Flow Continuity of Isothermal Elastohydrodynamic Point-Contact Lubrication Under Different Numerical Iteration Configurations

Abstract Elastohydrodynamic lubrication (EHL) in point contacts can be numerically solved with various iteration methods, but so far the flow continuity of such solutions has not been explicitly verified. A series of closed regions with the same inlet side boundary is defined, and two treatments to total all flows related to the other boundaries of the closed regions are defined to enable flow-continuity verifications. The multigrid method and the traditional single mesh method with different relaxation configurations are utilized to solve different cases to evaluate computation efficiencies. For the multigrid method, the combination of a pointwise solver together with hybrid-relaxation factors is identified to perform better than other combinations. The single mesh method has inferior degrees of flow continuity than the multigrid method and needs much smaller error control values of pressure to achieve a decent level of flow continuity. Because flow continuity has a physical meaning, its verifications should be routinely included in any self-validation process for any EHL results. Effects of control errors of pressure, mesh sizes, differential schemes, and operating conditions on flow continuities are studied. Then, trends of film thickness with respect to speed are briefly discussed with meshes up to 4097 by 4097.