Modelling heterogeneous interfaces using element-based finite volumes

Accurately depicting multiphysics interactions in interfacial systems requires computational frameworks capable of reconciling geometric adaptability with strict conservation fidelity. However, traditional spatiotemporal discretisation methods often compromise between mesh flexibility and flow conservation enforcement, hence constraining their effectiveness in elucidating the underlying mechanisms. Here, we respond to these computational demands by developing a novel three-dimensional adaptation of the Element-based Finite Volume Method (EbFVM) -- a hybrid numerical strategy that merges the geometric flexibility of Finite Element Methods with the conservation-centric principles of Finite Volume Methods. The proposed framework introduces advanced discretisation techniques tailored to unstructured, irregular mesh entities, including detailed parametric shape functions, robust flux integration schemes and rigorous body-fitted curvilinear coordinate mappings. Through a series of lubrication-driven benchmark problems, we demonstrate the EbFVM's capacity to capture intricate transport phenomena, strong field couplings and scale disparities across geometrically complex domains. By enabling accurate modelling in geometrically and physically challenging interfacial systems, the three-dimensional EbFVM offers a versatile and generalisable tool for simulating transport phenomena in a plethora of multiphysics applications.