Keywords: uncertainty quantification, computational fluid dynamics, finite volume methods.

In this paper, the deterministic propagation of statistical model parameter uncertainties in numerical approximations of nonlinear conservation laws with particular emphasis on the Reynolds-averaged Navier-Stokes equations is considered. As a practical matter, these calculations are often faced with many sources of parameter uncertainty. Some example sources of parameter uncertainty include empirical equations of state, initial and boundary data, turbulence models, chemistry models, catalysis models, radiation models, and many others.

To deterministically model the propagation of model parameter uncertainty, stochastic independent dimensions are introduced [2,1,3]. Piecewise polynomial basis representations are constructed in these new independent dimensions and the resulting discretized conservation law systems are then solved using a multilevel domain decomposition solution technique. Numerous computational examples in one, two, and three dimensions are presented in the paper to demonstrate accuracy and capabilities of the proposed method.

1

R.G. Ghamen, "Ingredients for a general purpose stochastic FE formulation", Comput. Meth. Appl. Mech. Eng, 1999.

2

M. Kleiber, T.D. Hien, "The Stochastic Finite Element Method", John Wiley & Sons, 1992.

3

D. Xiu, G. Karniadakis, "Modeling uncertainty in flow simulation via generalized polynomial chaos", J. Comp. Phys., 2002.

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