In this work we present a mixed-dimensional mathematical model to obtain the electric potential and current density in direct current simulations when a thin liner is included in the modelled domain. The liner is used in landfill management to prevent leakage of leachate from the waste body into the underground and is made of a highly-impermeable high-resistivity plastic material. The electrodes and the liner have diameters and thickness respectively that are much smaller than their other dimensions, thus their numerical simulation might be too costly in an equi-dimensional setting. Our approach is to approximate them as objects of lower dimension and derive the corresponding equations. The obtained mixed-dimensional model is validated against laboratory experiments of increasing complexity showing the reliability of the proposed mathematical model.

翻译：本文提出了一种混合维度数学模型，用于在模拟域包含薄层高阻衬里时获取直流电模拟中的电势与电流密度分布。该衬里采用高阻隔性塑料材料制成，在垃圾填埋场管理中用于防止渗滤液从废弃物堆体渗入地下环境。由于电极直径及衬里厚度远小于其他方向尺寸，若采用等维度数值模拟将产生高昂计算成本。本研究将电极与衬里近似为低维几何对象，并推导出相应控制方程。通过逐级复杂化的实验室实验验证了所提出的混合维度模型，结果表明该数学模型具有可靠的计算精度。