Navier–Stokes problems with random coefficients by the Weighted Least Squares Technique Stochastic Finite Volume Method

Abstract

The main aim of this article is numerical solution to the Navier–Stokes equations for incompressible, non-turbulent and subsonic fluid flows with Gaussian physical random parameters. It is done with the use of the specially adopted Finite Volume Method extended towards probabilistic analysis by the generalized stochastic perturbation technique. The key feature of this approach is the weighted version of the Least Squares Method implemented symbolically in the system MAPLE to recover nodal polynomial response functions of the velocities, pressures and temperatures versus chosen input random variable(s). Such an implementation of the Stochastic Finite Volume Method is applied to model 3D flow problem in the statistically homogeneous fluid with uncertainty in its viscosity and, separately, coefficient of the heat conduction. Probabilistic central moments of up to the fourth order and the additional characteristics are determined and visualized for the cavity lid driven flow owing to the specially adopted graphical environment FEPlot. 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 the exponential or hyperbolic ones.