SOLVING STOCHASTIC INVERSE PROBLEMS FOR CFD USING DATA-CONSISTENT INVERSION AND AN ADAPTIVE STOCHASTIC COLLOCATION METHOD

Abstract

We present a non-intrusive adaptive stochastic collocation method coupled with a data-consistent inference framework to optimize stochastic inverse problems solve in CFD. The purpose of the proposed data-consistent method is, given a model and some observed output probability density function (pdf), to build a new model input pdf which is consistent with both the model and the data. Solving stochastic inverse problems in CFD is however very costly, which is why we use a surrogate or metamodel in the data-consistent inference method. This surrogate model is built using an adaptive stochastic collocation approach based on a stochastic error estimator and simplex elements in the parameters space. The efficiency of the proposed method is evaluated on analytical test cases and two CFD configurations. The metamodel inference results are shown to be as accurate as crude Monte Carlo inferences while performing 103 less deterministic computations for smooth and discontinuous response surfaces. Moreover, the proposed method is shown to be able to reconstruct both an observed pdf on the data and a data-generating distribution in the uncertain parameter space under certain conditions.