Advanced modelling of lubricated interfaces in general curvilinear grids

Tackling fluid-flow problems involving intricate surface geometries has been the catalyst for a plethora of numerical investigations aimed at accommodating curved complex boundaries. An example is the application of body-fitted curvilinear coordinate transformation, where the one-to-one correspondence of grid points from a non-orthogonal curvilinear grid in the physical domain to an orthogonal grid in the computational domain is achieved. In lubricated interfaces, such conversion is challenging due to the complexity of the governing equations in the mapped-grid, the numerical instabilities exhibited by their non-linearities and the severity of the operating conditions. The present contribution proposes a Reynolds-based, finite volume fluid-structure interaction (FSI) framework for solving thermal elastohydrodynamic lubrication (TEHL) problems mapped onto orthogonal grids in the computational domain. We demonstrate how the strong conservation form of the pertinent governing equations can be expressed in three-dimensional curvilinear grids and discretised using the finite volume method to ensure fluid-flow conservation and enforce mass-conserving cavitation conditions. Numerical and experimental benchmarks showcase the robustness and versatility of the proposed framework to simulate a diverse range of lubrication problems, hence achieving a predictive computational tool that would enable a shift towards tribology-aware design.