CFD-driven Symbolic Identification of Algebraic Reynolds-Stress Models

Abstract: A CFD-driven deterministic symbolic identification algorithm for learning explicit algebraic Reynolds-stress models (EARSM) from high-fidelity data is developed building on the frozen-training SpaRTA algorithm of [1]. Corrections for the Reynolds stress tensor and the production of transported turbulent quantities of a baseline linear eddy viscosity model (LEVM) are expressed as functions of tensor polynomials selected from a library of candidate functions. The CFD-driven training consists in solving a blackbox optimization problem in which the fitness of candidate EARSM models is evaluated by running RANS simulations. Unlike the frozen-training approach, the proposed methodology is not restricted to data sets for which full fields of high-fidelity data are available. However, the solution of a high-dimensional expensive blackbox function optimization problem is required. Several steps are then undertaken to reduce the associated computational burden. First, a sensitivity analysis is used to identify the most influential terms and to reduce the dimensionality of the search space. Afterwards, the Constrained Optimization using Response Surface (CORS) algorithm, which approximates the black-box cost function using a response surface constructed from a limited number of CFD solves, is used to find the optimal model parameters. Model discovery and cross-validation is performed for three configurations of 2D turbulent separated flows in channels of variable section using different sets of training data to show the flexibility of the method. The discovered models are then applied to the prediction of an unseen 2D separated flow with higher Reynolds number and different geometry. The predictions for the new case are shown to be not only more accurate than the baseline LEVM, but also of a multi-purpose EARSM model derived from purely physical arguments.