Natural Convection in a Closed Cavity under Stochastic Non-Boussinesq Conditions

A stochastic projection method (SPM) is developed for quantitative propagation of uncertainty in compressible zero-Mach-number flows. The formulation is based on a spectral representation of uncertainty using the polynomial chaos (PC) system, and on a Galerkin approach to determining the PC coefficients. Governing equations for the stochastic modes are solved using a mass-conservative projection method. The formulation incorporates a specially tailored stochastic inverse procedure for exactly satisfying the mass-conservation divergence constraints. A brief validation of the zero-Mach-number solver is first performed, based on simulations of natural convection in a closed cavity. The SPM is then applied to analyze the steady-state behavior of the heat transfer and of the velocity and temperature fields under stochastic non-Boussinesq conditions.

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