Interior-exterior penalty approach for solving elasto-hydrodynamic lubrication problem: Part I
For researchers in tribology and computational mechanics, this provides a theoretically grounded numerical method for a realistic lubrication model, though results are limited to moderate loads and the approach is incremental.
The paper develops an interior-exterior penalty method within a discontinuous Galerkin finite volume framework to solve the elasto-hydrodynamic lubrication problem for two-dimensional point contacts, proving existence of a solution without constant assumptions on viscosity or density and achieving optimal error estimates under light load conditions.
A new interior-exterior penalty method for solving quasi-variational inequality and pseudo-monotone operators arising in two-dimensional point contact problem has been analyzed and developed in discontinuous Galerkin finite volume method environment. In this article, we proved the existence of solution for the more realistic model problem without taking any constant assumption in viscosity or density of the lubricant. We have shown that optimal error estimate of $H^{1}$ and $L^{2}$ norm can be achieved under a light load non-dimensional parameter condition. In addition, we provided a complete algorithm to tackle all numerical complexities appear in the solution procedure. We obtained results for moderate loaded conditions which have been discussed at the end of the section. Furthermore, results give a hope for the further development of the scheme for highly loaded condition appeared in a more realistic operating situation which will be discussed in part II. This method is well suited for solving elasto-hydrodynamic lubrication line as well as point contact problems and can probably be treated as commercial software.