Adaptive timestepping for elastohydrodynamic lubrication solvers

The application of variable-step time-integration techniques in a method of lines approach for the numerical solution of transient elastohydrodynamic lubrication calculations is described. Spatial discretization of the coupled integro-differential equations leads to a system of differential-algebraic equations in time. At each timestep a large system of nonlinear equations of 104-107 variables is solved by using multigrid methods and multilevel multi-integration. The application of temporal error control methods is considered with reference to both the differential-algebraic formulation of the system to be solved and the multigrid-based nonlinear equation solver to be used. The error control method used takes account of the magnitude of the spatial error present by using a local time error control based on the magnitude of this error. This approach is shown to be beneficial in reducing the computational work required. Experimental results on a variety of lubrication problems, including a challenging rough surface problem, are used to display the effectiveness of the methods.