The use of the Reynolds force vector in a physics informed machine learning approach for predictive turbulence modeling

• Published in: Computers & fluids 2019-10, Vol.192, p.104258, Article 104258
• Main Authors: Cruz, Matheus A., Thompson, Roney L., Sampaio, Luiz E.B., Bacchi, Raphael D.A.
• Format: Article
• Language: English
• Subjects: Artificial intelligence; Computational fluid dynamics; Computer simulation; Divergence; Machine learning; Mathematical analysis; Mathematical models; Neural networks; Reynolds force vector; Reynolds stress; Tensors; Turbulence; Turbulent flow; Turbulent flows; Velocity distribution
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2019.104258

•New measures of the propagation error in a DNS database for the turbulent flow in a square duct are provided.•Data-driven models that have the Reynolds stress tensor as target are subjected to this error.•We propose to have as target, the Reynolds force vector, the divergence of the Reynolds stress tensor.•Results show that the proposed approach is promissing. Data-driven turbulence modeling is receiving considerable attention specially when Direct Numerical Simulations (DNS) are the physics-informed learning environment and Reynolds average Navier–Stokes (RANS) simulations are the injected environment. A caveat of such approach, is that some studies indicate the existence of an intrinsic error in the Reynolds stress tensor provided by reputable DNS databases that, although small, lead to a reconstructed mean velocity field with a flagrant inaccuracy. This fact imposes a huge challenge in data-driven and traditional RANS models and is becoming a concern in the very recent literature. In the present work, we propose to replace the Reynolds stress tensor by its divergence, the Reynolds force vector, as a target for the machine learning technique. Since the Reynolds force vector can be computed from first order statistics, this estimate is not contaminated by the errors associated with applying the divergence onto the Reynolds stress tensor available in the DNS databases, circumventing the problem exposed above. The turbulent flow through a square duct was chosen as the case to be analyzed. Employing a κ–ϵ RANS model as injection environment, the non-persistence-of-straining tensor to compose the set of inputs, and a neural network architecture as the ML technique to bridge the injected and learning environments, we compared the proposed strategy with the approach commonly used in the literature, i.e. to correct the Reynolds stress tensor. The results demonstrate that the Reynolds force vector correction is able to reconstruct the mean velocity field with a higher fidelity with respect to the DNS data.