Isabelle Raspo

A spectral projection method for the simulation of complex three-dimensional rotating flows

Abstract In this paper, we present an efficient projection method to solve the three-dimensional time-dependent incompressible Navier–Stokes equations in primitive variables formulation using spectral approximations. This method is based on a modification of the algorithm proposed by Goda [J. Comp. Phys. 30 (1979) 76]. It brings an improvement by introducing a preliminary step for the pressure in order to allow a temporal evolution of the normal pressure gradient at the boundaries. Its efficiency is brought to the fore by comparison with the Godas algorithm. The modified projection method is then applied to the simulation of complex three-dimensional flows in rotating cavities, involving either a throughflow or a differential rotation.

Stability of a supercritical fluid diffusing layer with mixed boundary conditions

We consider a fluid close to its gas-liquid critical point in the Rayleigh-Benard configuration. Owing to thermoacoustic effects, the bottom heating induces thermal boundary layers along both the lower and the upper horizontal plates. The hydrodynamic stability of these diffusing layers, whose bounding conditions are interchanged, is studied numerically in a two-dimensional (2D) approximation. As far as the convection onset criterion and the critical wave number are concerned, some discrepancies are found between the simulations and the predictions obtained by means of linear analysis. The extension of the study to three-dimensional configurations confirms the validity of the 2D approximation for the analysis of the hydrodynamic stability and shows its inadequacy when the layers become convection dominated.

A direct spectral domain decomposition method for the computation of rotating flows in a T-shape geometry

This paper presents a direct domain decomposition method, coupled with a Chebyshev collocation approximation, for solving the incompressible Navier-Stokes equations in the vorticity-streamfunction formulation. The method is based on the influence matrix technique used to treat the lack of vorticity boundary conditions on no-slip walls as well as to enforce the continuity conditions at the interfaces between adjacent subdomains. The multi-domain approach is proposed in order to extend the use of spectral approximations to non-rectangular geometries and singular solutions. It is applied to the computation of a four domain configuration, corresponding to a forced throughflow in a rotating channel-cavity system which is important in air cooling devices and cannot be modeled by single-domain spectral approximations.