Artificial-neural-network-based nonlinear algebraic models for large-eddy simulation of compressible wall-bounded turbulence

Abstract

In this paper, we propose artificial-neural-network-based (ANN-based) nonlinear algebraic models for the large-eddy simulation (LES) of compressible wall-bounded turbulence. An innovative modification is applied to the invariants and the tensor bases of the nonlinear algebraic models through using the local grid widths along each direction to normalise the corresponding gradients of the flow variables. Furthermore, the dimensionless model coefficients are determined by the ANN method. The modified ANN-based nonlinear algebraic model (MANA model) has much higher correlation coefficients and much lower relative errors than the dynamic Smagorinsky model (DSM), Vreman model and wall-adapting local eddy-viscosity model in the a priori test. The significantly more accurate estimations of the mean subgrid-scale (SGS) fluxes of the kinetic energy and temperature variance are also obtained by the MANA models in the a priori test. Furthermore, in the a posteriori test, the MANA model can give much more accurate predictions of the flow statistics and the mean SGS fluxes of the kinetic energy and the temperature variance than other traditional eddy-viscosity models in compressible turbulent channel flows with untrained Reynolds numbers, Mach numbers and grid resolutions. The MANA model has a better performance in predicting the flow statistics in supersonic turbulent boundary layer. The MANA model can well predict both direct and inverse transfer of the kinetic energy and temperature variance, which overcomes the inherent shortcoming that the traditional eddy-viscosity models cannot predict the inverse energy transfer. Moreover, the MANA model is computationally more efficient than the DSM.

Reynolds number and wall cooling effects on correlations between the thermodynamic variables in hypersonic turbulent boundary layers

“…(2022) and Xu et al. (2023 b ) is introduced to demonstrate the correlations between the thermodynamic variables in the supersonic turbulent boundary layer. The fundamental parameters of the DNS with the free stream Mach number 2.25 used by Yu et al.…”

“…(2022) and Xu et al. (2023 b ) are listed in table 6. Similarly, the ‘M2T11-Re674’ case is extracted from the fully turbulent region of the ‘M2T11’ database and the fundamental parameters of the ‘M2T11-Re674’ case are listed in table 7.…”

Physics-agnostic and physics-infused machine learning for thin films flows: modelling, and predictions from small data

“…Flow control is also a popular field where machine learning is implemented (Sonoda et al 2023;Zhang, Fan & Zhou 2023). Recently, artificial neural network-based nonlinear algebraic models were presented for the LES of compressible wall-bounded turbulence (Xu et al 2023). A model based on a convolutional neural network is proposed so as to reconstruct the three-dimensional turbulent flows beneath a free surface using surface measurements, including the surface elevation and surface velocity (Xuan & Shen 2023).…”