An implicit multidomain spectral collocation method for stiff highly non-linear fluid dynamics problems Original Research Article

An implicit, multidomain, Chebyshev spectral collocation technique for solving highly non-linear stiff problems is presented. First, the accuracy and efficiency of the explicit—implicit Adams—Bashforth Crank—Nicolson (ABCN) and the implicit Crank—Nicolson (CN) methods in obtaining solutions to the Burgers equation are compared. Then, the implicit CN scheme is used to solve the highly non-linear Reynolds equation of lubrication for a gas bearing separating two textured surfaces. Surface texture is approximated by fifty sinusoidal waves each of which is assigned a separate subdomain. An additional subdomain is used to resolve the trailing edge boundary layer. The combined method is shown to be well suited for the simulation of highly non-linear phenomena that exhibit high frequency spatial variations in the desired solution and that possess very sharp interior or boundary layers.