Using adjoint error estimation techniques for elastohydrodynamic lubrication line contact problems

Abstract

SUMMARYThe use of an adjoint technique for goal-based error estimation described by Hart et al. (Int. J. Numer. Meth. Fluids 2005; 47:1069-1074) is extended to the numerical solution of free boundary problems that arise in elastohydrodynamic lubrication (EHL). EHL systems are highly nonlinear and consist of a thinfilm approximation of the flow of a non-Newtonian lubricant which separates two bodies that are forced together by an applied load, coupled with a linear elastic model for the deformation of the bodies. A finite difference discretization of the line contact flow problem is presented, along with the numerical evaluation of an exact solution for the elastic deformation, and a moving grid representation of the free boundary that models cavitation at the outflow in this one-dimensional case. The application of a goal-based error estimate for this problem is then described. This estimate relies on the solution of an adjoint problem; its effectiveness is demonstrated for the physically important goal of the total friction through the contact. Finally, the application of this error estimate to drive local mesh refinement is demonstrated.