An acoustic filtering procedure [1] has been applied to fluids above their critical point in order to decrease computational costs. The Navier-Stokes equations coupled with the energy and linearized state equations have been considered in order to solve problems related to thermal instabilities in such fluids. In the vicinity of the critical point, we showed that the Schwartchild criterion dominates over the classical one in the Rayleigh-Be´nard configuration. The numerical calculation by finite volume methods considered here, in comparison with the experiments of Meyer & Kogan [2], has given an interpretation of the unexpected oscillations at the convection onset. We have also studied the stability of two layers (hot and cold) of the same supercritical fluid (SCF) in an unstable configuration. The analogy with the stability of two miscible fluids has been clearly identified and stabilisation has been observed by reducing the height of the lower layer in this Rayleigh-Taylor like configuration.

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