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.

翻译：精确描述界面系统中的多物理场相互作用，需要计算框架能够兼顾几何适应性与严格的守恒保真度。然而，传统的时空离散化方法常在网格灵活性与流动守恒约束之间做出折衷，从而限制了其在揭示底层机制方面的有效性。为此，我们通过开发一种新颖的三维单元有限体积法（EbFVM）来应对这些计算需求——这是一种混合数值策略，融合了有限元法的几何灵活性与有限体积法以守恒为核心的原则。所提出的框架引入了针对非结构化、不规则网格实体量身定制的高级离散化技术，包括详细的参数化形函数、稳健的通量积分方案以及严格的贴体曲线坐标映射。通过一系列润滑驱动的基准问题，我们证明了EbFVM在几何复杂域中捕捉精细输运现象、强场耦合及尺度差异的能力。通过在几何和物理上具有挑战性的界面系统中实现精确建模，三维EbFVM为模拟众多多物理场应用中的输运现象提供了一种通用且可推广的工具。