On application of the Stochastic Finite Volume Method in Navier-Stokes problems

摘要

The main aim of this article is numerical solution of the fully coupled Navier-Stokes equations with Gaussian random parameters. It is provided thanks to the specially adopted Finite Volume Method, modified using the generalized stochastic perturbation technique. This Stochastic Finite Volume Method is applied to model 3D problem with uncertainty in liquid viscosity and a coefficient of the heat conduction, separately. Probabilistic moments and characteristics of up to the fourth order are determined with the use of the Response Function Method realized numerically via the polynomial interpolation. Although mathematical formulation of the SFVM has been proposed in addition to the problems including single random variable, it is possible to extend it towards multi-parametric cases, also for the correlated random variables. Inclusion of the boundary conditions in both global and local sense is quite straightforward but needs some prior experimental basic statistics.