Adjoint Error Estimation and Spatial Adaptivity for EHL-Like Models

Abstract

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.

Using adjoint error estimation techniques for elastohydrodynamic lubrication line contact problems

“…Such modifications are relatively straightforward, see [15]. Note that the one place where particular care does need to be taken is in the evaluation of the film thickness, given by (2) and approximated by (12), so as to ensure that the non-uniform mesh is accounted for appropriately [15].…”

“…This work only resolved the spike using up to 1000 points, however it did still highlight the importance of this area of the solution. More recent results in [11,12] used over a million mesh points and illustrated both the smoothness of the pressure spike and the need for appropriate levels of mesh refinement. Consequently, calculating the friction accurately depends on achieving the necessary resolution of the pressure profile.…”