AN IMPLICIT MULTIDOMAIN SPECTRAL COLLOCATION METHOD FOR THE SIMULATION ORF GAS-BEARINGS BETWEEN TEXTURED SURFACES

This work presents an implicit, multidomain, Chebyshev spectral colloc ation method for the solution of the compressible Reynolds equation of lubrication for a self-acting air bearing supporting a taper-flat sli der. The method maintains second-order accuracy in time and exponentia l accuracy in space. Multiple domains are introduced to allow for the distribution of additional collocation points in the boundary layer re gions without increasing the number of collocation points everywhere e lse in the computational domain. Multiple domains are also used to res olve individual sinusoidal roughness waves, demonstrating the method's utility in resolving geometric and/or flow features in rite interior of the computational domain. The ordinary differential equations gover ning the slider's two degrees of freedom are integrated in time by the use of a fourth-order Adams-Bashforth method which allows for accurat e and efficient coupling with the fluid dynamics of the gas bearing. T he strength of the multidomain pseudospectral method in resolving prob lems with important geometric features and boundary layers is demonstr ated by numerical experiments for sliders possessing different taper l engths and surface textures.