Keywords: stochastic finite volume method, Shannon entropy, Navier-Stokes equation, lid-driven cavity flow, weighted least squares method, Monte-Carlo simulation, stochastic perturbation technique.

The main aim here is the numerical solution to the Navier-Stokes equations for incompressible, non-turbulent, and subsonic fluid flows with some Gaussian physical random parameters. The stochastic finite volume method implemented according to the generalized stochastic perturbation technique is engaged for this purpose. It is based upon the polynomial bases for the PVT solutions obtained with the weighted least squares method algorithm. The deterministic problem is solved using the freeware OpenFVM in conjunction with the computer algebra software MAPLE, where the LSM local fittings and the resulting probabilistic quantities are computed. The first two probabilistic moments as well as the Shannon entropy spatial distributions are determined with this apparatus and visualized in the FEPlot software. The spatial distribution of Shannon entropy has been completed thanks to the Monte-Carlo simulation scheme applied at the discrete volume level for each polynomial basis. Such an implementation of the stochastic finite volume method is applied to model 2D lid-driven cavity flow problem for statistically homogeneous fluid with limited uncertainty in its viscosity and heat conductivity. Further numerical extension of this technique is seen in an application of the Taylor-Newton-Gauss approximation technique, where polynomial approximation may be replaced with some exponential or hyperbolic bases.

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