An implicit multidomain spectral collocation method for stiff highly nonlinear fluid dynamics problems (Q1913211)

An implicit multidomain, Chebyshev spectral collocation technique for solving highly nonlinear stiff problems is presented. First, the accuracy and efficiency of the explicit-implicit Adams-Bashforth Crank-Nicolson 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 nonlinear Reynolds equation of lubrication for a gas bearing separating two textured surfaces. Surface texture is approximated by fifty sinusoidal waves, to each of which is assigned a separate subdomain. An additional subdomain is used to resolve the trailing edge boundary layer.