School of Computing Research Colloquia

Efficient Finite Element Simulation of Full-System Elastohydrodynamic Lubrication Problems

Sarfraz Ahmed, Scientific Computation research group

Abstract: This study is concerned with the efficient numerical solution of problems of elastohydrodynamic lubrication (EHL). Our approach is to consider fully-coupled models in which the governing equations for the lubricating film, the elastic deformation and the force balance are each discretized and solved as a single monolithic nonlinear system of algebraic equations. The main contributions of this work are to propose, implement and analyse a novel, optimal, preconditioner for the Newton linearization of this algebraic system, and to assess the development of efficient finite element meshes through both manual tuning and the use of adaptive mesh refinement based upon a posterior error estimation and control. In particular, a new block-wise preconditioner is developed which is designed to exploit the specific structure that is present in this class of problem. This preconditioner combines the use of algebraic multigrid (AMG) /geometric multigrid (GMG) preconditioning for the linear elasticity block and a separate, efficient, approximation to precondition the Reynolds block.

Numerical results (for line and point contact cases) will be presented to illustrate the performance and efficiency of this preconditioning strategy both in terms of computational time and memory usage. These results demonstrate that the preconditioned iterative approach is both computationally and memory superior to the sparse direct solver. Most importantly, both the computational and memory costs are seen to grow linearly with the number of unknowns.

A locally adaptive solution scheme is also developed for fully-coupled EHL point contact problems. This automates the refinement process to the regions of the domain which exhibit large error in their solutions. Numerical results are presented which demonstrate the performance and effectiveness of the proposed procedure.