A spectral element method for the time-dependent two-dimensional Euler equations: applications to flow simulations

A numerical spectral element method for the computation of fluid flows governed by the incompressible Euler equations in a complex geometry is presented. The appropriate elemental interface conditions for the velocity and the pressure are found by using variational formulation. It is proven that spectral approximations of same degrees for the velocity and the pressure, called PN × PN version, conduct to well-posed discrete problems, which is not true in general in the case of the Navier-Stokes equations. Applications to fluid flow simulation using the Navier-Stokes/Euler coupled model are presented.