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Data-driven turbulence modeling studies have reached such a stage that thefundamental framework is basically settled, but several essential issues remainthat strongly affect the performance, including accuracy, smoothness, andgeneralization capacity. Two problems are studied in the current research: (1)the processing of the Reynolds stress tensor and (2) the coupling methodbetween the machine learning turbulence model and flow solver. The firstdetermines the form of predicting targets and the resulting physicalcompleteness and interpretability. The second determines the training processand intrinsic relevance between the mean flow features and Reynolds stress. Forthe Reynolds stress processing issue, we perform the theoretical derivation toextend the relevant tensor arguments of Reynolds stress in addition to thestrain rate and rotation rate. Then, the tensor representation theorem isemployed to give the complete irreducible invariants and integrity basis. Inaddition, an adaptive regularization term is employed to enhance therepresentation performance. For the coupling issue, an iterative couplingdata-driven turbulence modeling framework with consistent convergence isproposed. The training data preparation, predicting target selection, andcomputation platform are illustrated. The framework is then applied to acanonical separated flow for verification. The mean flow results obtained bycoupling computation of the trained machine learning model and flow solver havehigh consistency with the direct numerical simulation true values, which provesthe validity of the current approach.

An iterative data-driven turbulence modeling framework based on Reynolds stress representation