Soil-based water filtering devices can be described by models of viscous flow in porous media coupled with an advection–diffusion–reaction system modelling the transport of distinct contaminant species within water, and being susceptible to adsorption in the medium that represents soil. Such models are analysed mathematically, and suitable numerical methods for their approximate solution are designed. The governing equations are the Navier–Stokes–Brinkman equations for the flow of the fluid through a porous medium coupled with a convection-diffusion equation for the transport of the contaminants plus a system of ordinary differential equations accounting for the degradation of the adsorption properties of each contaminant. These equations are written in meridional axisymmetric form and the corresponding weak formulation adopts a mixed-primal structure. A second-order, (axisymmetric) divergence-conforming discretisation of this problem is introduced and the solvability, stability, and spatio-temporal convergence of the numerical method are analysed. Some numerical examples illustrate the main features of the problem and the properties of the numerical scheme.

基于土壤的水过滤装置可以用多孔介质中的粘性流动模型与对流扩散反应系统相结合来描述，该对流扩散系统对水中不同污染物的迁移进行建模，并且易于吸附在代表土壤的介质中。对这些模型进行数学分析，并为它们的近似解设计合适的数值方法。控制方程是用于流体流经多孔介质的Navier–Stokes–Brinkman方程，以及用于污染物输送的对流扩散方程，以及考虑了吸附性能下降的常微分方程组。每种污染物。这些方程以子午轴对称形式编写，相应的弱公式采用混合原始结构。引入了该问题的二阶（轴对称）发散协调离散，并分析了数值方法的可解性，稳定性和时空收敛性。一些数值示例说明了问题的主要特征以及数值方案的性质。