A pseudospectral method for solution of the three-dimensional incompressible Navier-Stokes equations

Abstract

A new Chebyshev pseudospectral technique (based on the projection method that was previously applied by the authors to the solution of two-dimensional incompressible Navier-Stokes equations in primitive variables for nonperiodic boundary conditions) is extended to solve the three-dimensional Navier-Stokes equations. The crucial point of the method is the requirement that the continuity equation be satisfied everywhere in the domain, on the boundaries as well as in the interior. The key feature of the work presented in this paper is that the computer storage requirements of the full matrix inversion resulting from direct solution of the pressure Poisson equation in three dimensions is greatly reduced by considering an eigenfunction decomposition. The method was tested on a two-dimensional driven cavity flow and the results were compared with those of the most accurate finite-difference calculation. The three-dimensional driven cavity flow was then calculated at the same Reynolds numbers as the two-dimensional cases, i.e., Re = 100, 400, and 1000. In the calculated results, three-dimensional boundary effects were observed in all cases and became more apparent with increasing Reynolds number.