CFD-driven symbolic identification of algebraic Reynolds-stress models

• Published in: Journal of computational physics Vol. 457; p. 111037
• Main Authors: Ben Hassan Saïdi, Ismaïl, Schmelzer, Martin, Cinnella, Paola, Grasso, Francesco
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 15.05.2022; Elsevier Science Ltd; Elsevier
• Subjects: Accuracy; Algebra; Algorithms; Computational fluid dynamics; Computational physics; Computing costs; Configuration management; Cost function; Eddy viscosity; Engineering Sciences; Flow separation; Fluid flow; Machine learning; Optimization; Polynomials; Response surface methodology; Reynolds number; Reynolds stress; Sensitivity analysis; Separated flows; Symbolic identification; Tensors; Training; Turbulence modelling; Two dimensional flow; Two dimensional models; Symbolic identification; Separated flows; Turbulence modelling; Symbolic identification Turbulence modelling Separated flows
• ISSN: 0021-9991; 1090-2716; 1090-2716
• DOI: 10.1016/j.jcp.2022.111037

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. The procedure enables training models against any target quantity of interest, computable as an output of the CFD model. Unlike the frozen-training approach, the proposed methodology is not restricted to data sets for which full fields of high-fidelity data, including second flow order statistics, 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 of the discovered models 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. The proposed deterministic symbolic identification approach constitutes a promising candidate for building accurate and robust RANS models customized for a given class of flows at moderate computational cost. •A symbolic identification method for data-driven learning of EARSMs is proposed•CFD-driven training may use sparse high-fidelity data for any quantity of interest•The approach is successfully applied to learn EARSMs for 2D separated flows•The learned models improve predictions over standard RANS models•The learned models generalize well to other 2D separated flows