Pseudospectral methods for solution of the incompressible Navier-Stokes equations (Q1091195)

Four numerical schemes for solving the incompressible Navier-Stokes equations in primitive variables are discussed and compared. All use the Chebyshev pseudospectral matrix (CPSM) approach for evaluating spatial derivatives. Two of the methods are new and two are previously reported methods [\textit{A. J. Chorin}, Math. Comput. 22, 745-762 (1968), and \textit{L. Kleiser} and \textit{U. Schumann}, Numerical methods in fluid mechanics, Proc. 3rd GAMM Conf., Köln 1979, Notes Numer. Fluid Mech. 2, 165-174 (1980; Zbl 0463.76020)] that have been recast in CPSM form in order to compare results. The two-dimensional Navier-Stokes equations have been solved for a thermally deriven cavity using the four techniques. Details are given and numerical results are presented.