Finite-volume solution of the compressible Reynolds equation: linear and non-linear analysis of gas bearings

The present work deals with several aspects of the finite-volume numerical solution of the Reynolds equation for a compressible fluid. First, the upwind procedure used for stabilizing the solution is given a new interpretation. It is shown next how film thickness discontinuities can be handled in a mathematically correct way and finally, the finite-volume numerical solution is presented for unstructured grids. After validating these numerical aspects, the static and dynamic characteristics of cylindrical hydrodynamic and externally pressurized hybrid gas bearings are presented. The dynamic coefficients are obtained by using both a small perturbation and a non-linear approach.