chen and Wang, 2016) and Peng et al (2020), refer to the majority of works done on the subject. The motivation to work on boundary elements resides in the fact that when applying the first two mentioned approaches, several numerical problems such as oscillations and smoothing of wave fronts have been reported.…”

Numerical Simulation for Transient Diffusion Convection Reaction Problems of a Class of Anisotropic FGMs

“…Some of these studies include Fendoglu et al [1] in 2018, Wang and Ang [2] in 2018, Sheu et al [3] in 2000, Xu [4] in 2018, and AL-Bayati and Wrobel [5] in 2019, who considered the DCR equation with constant coefficients. Samec and Škerget [6] in 2004, Rocca et al [7] in 2005, and AL-Bayati and Wrobel [8,9] in 2018 studied the DCR equation with variable velocity. Martinez et al [10] used nonstandard finite difference schemes based on Green's function formulations for reaction-diffusion-convection systems in 2013.…”

Técnica de Interpolação Direta de Elementos de Contorno aplicada a um Modelo Advectivo-Difusivo com Campo de Velocidade Variável Incompressível

“…Em casos de velocidade variável, propostas que usam a decomposição do campo de velocidade como uma média adicionada de uma flutuação, respectivamente abordadas pela formulação clássica e pela dupla reciprocidade, apresentam desempenho satisfatório para Péclet globais de baixos a altos [1,10]. Entretanto, a aplicação isolada da formulação da técnica da dupla reciprocidade em problemas advectivos difusivos é escassa na literatura tanto para campos uniformes de velocidade quanto para campos variáveis o que cria uma maior demanda por comparar a performance da mesma frente a outras técnicas baseadas em aproximações por bases radiais como a MECID, por exemplo.…”