A spectral embedding method for the incompressible Navier-Stokes equations

In order to solve the incompressible Navier-Stokes equations in geometries of complex shape with a spectral type method, one uses an embedding approach based on Fourier expansions and boundary integrals equations. By using appropriate formulations of these equations, we propose algorithms that simply require efficient solvers of scalar elliptic equations. The capabilities of the ''spectral embedding method'' method are pointed out by considering the classical 2D driven cavity problem with comparisons to spectral Chebyshev results.