A mortar-based cavitation formulation using NURBS-based isogeometric analysis

Abstract

This paper applies NURBS-based isogeometric analysis to hydrodynamic lubrication problems considering cavitation effects. For this purpose, a mass-conserving cavitation formulation analog to the Augmented Lagrangian method is developed. It describes the complementarity constraints between pressure and void fraction and converts the constrained problem to an unconstrained one. This formulation is discretized using a mortar-based approach to avoid oscillations resulting from over-constrained issues. Additionally, both NURBS basis functions and Lagrange polynomials are employed to discretize the fluid domain for comparison. Several numerical examples indicate that the proposed cavitation formulation can provide more accurate and robust solutions when combined with the mortar method and NURBS basis functions. Furthermore, this combination is adopted to investigate systems with rough surfaces and gaps partially filled with lubricants to demonstrate its excellent performance.