Pseudospectral methods for solution of the incompressible navier-stokes equations

Abstract

Abstract 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 that have been recast in CPSM form in order to compare results. The methods are (1) time-splitting of velocity and pressure (the projection method) with prescribed boundary conditions on the velocity only and satisfaction of the continuity equation at boundaries to close the system (no pressure boundary conditions required), (2) a quasi-velocity potential formulation with either continuity or Neumann boundary conditions, (3) direct solution of velocity and pressure with prescribed boundary conditions on velocity and either Neumann or continuity conditions for the pressure, and (4) the influence matrix technique with prescribed velocity and pressure boundary conditions specified to satisfy continuity. All the methods share one characteristic: a Poisson equation must be solved for either the pressure or quasi-potential field. When applied to the test problem of a thermally driven cavity flow, it was found that the best accuracy was obtained by all methods that employed satisfaction of continuity as the boundary condition for solution of the Poisson equation.