Chebyshev methods for the Navier-Stokes equations: Algorithms and applications

Two types of Chebyshev-collocation methods for the solution of the Navier-Stokes equations are considered according to the elliptic problem to be solved at each time-cycle: Stokes-type problem or Darcy problem. Typical features associated with the solution of these problems are discussed: spurious modes of pressure, multi-domain technique, outflow boundary conditions, modeling of bodies by penalization, singularities, form of the nonlinear term. Examples of application (wake flow behind a cylinder, flow in a piston engine) are presented.