A GLOBAL SPECTRAL METHOD FOR WAVY CHANNEL FLOW IN TWO DIMENSIONS

Abstract A global spectral method is presented for unsteady incompressible fluid flow in smoothly varying channels. Recombined Chebyshev bases are implemented with numerical conformal mapping, ensuring boundary conditions are met for both straight walls and smoothly varying walls. The pressure calculation reduces to matrix operations that comprise 8% of runtime, while maintaining spectral accuracy and mass continuity. The method is demonstrated for Reynolds numbers from $Re=1$ up to $Re=10^5$ . The method is verified by comparison with known results for a straight-walled channel, and with lubrication theory and linearization estimates for a channel with a periodic wavy lower wall. Some simple wall shapes are modelled at low Reynolds number. Long term stability is demonstrated for high Reynolds number flow, with an analysis of convergence against grid spacing.