A Non-Intrusive Polynomial Chaos Method For Uncertainty Propagation in CFD Simulations

Abstract

In this extended abstract, we present a Non-Intrusive Polynomial Chaos (PC) method for the propagation of input uncertainty in Computational Fluid Dynamics (CFD) simulations. By the “non-intrusive” term, we specify a method which does not modify the original deterministic code used in the simulations. In our proposed paper, we focus on investigating such a method which uses deterministic solutions in a stochastic model to simulate the propagation of the input uncertainties for obtaining various statistics of output variables. In a previous study [1], an intrusive PC formulation was implemented to a deterministic Euler code. This intrusive method involves substituting the PC expansions into fluxes and Jacobians, and projecting them onto a random basis function in the form of Hermite Polynomials. Despite its power in uncertainty propagation modeling, this intrusive method can be relatively difficult, expensive, and time consuming to implement to complex problems such as the full Navier-Stokes simulation of 3-D, viscous, turbulent flows around realistic aerospace vehicles or multi-system level simulations which include the interaction of many different codes from different disciplines. In this abstract, we give a brief description of a non-intrusive PC method, which is relatively easy to implement. Our preliminary results with this method includes two stochastic flow problems: (a) steady, subsonic, 2-D, zero-pressure gradient laminar boundary layer over a flat plate, which has the free-stream dynamic viscosity as the uncertain parameter and (b) inviscid, steady, supersonic, 2-D flow over a wedge which has an uncertainty in the wedge