A Multigrid Method for Elasto-hydrodynamic Contact Simulations of Radial Slider Bearings

The well-known Reynolds equation is typically used to compute the pressure distribution for elasto-hydrodynamic contacts of parts, as, for instance, in radial slider bearings. In order to resolve local pressure phenomena like edge loading, a higher spatial resolution is needed. This causes problems for stationary solvers, like Gauss-Seidel iteration, which are well suited for the occurring nonlinearities. These problems can be overcome by applying multigrid methods. Since the Reynolds equation is nonlinear, expensive nonlinear multigrid methods are expected to be required. This paper introduces an approach to combine a linear multigrid method with a Gauss-Seidel solver on the finest level, which yields a similar convergence behavior as a nonlinear multigrid method but at much lower computational cost. The formulations are general so that analogous applications of the Reynolds equation, as, for instance, for axial slider bearings or hydrodynamic piston-liner contacts, are straightforward.