Random field solutions including boundary condition uncertainty for the steady-state generalized Burgers equation

Abstract

CFD results are subject to considerable uncertainty associated with the operating conditions. Even when the operational uncertainty is omitted under very controlled circumstances during wind tunnel experiments, substantial disagreement between experimental and CFD results persists. This discrepancy must be attributed to model uncertainty. This report discusses the various sources of uncertainty. The need for advanced uncertainty modeling is illustrated by means of a computationally inexpensive 1-D Burgers equation model. We specifically address the uncertainty due to missing variables (inexact or incomplete differential equations). To this extent a random field model is used for the viscosity and the fundamental differences between the solutions of the stochastic differential equations and a simple random variable model is highlighted. The Burgers equation theoretically needs to be integrated over an infinite domain. In a deterministic approach, the integration domain is cut off at some far field boundary. This truncation effectively ignores all variability outside this far field boundary. We present a practical treatment for the uncertainty on the boundary conditions. The results indicate that ignoring the boundary condition uncertainty dramatically underestimates the variance of the velocity u(x) in the interior of the domain.

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