On the Development of the 3d Euler Equations Using Intrusive Pce for Uncertainty Quantification

Abstract

Abstract. This paper presents a method for the quantification of uncertainty propagation using intrusive Polynomial Chaos Expansion (iPCE) in CFD. In constrast to commonly implemented non-intrusive methods which take advantage of existing CFD evaluation software in order to quantify the statistical behavior of the flow, an intrusive PCE method is developed and implemented to the 3D Euler equations. Uncertainties are introduced through the flow conditions and their propagation throughout the flow field is quantified. A Probability Density Function (PDF) is assumed for each uncertain flow condition and the generalized PCE inviscid equations for the corresponding coefficient fields of the flow variables are derived. Already known properties of the equations, such as the first order-homogeneity, are found to hold in the new set of the equations. The discretization schemes are adapted to the new set of governing equations while a systematic approach to the corresponding eigenproblem is introduced. The method is applied to 3D inviscid flow cases for which the mean value and the standard deviation of specific flow quantities characterizing the flow are quantified and compared with those computed by the non-intrusive PCE and Monte-Carlo methods.