Neural networks of simple structures are used to construct a turbulence model for large-eddy simulation (LES). Data obtained by direct numerical simulation (DNS) of homogeneous isotropic turbulence are used to train neural networks. It is shown that two methods are effective for improvement of accuracy of the model: weighting data for training and addition of the second-order derivatives of velocity to the input variables. As a result, high correlation between the exact subgrid scale stress and the prediction by the neural network is obtained for large filter width; the correlation coefficient is about 0:9 and 0:8 for filter widths 48:8ηand 97:4η, respectively, where ηis the Kolmogorov scale. The models established by neural networks are close to but not identical with the gradient models. LES with the neural network model is performed for the homogeneous isotropic turbulence and the initial-value problem of the Taylor-Green vortices. The results obtained with the neural network model are in reasonable agreement with those of the filtered DNS. However, symmetry in the latter problem is broken since the neural network model does not possess rigorous symmetry under orthogonal transformations.
Improving turbulence control through explainable deep learning
The University of Manchester（曼彻斯特大学）；KTH Royal Institute of Technology（皇家理工学院）；Universitat Politécnica de Valéncia（瓦伦西亚理工大学）；Technical University Munich（慕尼黑工业大学）；University of Michigan（密歇根大学）
High accuracy and dynamic range have been some of the most prominent challenges when it comes to fine-scale turbulence measurements. The current commercial LDA processors, which perform the signal processing of Doppler bursts directly using hardware components, are essentially black boxes and in particular are renown for suffering from practical limitations that reduce the measurement reliability and accuracy. A transparently functioning novel LDA, utilizing advanced technologies and up-to-date hardware and software has therefore been developed to enhance the measurement quality and the dynami…
A recently introduced family of lattice Boltzmann (LB) models (Karlin, Bösch, Chikatamarla, Phys. Rev. E, 2014) is studied in detail for incompressible two-dimensional flows. A framework for developing LB models based on entropy considerations is laid out extensively. Second order rate of convergence is numerically confirmed and it is demonstrated that these entropy based models recover the Navier-Stokes solution in the hydrodynamic limit. Comparison with the standard Bhatnagar-Gross-Krook (LBGK) and the entropic lattice Boltzmann method (ELBM) demonstrates the superior stability and accuracy …
Jin (Phys. Fluids, vol. 31, 2019, p. 125102) proposed a new turbulence simulation method which shows better performance than other classic turbulence models. It is composed of a small-eddy-dissipation mixing length (SED-ML) model for calculating the reference solution and a parameter extension method for correcting the solution. The mechanism of this method is more deeply analyzed in this study to find out how to develop a turbulence model with a high accuracy and a low computational cost. The turbulent channel flows with Re_tau=821 and 2003 and decaying homogenous and isotropic turbulence are…
Data-driven turbulence modeling has been considered an effective method for improving the prediction accuracy of Reynolds-averaged Navier-Stokes equations. Related studies aimed to solve the discrepancy of traditional turbulence modeling by acquiring specific patterns from high-fidelity data through machine learning methods, such as artificial neural networks. The present study focuses on the unsmoothness and prediction error problems from the aspect of feature selection and processing. The selection criteria for the input features are summarized, and an effective input set is constructed. The…
This paper presents experimental and numerical analysis of grid generated turbulence with and without the effects of applied mean strain. We conduct a series of experiments on decaying grid generated turbulence and grid turbulence with mean strain. Experimental data of turbulence statistics including Reynolds stress anisotropies is collected, analyzed and then compared to the predictions of Reynolds Stress Models to assess their accuracy. The experimental data is used to evaluate the variability in the coefficients of the rate of dissipation model and the pressure strain correlation models use…
To fully evaluate a turbulent flow, Direct Numerical Simulation (DNS) is the most accurate method by far and requires considerable computational power and time; not optimum for industry standards. Developing an alternative model, providing results with reasonable accuracy would resolve this issue. Reynolds Averaged Navier Stokes (RANS) modeling has proven its worth in addressing this phenomenon. In this study, we investigated the RANS turbulence models from COMSOL for fully developed single-phase flow in a two-dimensional axisymmetric pipe domain with constant heating at the wall and periodic …
Modelling the sudden depressurisation of superheated liquids through nozzles is a challenge because the pressure drop causes rapid flash boiling of the liquid. The resulting jet usually demonstrates a wide range of structures, including ligaments and droplets, due to both mechanical and thermodynamic effects. As the simulation comprises increasingly numerous phenomena, the computational cost begins to increase. One way to moderate the additional cost is to use machine learning surrogacy for specific elements of the calculations. The present study presents a machine learning-assisted computatio…
This paper introduces open-source computational fluid dynamics software named open computational fluid dynamic code for scientific computation with graphics processing unit (GPU) system (OpenCFD-SCU), developed by the authors for direct numerical simulation (DNS) of compressible wall-bounded turbulence. This software is based on the finite difference method and is accelerated by the use of a GPU, which provides an acceleration by a factor of more than 200 compared with central processing unit (CPU) software based on the same algorithm and number of message passing interface (MPI) processes, an…
A new sub-grid-scale model is developed for studying influences of the Hall term on macroscopic aspects of magnetohydrodynamic turbulence. Although the Hall term makes numerical simulations extremely expensive by exciting high-wave-number coefficients and makes magnetohydrodynamic equations stiff, studying macroscopic aspects of magnetohydrodynamic turbulence together with the Hall term is meaningful since this term often influences not only sub-ion-scales but also macroscopic scales. A new sub-ion-scale sub-grid-scale model for large eddy simulations of Hall magnetohydrodynamic turbulence is …
In this paper, a turbulence model based on deep neural network is developed for turbulent flow around airfoil at high Reynolds numbers. According to the data got from the Spalart-Allmaras (SA) turbulence model, we build a neural network model that maps flow features to eddy viscosity. The model is then used to replace the SA turbulence model to mutually couple with the CFD solver. We build this suitable data-driven turbulence model mainly from the inputs, outputs features and loss function of the model. A feature selection method based on feature importance is also implemented. The results sho…
We study turbulent flows in pressure-driven ducts with square cross-section through direct numerical simulation in a wide enough range of Reynolds number to reach flow conditions which are representative of fully developed turbulence. Numerical simulations are carried out over extremely long integration times to get adequate convergence of the flow statistics, and specifically high-fidelity representation of the secondary motions which arise. The intensity of the latter is found to be in the order of 1-2% of the bulk velocity, and unaffected by Reynolds number variations. The smallness of the …
Physics-Informed Transformer operator for the prediction of three-dimensional turbulence
Southern University of Science and Technology（南方科技大学）；Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology（南方科技大学广东省湍流研究与应用重点实验室）；Shenzhen Key Laboratory of Complex Aerospace Flows, Southern University of Science and Technology（南方科技大学深圳市复杂航空航天流动重点实验室）
Turbulent problems in industrial applications are predominantly solved using Reynolds Averaged Navier Stokes (RANS) turbulence models. The accuracy of the RANS models is limited due to closure assumptions that induce uncertainty into the RANS modeling. We propose the use of deep learning algorithms via convolution neural networks along with data from direct numerical simulations to extract the optimal set of features that explain the evolution of turbulent flow statistics. Statistical tests are used to determine the correlation of these features with the variation in the quantities of interest…
We perform direct numerical simulations (DNSs) of emulsions in homogeneous, isotropic turbulence using a pseudopotential lattice-Boltzmann (PP-LB) method. Improving on previous literature by minimizing droplet dissolution and spurious currents, we show that the PP-LB technique is capable of long, stable simulations in certain parameter regions. Varying the dispersed phase volume fraction $ϕ$, we demonstrate that droplet breakup extracts kinetic energy from the larger scales while injecting energy into the smaller scales, increasingly with higher $ϕ$, with the Hinze scale dividing the two effec…
Accurate simulation of turbulent flow with separation is an important but challenging problem. In this paper, a data-driven Reynolds-averaged turbulence modeling approach, field inversion and machine learning is implemented to modify the Spalart-Allmaras model separately on three cases, namely, the S809 airfoil, a periodic hill and the GLC305 airfoil with ice shape 944. Field inversion based on a discrete adjoint method is used to quantify the model-form uncertainty with limited experimental data. An artificial neural network is trained to predict the model corrections with local flow features…
Motivated by specific data and accuracy requirements for building numerical databases of turbulent flows, data compression using spatio-temporal sub-sampling and local re-simulation is proposed. Numerical re-simulation experiments for decaying isotropic turbulence based on sub-sampled data are undertaken. The results and error analyses are used to establish parameter choices for sufficiently accurate sub-sampling and sub-domain re-simulation.
We compute, model, and predict drag reduction of an actuated turbulent boundary layer at a momentum thickness based Reynolds number of Reθ = 1000. The actuation is performed using spanwise traveling transversal surface waves parameterized by wavelength, amplitude, and period. The drag reduction for the set of actuation parameters is modeled using 71 large-eddy simulations (LES). This drag model allows to extrapolate outside the actuation domain for larger wavelengths and amplitudes. The modeling novelty is based on combining support vector regression for interpolation, a parameterized ridgelin…
Many numerical algorithms have been established to reconstruct pressure fields from measured kinematic data with noise by Particle Image Velocimetry (PIV), such as the Pressure Poisson solver and the Omni-Directional Integration (ODI) method. This study adopts Gaussian Process Regression (GPR), a probabilistic framework with an intrinsic de-noising mechanism to tackle drawbacks of traditional Pressure Poisson solver and compares the performance with ODI. To evaluate the accuracy of the algorithm, GPR and ODI are tested in detail in a canonical setup of forced homogeneous isotropic turbulence f…
Numerical schemes used for the integration of complex flow simulations should provide accurate solutions for the long time integrations these flows require. To this end, the performance of various high-order accurate numerical schemes is investigated for direct numerical simulations (DNS) of homogeneous isotropic two-dimensional decaying turbulent flows. The numerical accuracy of compact difference, explicit central difference, Arakawa, and dispersion-relation-preserving schemes are analyzed and compared with the Fourier-Galerkin pseudospectral scheme. In addition, several explicit Runge-Kutta…
In this paper we study decaying turbulence in fixed and rotating boxes in two dimen- sions using the particle method SPH. The boundaries are specified by boundary force particles, and the turbulence is initiated by a set of gaussian vortices. In the case of fixed boxes we recover the results of Clercx and his colleagues obtained using both a high accuracy spectral method and experiments. Our results for fixed boxes are also in close agreement with those of Monaghan1 and Robinson and Monaghan2 obtained using SPH. A feature of decaying turbulence in no-slip, square, fixed boundaries is that the …
In this paper, we train turbulence models based on convolutional neural networks. These learned turbulence models improve under-resolved low resolution solutions to the incompressible Navier-Stokes equations at simulation time. Our study involves the development of a differentiable numerical solver that supports the propagation of optimisation gradients through multiple solver steps. The significance of this property is demonstrated by the superior stability and accuracy of those models that unroll more solver steps during training. Furthermore, we introduce loss terms based on turbulence phys…
High-order methods and hybrid turbulence models have independently shown promise as means of decreasing the computational cost of scale-resolving simulations. The objective of this work is to develop the combination of these methods and analyze the effects of high-order discretizations on hybrid turbulence models, particularly with respect the optimal model parameters and the relative accuracy benefits compared to approaches such as under-resolved direct numerical simulation (URDNS). We employ the Partially-Averaged Navier-Stokes (PANS) approach using the flux reconstruction scheme on the flow…
The accuracy and resource consumption of the four different turbulence models based on the eddy viscosity assumption, namely, $k-\varepsilon$, two $k-ω$ and Spallart-Allmaram models, in modeling airships are investigated. The test airship shape is a conventional shape. Three different angles of attack are considered. The results are checked against the wind tunnel experimental data. The resource consumption study is based on the benchmark of 1500 iterations. Based on all data obtained it is evident that Spallart-Allmaras model is the most optimal one in the majority of cases.
Elastic turbulence is a chaotic regime that emerges in polymer solutions at low Reynolds numbers. A common way to ensure stability in numerical simulations of polymer solutions is to add artificially large polymer-stress diffusion. In order to assess the accuracy of this approach in the elastic-turbulence regime, we compare numerical simulations of the two-dimensional Oldroyd-B and FENE-P models sustained by a cellular force with and without artificial diffusion. We find that artificial diffusion can have a dramatic effect even on the large-scale properties of the flow and we show some of the …
PT-PINNs: A Parametric Engineering Turbulence Solver based on Physics-Informed Neural Networks
Zhejiang University（浙江大学）；Shanghai Institute for Advanced Study of Zhejiang University（浙江大学上海高等研究院）；State Key Laboratory of Clean Energy Utilization（清洁能源利用国家重点实验室）
The aim of the present paper is to provide a comparison between several finite-volume methods of different numerical accuracy: second-order Godunov method with PPM interpolation and high-order finite-volume WENO method. The results show that while on a smooth problem the high-order method perform better than the second-order one, when the solution contains a shock all the methods collapse to first-order accuracy. In the context of the decay of compressible homogeneous isotropic turbulence with shocklets, the actual overall order of accuracy of the methods reduces to second-order, despite the u…
The performance of high-order gas-kinetic scheme (HGKS) has been investigated for the direct numerical simulation (DNS) of isotropic compressible turbulence up to the supersonic regime. Due to the multi-scale nature and coupled temporal-spatial evolution process, HGKS provides a valid tool for the numerical simulation of compressible turbulent flow. Based on the domain decomposition and message passing interface (MPI), a parallel HGKS code is developed for large-scale computation in this paper. The standard tests from the nearly incompressible flow to the supersonic one, including Taylor-Green…
Quantifying Out-of-Training Uncertainty of Neural-Network based Turbulence Closures
Mechanical and Aerospace Engineering, Utah State University（犹他州立大学机械与航空航天工程学院）；Idaho National Laboratory（爱达荷国家实验室）；School of Nuclear Science and Engineering, Oregon State University（俄勒冈州立大学核科学与工程学院）
(Abridged) In the implicit large eddy simulation (ILES) paradigm, the dissipative nature of high-resolution shock-capturing schemes is exploited to provide an implicit model of turbulence. Recent 3D simulations suggest that turbulence might play a crucial role in core-collapse supernova explosions, however the fidelity with which turbulence is simulated in these studies is unclear. Especially considering that the accuracy of ILES for the regime of interest in CCSN, weakly compressible and strongly anisotropic, has not been systematically assessed before. In this paper we assess the accuracy of…
