Mixed boundary element solution for three-dimensional convection-diffusion problem with a velocity profile

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

“…The type of RBF used in the interpolation of the unknown variables normally plays an important role in determining the accuracy of the DRM [17]. Partridge et al [1] have shown that a variety of functions can in principle be used as global interpolation functions f k . The approach used by Wrobel and DeFigueiredo [4] was based on practical experience rather than formal mathematical analyses and motivated by a previous successful experience with axisymmetric diffusion problems in which a similar approach was used [18].…”

“…This is due to the lack of information on choosing the best shape parameter available in the literature, forcing the user having to make an 'ad-hoc' decision. It is important to note that the value of the multiquadric shape-parameter, c, has not been explicitly defined (see table (1)). After a process of investigation, the authors found the optimal value of the shape parameter for the current problems to be c = 75.…”

“…The boundary element method (BEM) has been applied to steady-state convection-diffusion-reaction problems with variable velocity by various researchers [1,2,3,4,5,6,7,8,9]. However, the solution of this problem is still considered a big challenge, particularly for variable and high velocities.…”

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

“…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.…”