In our previous work, macroscopic models for multi-species diffusion/heterogeneous reaction with different diffusion coefficients in porous media were derived from the homogenization technique based on a spectral approach (Le et al., Applied Mathematical Modelling, 104, 666–681, 2022). This work aims to analyze numerically the properties of the eigenvalues and eigenfunctions of the spectral problem, the solution of the closure problems and the effective coefficients as a function of key parameters such as the Damköhler number, the ratios of the reaction rates and diffusion coefficients. This provides in-depth understanding of the role of the coefficients involved in the macroscopic models in the whole range of the Damköhler number. Simulation results of the macroscopic equations are compared with direct numerical simulations in unsteady regime, showing a very satisfactory agreement and thus numerically validating the proposed models.

在我们之前的工作中，多孔介质中不同扩散系数的多物质扩散/非均相反应的宏观模型是从基于光谱方法的均质化技术推导出来的（ Le et al. , Applied Mathematical Modelling, 104 , 666–681, 2022 ）。这项工作旨在数值分析特征值和特征函数的性质谱问题的解、闭合问题的解和作为关键参数的函数的有效系数，例如 Damköhler 数、反应速率比和扩散系数。这提供了对涉及在 Damköhler 数的整个范围内的宏观模型中的系数的作用的深入理解。将宏观方程的模拟结果 与非定常状态下的直接数值模拟进行比较，显示出非常令人满意的一致性，从而在数值上验证了所提出的模型。