DIRECT NUMERICAL-SIMULATION OF FLOW IN A CHANNEL WITH COMPLEX, TIME-DEPENDENT WALL GEOMETRIES - A PSEUDOSPECTRAL METHOD

An algorithm has been developed which extends the scope of spectral me thods to include solution of non-canonical channel flows arising from more complicated wall geometries. This significantly broadens the dire ct numerical simulation data base and its range of application, provid ing an accurate tool for the investigation of flows over three-dimensi onal surfaces which move in time. Through a time-dependent, curvilinea r transformation a general domain is mapped to one which permits spect ral representation of the solution and preserves exact boundary condit ions. Beginning with the Navier-Stokes equation in general tenser form , application of a metric operator effects the transformation. The pri mitive variables are represented pseudospectrally (Fourier in the stre am- and spanwise directions, Chebyshev wall-normal). Covariant differe ntiation generates variable coefficient terms in the equations for pre ssure and velocity, necessitating an iterative solution scheme. Standa rd benchmark tests validate flat-wall flow simulations. Static and dyn amic tests of one-dimensional flow over a perturbed wall confirm the a ccuracy of the time-dependent transformation. Low Reynolds number simu lations replicate the appropriate qualitative features of Stokes flow across two- and three-dimensional wall topographies. Results from a hi gher Reynolds number simulation of separated flow behind a three-dimen sional Gaussian protuberance match well with an independent solution f rom Mason and Morton who have used a finite-difference method. (C) 199 5 Academic Press, Inc.