A general numerical framework is designed for the two-dimensional convection–diffusion–reaction (CDR) system. The compatibility of differential quadrature and finite difference methods (FDM) are utilized for the formulation. The idea is to switch one numerical scheme to another numerical scheme without changing the formulation. The only requirement is to input the weighting coefficients associated with the derivative discretizations to the general algorithm. Three numerical schemes comprising combinations of differential quadrature and FDMs are studied using the general algorithm. Properties of numerical schemes and the algorithm are analyzed by using the simulations of two-dimensional linear CDR system, Burgers’ equation, and Brusselator model.

中文翻译：

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解决二维对流-扩散-反应系统的通用数值框架的系统表示

为二维对流扩散反应（CDR）系统设计了一个通用的数值框架。差分正交方法和有限差分方法（FDM）的兼容性可用于该公式。这个想法是在不更改公式的情况下将一个数值方案转换为另一个数值方案。唯一的要求是将与导数离散化关联的加权系数输入到通用算法。使用通用算法研究了三种包含差分正交和FDM组合的数值方案。通过对二维线性CDR系统，Burgers方程和Brusselator模型的仿真，分析了数值方案和算法的特性。