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SUMMARYThe calculation of friction when solving elastohydrodynamic lubrication (EHL) problems is of considerable practical engineering importance. Adjoint techniques allow the error in this integral quantity to be estimated and controlled as part of an adaptive solution strategy. This paper considers two simpliÿed EHL models and demonstrates the successful application of the adjoint approach to error estimation of friction-like quantities for this challenging class of problem.

Abstract:The use of adjoint error estimation techniques is described for a model problem that is a simplified version of an EHL line contact. Quantities of interest, such as friction, may be dependent upon the accuracy of the solution in some parts of the domain more than in others. The use of an inexpensive extra solve to calculate an adjoint solution is described for estimating the intergrid error in the value of friction calculated, and as a basis for local refinement. It is demonstrated that this enables an accurate estimate for the quantity of interest to be obtained from a less accurate solution of the model problem.

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.