Evolutionary Algorithm applied to Differential Reynolds Stress Model for Turbulent Boundary Layer subjected to an Adverse Pressure Gradient

Abstract

In this paper, an evolutionary algorithm is implemented for the purpose of performing symbolic regression in an attempt to improve Reynolds-Averaged-Navier-Stokes models predictions. In contrast to most machine learning algorithms, Gene Expression Programming generates a mathematical expression that can be directly interpreted and implemented into the Computational Fluid Dynamics solver. In this paper, the latter feature is exploited based on high-fidelity data to ascertain novel correlations for the pressure-strain correlation within a particular Differential Reynolds Stress Model, the Speziale-Sarkar-Gatski (SSG) model. The CFD-driven Gene Expression Programming is considered for the curved backward-facing step. Two models are obtained regarding the industrially relevant phenomenon of a turbulent boundary layer under adverse pressure gradient. The models are tested on a range of validation cases.

Modeling the wall shear stress in large-eddy simulation using graph neural networks

“…The machine-learning wall-shear-stress model developed in this paper relies on a database of direct numerical simulations or high-fidelity wall-resolved LESs which have been produced by various research groups (Figure 1). Namely, the database includes the simulations of: a fully developed channel flow at friction Reynolds number Re τ ¼ 180 (CF1), performed at Imperial College London (Agostini and Vincent, 2020) using the high-order flux reconstruction method of Huynh (2007) in the CFD code PyFR (Witherden et al, 2014); a fully developed channel flow at friction Reynolds number Re τ ¼ 950 (CF2), performed at the Polytechnic University of Madrid (Del Álamo and Jiménez, 2003;Lozano-Durán and Jiménez, 2014; using a hybrid Fourier-Chebyshev spectral method; a three-dimensional diffuser (3DD) corresponding to the geometry "Diffuser 1" of Cherry et al (2008), performed at Barcelona Supercomputing Center (Ercoftac, 2022) using the low-dissipation finite element scheme of Lehmkuhl et al (2019); a BFS, performed at CERFACS (Pouech et al, 2019;Pouech et al, 2021) using a cell-vertex finite-element method (Schönfeld and Rudgyard, 1999 with second-order accurate convection and diffusion schemes (Lax and Wendroff, 1960); a curved BFS based on the geometry of Disotell and Rumsey (Disotell and Rumsey, 2017;Alaya et al, 2020), hereafter referred to as adverse-pressuregradient (APG) simulation and performed at the University of Bergamo (Ercoftac, 2022) using discontinuous Galerkin method and a fifth order linearly implicit Rosenbrock scheme (Bassi et al, 2015;; and a NACA 65-009 blade cascade (N65) such as studied experimentally by Ma et al (2011) and Zambonini et al (2017), performed using a cell-vertex finite-element method (Schönfeld andRudgyard, 1999 anda two-step Taylor-Galerkin scheme (Colin andRudgyard, 2000). The N65 case is subdivided into two sub-configurations that differ only by the inlet boundary condition: a simulation with an incidence angle of 4°(N65a) and a simulation with an incidence angle of 7°(N65b).…”