A Galerkin/hyper-reduction technique to reduce steady-state elastohydrodynamic line contact problems

Abstract

A novel model order reduction technique for the elastohydrodynamic problem consisting of the Reynolds equation and the elasticity equation is proposed that drastically reduces the dimensionality of the problem and the computing time. The method is developed for stationary Newtonian isothermal line contacts. It employs the Galerkin projection method for the structural part combined with a hyper-reduction technique for the Reynolds equation. The model order reduction strategy consists of two phases. A first offline phase where snapshots of the full order model solution are computed using a selective refinement technique; and an online phase where the precomputed bases are used to compute the reduced order model. The method leads to a large reduction in the dimensionality of the full order model which results in a considerable reduction of the computing time, in a o(103) speedup factor, with an excellent correlation to the results obtained with the full order model.