Intrusive polynomial chaos for CFD using OpenFOAM

We present the formulation and implementation of a stochas- tic Computational Fluid Dynamics (CFD) solver based on the widely used finite volume library - OpenFOAM. The solver employs General- ized Polynomial Chaos (gPC) expansion to (a) quantify the uncertainties associated with the fluid flow simulations, and (b) study the non-linear propagation of these uncertainties. The aim is to accurately estimate the uncertainty in the result of a CFD simulation at a lower computational cost than the standard Monte Carlo (MC) method. The gPC approach is based on the spectral decomposition of the random variables in terms of basis polynomials containing randomness and the unknown determin- istic expansion coefficients. As opposed to the mostly used non-intrusive approach, in this work, we use the intrusive variant of the gPC method in the sense that the deterministic equations are modified to directly solve for the (coupled) expansion coefficients. To this end, we have tested the intrusive gPC implementation for both the laminar and the turbulent flow problems in CFD. The results are in accordance with the analytical and the non-intrusive approaches. The stochastic solver thus developed, can serve as an alternative to perform uncertainty quantification, espe- cially when the non-intrusive methods are significantly expensive, which is mostly true for a lot of stochastic CFD problems