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In this work we present a mixed-dimensional mathematical model to obtain theelectric potential and current density in direct current simulations when athin liner is included in the modelled domain. The liner is used in landfillmanagement to prevent leakage of leachate from the waste body into theunderground and is made of a highly-impermeable high-resistivity plasticmaterial. The electrodes and the liner have diameters and thicknessrespectively that are much smaller than their other dimensions, thus theirnumerical simulation might be too costly in an equi-dimensional setting. Ourapproach is to approximate them as objects of lower dimension and derive thecorresponding equations. The obtained mixed-dimensional model is validatedagainst laboratory experiments of increasing complexity showing the reliabilityof the proposed mathematical model.

A mixed-dimensional model for direct current simulations in presence of a thin high-resistivity liner