An Implicit Multidomain Spectral Collocation Method for the Simulation of Gas Bearings Between Textured Surfaces

Abstract

This work presents an implicit, multidomain, Chebyshev spectral collocation method for the solution of the compressible Reynolds equation of lubrication for a self-acting air bearing supporting a taper-flat slider. The method maintains second-order accuracy in time and exponential accuracy in space. Multiple domains are introduced to allow for the distribution of additional collocation points in the boundary layer regions without increasing the number of collocation points everywhere else in the computational domain. Multiple domains are also used to resolve individual sinusoidal roughness waves, demonstrating the method’s utility in resolving geometric and/or flow features in the interior of the computational domain. The ordinary differential equations governing the slider’s two degrees of freedom are integrated in time by the use of a fourth-order Adams-Bashforth method which allows for accurate and efficient coupling with the fluid dynamics of the gas bearing. The strength of the multidomain pseudospectral method in resolving problems with important geometric features and boundary layers is demonstrated by numerical experiments for sliders possessing different taper lengths and surface textures.