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

Abstract

Purpose The purpose of this paper is to describe an extension of the boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) formulations developed for one- and two-dimensional steady-state problems, to analyse transient convection–diffusion problems associated with first-order chemical reaction. Design/methodology/approach The mathematical modelling has used a dual reciprocity approximation to transform the domain integrals arising in the transient equation into equivalent boundary integrals. The integral representation formula for the corresponding problem is obtained from the Green’s second identity, using the fundamental solution of the corresponding steady-state equation with constant coefficients. The finite difference method is used to simulate the time evolution procedure for solving the resulting system of equations. Three different radial basis functions have been successfully implemented to increase the accuracy of the solution and improving the rate of convergence. Findings The numerical results obtained demonstrate the excellent agreement with the analytical solutions to establish the validity of the proposed approach and to confirm its efficiency. Originality/value Finally, the proposed BEM and DRBEM numerical solutions have not displayed any artificial diffusion, oscillatory behaviour or damping of the wave front, as appears in other different numerical methods.

Numerical simulation of fluid flow with a fast Boundary‐Domain Integral Method

“…In (11), ω i and v i are the absolute values of the vorticity and velocity that were solved with the original matrices formulation and ωi , ṽi denote the solution obtained with the H 2 -formulation. In figure 4, this error is plotted versus the interpolation order.…”

“…The dual reciprocity method transforms the domain integral into a boundary integral operator. Al-Bayati and Wrobel employed the dual reciprocity method to solve the convection-diffusion problems with first-order chemical reaction [11]. An extension is the triple reciprocity method.…”

Simulation of predator–prey system with two-species, two chemicals and an additional chemotactic influence via direct meshless local Petrov–Galerkin method

“…The main aim of Harris et al (2015) is to demonstrate the use of RBF interpolation in the approximation of sharp gradients or shocks by use of a RBF blending interpolation approach. Al-Bayati and Wrobel (2021) described an extension of the BEM and the dual reciprocity BEM formulations developed for one- and two-dimensional steady-state problems, to analyze transient convection–diffusion problems associated with first-order chemical reaction. A novel formulation of the BEM with the radial integration method is proposed in Soares et al (2020) to calculate the critical loads of the plate buckling problem with shear deformation.…”