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.

中文翻译：

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使用双互易边界元法对具有一级化学反应的对流扩散问题进行数值模拟

目的

本文的目的是描述为一维和二维稳态问题开发的边界元法 (BEM) 和双互易边界元法 (DRBEM) 公式的扩展，以分析相关的瞬态对流-扩散问题与一级化学反应。

设计/方法/方法

数学建模已使用对偶互易近似将瞬态方程中出现的域积分转换为等效边界积分。对应问题的积分表示公式是从格林的第二恒等式得到的，使用对应的常系数稳态方程的基本解。有限差分法用于模拟求解所得方程组的时间演化过程。三种不同的径向基函数已成功实现，以提高求解的准确性并提高收敛速度。

发现

获得的数值结果证明了与解析解的良好一致性，以建立所提出方法的有效性并确认其效率。

原创性/价值

最后，所提出的 BEM 和 DRBEM 数值解没有显示任何人工扩散、振荡行为或波前阻尼，正如在其他不同数值方法中出现的那样。