Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena in both time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade with the primary goal to decompose complex flows into a set of features most important for future state prediction and control, typically using a dimensionality reduction technique. In this work, a novel data-driven technique based on the power of deep neural networks for ROM of the unsteady fluid flows is introduced. An autoencoder network is used for nonlinear dimension reduction and feature extraction as an alternative for singular value decomposition (SVD). Then, the extracted features are used as an input for a long short-term memory (LSTM) network to predict the velocity field at future time instances. The proposed autoencoder-LSTM method is compared with non-intrusive reduced order models based on dynamic mode decomposition (DMD) and proper orthogonal decomposition. Moreover, an autoencoder-DMD algorithm is introduced for ROM, which uses the autoencoder network for dimensionality reduction rather than SVD rank truncation. The results show that the autoencoder-LSTM method is considerably capable of predicting fluid flow evolution, where higher values for the coefficient of determination R2 are obtained using autoencoder-LSTM compared to other models.

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Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations (PDEs). We employ PINNs for solving the Reynolds-averaged Navier-Stokes (RANS) equations for incompressible turbulent flows without any specific model or assumption for turbulence, and by taking only the data on the domain boundaries. We first show the applicability of PINNs for solving the Navier-Stokes equations for laminar flows by solving the Falkner-Skan boundary layer. We then apply PINNs for the simulation of four turbulent-flow cases, i.e. zero-pressure-gradient boundary layer, adverse-pressure-gradient boundary layer, and turbulent flows over an airfoil and the periodic hill. Our results show the excellent applicability of PINNs for laminar flows with strong pressure gradients, where predictions with less than 1% error can be obtained. For turbulent flows, we also obtain very good accuracy on simulation results even for the Reynolds-stress components.

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Purpose This paper aims to investigate numerical solution of transonic flow around NACA0012 airfoil under sinusoidal pitch oscillation. Accordingly, effects of the amplitude and frequency of oscillations on aerodynamic coefficients are evaluated and the efficiency of the turbulent models, K-ω shear-stress transport (SST), scale adaptive simulation (SAS) and delayed detached eddy simulation (DDES), in simulation of the nonlinear phenomena – i.e. the interaction between shock and boundary layer and the shock oscillations – is studied. Design/methodology/approach K-ω SST, SAS and DDES models are used as turbulence approaches. The numerical results are compared with available experimental and numerical information. Findings According to the results inside the buffet boundaries, the DDES turbulent model expresses results that are more appropriate; however, SAS and SST models are not efficient enough in evaluating the characteristics of nonlinear flow. Originality/value In this research study, hybrid RANS-LES turbulence model is engaged to simulate transonic flow around pitching NACA0012 airfoil, and results are compared to the SAS and Reynolds Average Navier–Stocks simulations as well as available numerical and experimental data. In addition, effects of the amplitude and frequency of oscillations on aerodynamic coefficients are evaluated in buffet regions.

We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulentflow-field data useful for flow analysis, reduced-order modeling, and flow control. Our approach is based on β-variational autoencoders (β-VAEs) and convolutional neural networks (CNNs), which allow us to extract non-linear modes from multi-scale turbulent flows while encouraging the learning of independent latent variables and penalizing the size of the latent vector. Moreover, we introduce an algorithm for ordering VAE-based modes with respect to their contribution to the reconstruction. We apply this method for non-linear mode decomposition of the turbulent flow through a simplified urban environment, where the flowfield data is obtained based on well-resolved large-eddy simulations (LESs). We demonstrate that by constraining the shape of the latent space, it is possible to motivate the orthogonality and extract a set of parsimonious modes sufficient for high-quality reconstruction. Our results show the excellent performance of the method in the reconstruction against linear-theory-based decompositions. Moreover, we compare our method with available AE-based models. We show the ability of our approach in the extraction of near-orthogonal modes that may lead to interpretability.

High-resolution reconstruction of flow-field data from low-resolution and noisy measurements is of interest due to the prevalence of such problems in experimental fluid mechanics, where the measurement data are in general sparse, incomplete and noisy. Deep-learning approaches have been shown suitable for such super-resolution tasks. However, a high number of high-resolution examples is needed, which may not be available for many cases. Moreover, the obtained predictions may lack in complying with the physical principles, e.g. mass and momentum conservation. Physics-informed deep learning provides frameworks for integrating data and physical laws for learning. In this study, we apply physics-informed neural networks (PINNs) for super-resolution of flow-field data both in time and space from a limited set of noisy measurements without having any high-resolution reference data. Our objective is to obtain a continuous solution of the problem, providing a physically-consistent prediction at any point in the solution domain. We demonstrate the applicability of PINNs for the super-resolution of flow-field data in time and space through three canonical cases: Burgers' equation, two-dimensional vortex shedding behind a circular cylinder and the minimal turbulent channel flow. The robustness of the models is also investigated by adding synthetic Gaussian noise. Our results show excellent capabilities of PINNs in the context of data augmentation for experiments in fluid mechanics.