This paper presents a spectral multidomain method for solving the
Navier‐Stokes equations in the vorticity‐stream function formulation. The
algorithm is based on an extensive use of the influence matrix technique and
so leads to a direct method without any iterative process. Numerical results
concerning the Czochralski melt configuration are reported and compared with
spectral monodomain solutions to show the advantage of the domain
decomposition for such a problem which solution presents a singular
behaviour.
We consider a fluid close to its gas-liquid critical point in a bottom-heated cavity. Due to strong density stratification, both the Schwarzschild and the Rayleigh stability criteria are relevant at the same space scale. Taking advantage of the competition between these two limits of the convection-onset criterion, we numerically exhibit striking non-Boussinesq effects: the reverse transition to stability through the Schwarzschild line of a heat diffusing layer subjected to convection, and the convection onset inside a few-millimeters-thick layer according to the Schwarzschild criterion.
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