Adaptive Numerical Methods for Elastohydrodynamic Lubrication

Numerical solutions to elastohydrodynamic lubrication problems have been computed for the last half century. Over the past decade multilevel techniques have been successfully applied in several solvers and significant speed-ups achieved. The aim of numerical research in this field is to develop techniques in order to calculate accurate solutions to demanding industrial problems as efficiently as possible.

In this work the numerical solver, previously developed by Nurgat, is examined. Despite being successful in achieving converged results on a single grid, there were some unresolved issues relating to the multigrid performance. These problems are explained and the necessary modifications to the method used are detailed.

There is much current interest in obtaining results to transient elastohydrodynamic lubrication problems. These are examined in detail and the justification for the methods used are discussed. Example results for industrially relevant cases, such as variation of lubricant entrainment, oscillation of the applied load and the presence of surface defects are considered.

In many other fields, adaptation in both space and time is used to increase performance and accuracy. However, these techniques are not currently used for elastohydrodynamic lubrication problems. It is shown that they can be successfully applied and substantial benefits accrued.

A method of variable timestepping has been introduced and results are presented showing that not only is it as accurate as fixed time stepping methods, but that the computational work required to obtain these solutions is significantly reduced. Local error control on each individual timestep is also implemented.

Adaptation of the spatial mesh is also developed. By developing a hierarchy of refined meshes within the multigrid structure it is seen how significantly fewer computational points are used in the most expensive numerical calculations. This, in turn, means that the computational time required is reduced. Different criteria for adaptation are explained and results presented showing the relative levels of accuracy and speed-up achieved.