A Data-Driven k-Equation-Based Framework for Modeling
Turbulence Using Sparse Regression
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cairney-hcairney-sm-aeroastro-2026-thesis.pdf
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Author(s)
Cairney, Hugh I.
Advisor(s)
Harris, Wesley L.
Date Issued
May 2026
Publisher
Massachusetts Institute of Technology
Abstract
This thesis presents a novel framework for modeling turbulence within the the context of the Reynolds-Averaged Navier-Stokes (RANS) equations. The proposed framework takes the form of a one-equation linear eddy viscosity model, leveraging the turbulent kinetic energy (TKE) to provide a velocity scale. The turbulent length scale is then obtained through the use of sparsity-promoting regression. This sparse regression approach enables the discovery of simple and interpretable expressions which relate the turbulent length scale to a set of local and non-dimensional mean flow features directly from data. In addition, the dissipation term in the TKE equation is modeled in one of two ways. In the first, a second regression is performed to learn a second length scale which represents the dissipative processes. In the second, the turbulent length scale is used directly to model the dissipation. The models are trained and tested using DNS data from a set of periodic hill channel flows, and the learned models are implemented in the open-source finite-volume solver OpenFOAM. Model consistency is enforced by using a CFD-in-the-loop iterative training procedure. A CFD-driven cross validation procedure reveals that the training procedure is able to learn models which provide improved predictions for three out of the four testing cases considered (where the degraded performance corresponds to a case where the baseline model already performs well). In addition, the learned models are found to correctly reduce the extent of the separated region when the baseline significantly overpredicts it. A comparison of the two treatments of the dissipation term also reveals that the case using the turbulent length scale directly to model dissipation also yields much more physically consistent results than the baseline or the other modeling case which attempts to learn an additional length scale for the dissipation.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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