A Finite Volume-Based Unified Transient Deterministic Framework for Lubrication Modelling

A unified transient deterministic lubrication model is developed for the analysis of rough, starved, and coated contacts within a single, fully-coupled numerical framework capable of resolving boundary, mixed, and full-film lubrication regimes. The model is formulated with the finite volume method on a curvilinear grid and extends conventional full-film formulations through the introduction of a semi-system methodology, enabling robust treatment of complex multi-regime conditions. A key distinguishing feature of the framework is the direct resolution of thermal effects within both the lubricant and solid domains through solution of the energy equation. Unlike many existing mixed lubrication models that rely on analytical temperature approximations, the present approach captures transient, asperity-scale temperature evolution explicitly, allowing accurate representation of local thermo-mechanical interactions. Two case studies are presented to demonstrate the capabilities of the model. The first examines transient starvation in rough contacts with isotropic sinusoidal topographies of varying wavelength, as well as random machined surfaces, revealing a strong dependence of lubricant entrainment, asperity interaction, and localised heating on surface morphology. The second study investigates the role of coating thermal properties under transient starved conditions, demonstrating strong coupling between heat transport, viscosity variations, and frictional response. Overall, the proposed framework provides a robust and physically consistent platform for the simulation of transient lubrication phenomena under realistic operating conditions, enabling detailed insight into roughness, starvation, and thermal effects across regimes using a fully-coupled approach.