A spectral anelastic Navier–Stokes solver for a stratified two-miscible-layer system in infinite horizontal channel
Résumé
We present a consistent Chebyshev–Fourier–Fourier pseudo-spectral algorithm for the numerical solution of anelastic models. These models satisfy the constraint , where is a mean density profile and u the velocity field. The choice of the decoupling method is discussed and the Uzawa approach is generalized to such a constraint. The pressure operator properties are detailed and the solution of the zeroth Fourier mode case is discussed. The solution of linear systems is obtained and refined, using an iterative method. The Uzawa algorithm is embedded in an auto-adaptive multidomain approach in order to handle steep evolving gradients. The algorithm is reduced to the Boussinesq approximation. The characteristics and performance of the resulting numerical code are analyzed. The validation includes comparisons with linear stability results and with the Waddell et al. [55] single-mode experiment. We also compute the nonlinear growth rate of a Boussinesq turbulent mixing layer. A comparison between Boussinesq and anelastic models is then sketched out. Finally four 3D simulations are carried out (with the anelastic and Boussinesq models). These results illustrate the capability of the entire method to handle stiff problems such as the Rayleigh–Taylor configuration.
