AN IMPLICIT MULTIDOMAIN SPECTRAL COLLOCATION METHOD FOR STIFF HIGHLY NONLINEAR FLUID-DYNAMICS PROBLEMS

An implicit, multidomain, Chebyshev spectral collocation technique for solving highly non-linear stiff problems is presented. First, the acc uracy and efficiency of the explicit-implicit Adams-Bashforth Crank-Ni colson (ABCN) and the implicit Crank-Nicolson (CN) methods in obtainin g solutions to the Burgers equation are compared. Then, the implicit C N scheme is used to solve the highly non-linear Reynolds equation of l ubrication for a gas bearing separating two textured surfaces. Surface texture is approximated by fifty sinusoidal waves each of which is as signed a separate subdomain. An additional subdomain is used to resolv e the trailing edge boundary layer. The combined method is shown to be well suited for the simulation of highly non-linear phenomena that ex hibit high frequency spatial variations in the desired solution and th at possess very sharp interior or boundary layers.