A PROBABILISTIC TREATMENT OF UNCERTAIN BOUNDARY CONDITIONS IN CFD APPLICATIONS

Abstract eng:
The computation of stochastic solutions to model equations in CFD applications faces some specific challenges, which are different from many SFEM applications in structural mechanics. Frequently, in CFD applications the differential equations have to be integrated over an infinite or semi-infinite domain. In practice the integration domain is cut-off at some “far field” boundary. Sometimes deterministic correction methods for the introduced error exist. In this paper, we assess the impact of the uncertainty modeling on the far field boundaries on the statistics of the solution in the interior of the integration domain. We anticipate that the developed techniques will also be of interest to geotechnical and other applications where one can find (semi-)infinite domains. The nonlinear generalized Burgers equation is used as a model problem. We model the viscosity as a homogeneous random field. For selected expressions of the flux, there is an analytical closed-form solution for the deterministic equation. This exact solution is the gold standard against which numerical results obtained using the midpoint and locally averaged discretization method or polynomial chaos expansions, are compared. We assess the convergence of the algorithms in terms of the number of grid cells, the order of the chaos, and the quality of the boundary condition modeling.

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