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u þ as a function of y þ . The black dotted lines are the DNS reference from Moser et al. 51 The blue dots represent the LES-LBM periodic channel flow results. The red hollow round dots are the present STG-LBM LES results.
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The paper presents a synthetic turbulence generator (STG) for the lattice Boltzmann method (LBM) at the interface of the Reynolds averaged Navier–Stokes (RANS) equations and the LBM large eddy simulation (LES). We first obtain the RANS velocity field from a finite volume solver at the interface. Then, we apply a numerical interpolation from the RAN...
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... all statistics will be gathered for another 8T. Figure 6 shows u þ as function of y þ at different streamwise positions, where ...
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... s w is the wall shear stress. In Fig. 6, mean velocity profiles at different cross sections at the streamwise direction have been compared with the DNS data by Moser et al. 51 and the periodic LES-LBM results. For x=d < 2, the STG-LBM captures the velocity near the wall well but gives slightly too small values for y þ > 10. However, for x=d ! 2 the STG-LBM predicts a mean ...
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... hÁi denotes the velocity field averaged in time. Similar to Fig. 6, STG-LBM failed to predict the normalized RMS results for the cross section at x=d ¼ 0 and x=d ¼ 1. This is reasonable since the inflow STG needs some space to develop into fully turbulent flow. For x=d ! 2, the STG-LBM LES simulations agree well with DNS data and the periodic LES-LBM reference. Figure 8 presents the normalized shear ...
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... results in Fig. 8, Figs. 6 and 7 show that the STG-LBM has an adaptation length of around x=d ¼ 2. Near the outlet (for x=d > 18:0), the normalized shear decreases due to the influence of the sponge zone. For SEM-LBM case, the SEM forcing takes place in the region of x=d ¼ 3:0 6 0:8, and the normalized shear velocity becomes trustworthy after x=d ¼ 7:5. As reported in ...
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... to Fig. 6, STG-LBM results match DNS data well for x=d ! 2. In Fig. 10, we present STG-LBM ensemble time and space average of u þ at cross sections along the streamwise direction from x=d ¼ 2 to x=d ¼ 16 at various time intervals, namely, from 1T to 2T, from 1:5T to 3T, from 3T to 6T. At t ¼ 2T, the STG-LBM shows acceptable discrepancies at x=d ...
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... The fully developed 3D turbulent channel flow simulation follows the configuration outlined in reference (Xue et al., 2022). The simulation begins from an initial zero-velocity field, with a square block of size 20 × 20 × 100 grid points positioned at x = 192. ...
Generating long-term trajectories of dissipative chaotic systems autoregressively is a highly challenging task. The inherent positive Lyapunov exponents amplify prediction errors over time. Many chaotic systems possess a crucial property - ergodicity on their attractors, which makes long-term prediction possible. State-of-the-art methods address ergodicity by preserving statistical properties using optimal transport techniques. However, these methods face scalability challenges due to the curse of dimensionality when matching distributions. To overcome this bottleneck, we propose a scalable transformer-based framework capable of stably generating long-term high-dimensional and high-resolution chaotic dynamics while preserving ergodicity. Our method is grounded in a physical perspective, revisiting the Von Neumann mean ergodic theorem to ensure the preservation of long-term statistics in the space. We introduce novel modifications to the attention mechanism, making the transformer architecture well-suited for learning large-scale chaotic systems. Compared to operator-based and transformer-based methods, our model achieves better performances across five metrics, from short-term prediction accuracy to long-term statistics. In addition to our methodological contributions, we introduce a new chaotic system benchmark: a machine learning dataset of 140k snapshots of turbulent channel flow along with various evaluation metrics for both short- and long-term performances, which is well-suited for machine learning research on chaotic systems.
... In the current study, IDDES data is trained at friction Reynolds number Re τ = 5200. Subsequently, this data is applied to the NN wall model for turbulent channel flow, incorporating a synthetic turbulent generator (STG) at the inlet as described by Xue et al. 46 , at Re τ = 1000, 2000, 5200. The results show good agreement with DNS data at coarse resolutions with the channel height of 20 lattice grid separations. ...
... Physics-informed neural network wall modelling framework for LBM In this subsection, we demonstrate the neural network wall model framework for the LBM. We simulate turbulent channel flow equipped with the STG at the inlet, while the outlet features a sponge region 46 . The coordinates of the LBM channel flow are denoted as x, y, z, corresponding to the streamwise, vertical, and span-wise directions, respectively. ...
... The turbulent channel flow serves as the validation case for the neural network wall model. In this setup, the channel flow employs a LBM-based synthetic turbulence generator at the inlet, as described in 46 , and incorporates a sponge layer at the outlet. The volume force, F w (x, t), exerted on the first layer of cells near the wall, can be characterized at location x as ...
Data-driven approaches offer novel opportunities for improving the performance of turbulent flow simulations, which are critical to wide-ranging applications from wind farms and aerodynamic designs to weather and climate forecasting. However, current methods for these simulations often require large amounts of data and computational resources. While data-driven methods have been extensively applied to the continuum Navier-Stokes equations, limited work has been done to integrate these methods with the highly scalable lattice Boltzmann method. Here, we present a physics-informed neural network framework for improving lattice Boltzmann-based simulations of near-wall turbulent flow. Using a small amount of data and integrating physical constraints, our model accurately predicts flow behaviour at a wide range of friction Reynolds numbers up to 1.0 × 10⁶. In contradistinction with other models that use direct numerical simulation datasets, this approach reduces data requirements by three orders of magnitude and allows for sparse grid configurations. Our work broadens the scope of lattice Boltzmann applications, enabling efficient large-scale simulations of turbulent flow in diverse contexts.
... Combined with an LES approach, this model accomplishes a standard Smagorinsky turbulence model which describes the energy damping of the sub-grid turbulence by a local eddy viscosity , t n such that . t 0 n n n = + Combined with an LES approach, this model utilizes a standard Smagorinsky turbulence model which describes the energy damping of the sub-grid turbulence by a local eddy viscosity [35][36][37][38]. The Smagorinsky model offers an intuitive appeal by providing a direct link between the resolved scales of motion and the subgrid-scale stresses, which are crucial for capturing the effects of turbulence. ...
In this paper, we used Lattice Boltzmann Method (LBM) to simulate the motion of saline gravity currents, considering different cases of water depth and salinity, aiming to evaluate the reliability of the LBM model and investigate the longitudinal properties of the gravity currents. The study in this paper was divided into two phases. The first phase explained the basic principles and the implementation process of the numerical model. By comparing the simulation results with laboratory experimental data, it was found that the simulation results were in good agreement with the laboratory experiments. The second phase of the study simulated the saline gravity currents with different water depths and salinities. It was observed that, due to the increasing density gradient, the front velocity of dense current increased with rising water depth and saltwater salinity, and the intensity of turbulence at the interface was enhanced.
... The lattice Boltzmann method(LBM) as a mesoscopic scale computational fluid dynamics method [1] has been widely recognized as an effective means of dealing with complex fluid flows [2]. For example, simulating the fluid flow of an infinitely wide wedge [3], coupled conduction and radiative heat transfer in composite materials [4] or indoor airflow [5]. ...
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... being K ¼ 1000, p ¼ À3, and z start ¼ N z À 50 grid points. 40 Finally, for the inlet velocity, we set a uniform profile with a superimposed, time-varying Gaussian noise, 41 needed to trigger the onset of instability at the outlet and aimed at mimicking the fully Physics of Fluids ARTICLE pubs.aip.org/aip/pof turbulent flow inside the round inlet pipe (not simulated to reduce the computational burden). ...
We present a highly optimized thread-safe lattice Boltzmann model in which the non-equilibrium part of the distribution function is locally reconstructed via recursivity of Hermite polynomials. Such a procedure allows the explicit incorporation of non-equilibrium moments of the distribution up to the order supported by the lattice. Thus, the proposed approach increases accuracy and stability at low viscosities without compromising performance and amenability to parallelization with respect to standard lattice Boltzmann models. The high-order thread-safe lattice Boltzmann is tested on two types of turbulent flows, namely, the turbulent channel flow at R e τ = 180 and the axisymmetric turbulent jet at Re = 7000; it delivers results in excellent agreement with reference data [direct numerical simulations (DNS), theory, and experiments] and (a) achieves peak performance [ ∼ 5 × 10 12 floating point operations (FLOP) per second and an arithmetic intensity of ∼ 7 FLOP / byte on a single graphic processing unit] by significantly reducing the memory footprint, (b) retains the algorithmic simplicity of standard lattice Boltzmann computing, and (c) allows to perform stable simulations at vanishingly low viscosities. Our findings open attractive prospects for high-performance simulations of realistic turbulent flows on GPU-based architectures. Such expectations are confirmed by excellent agreement among lattice Boltzmann, experimental, and DNS reference data.
... This methodology was further implemented into the lattice Boltzmann method framework for utilization at a hybrid RANS/LES-LBM interface. 33 Meanwhile, Saad et al. 34,35 addressed the shortcomings in mass conservation during the equation discretization process of the original method and developed open-source code for generating HIT. Recently, Guo et al. 36 extended the methodology introduced in Ref. 16 by employing Lund matrix transformations to more efficiently generate low-divergence inhomogeneous and anisotropic turbulence with arbitrary energy spectra. ...
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Resonant acoustic mixing (RAM) is a widely applied technology that utilizes low-frequency vertical harmonic vibration for fluid transfer and mixing. However, the current research on the mixing mechanism of RAM technology primarily focuses on the initial mixing stages, neglecting the subsequent turbulent transition. This lack of understanding hinders the further improvement of RAM technology. This paper aims to investigate the mixing mechanism of power-law non-Newtonian fluids (NNF) in RAM using the phase field model and the spectral analysis. The study focuses on understanding the facilitating effect of turbulent transition in mixing and explores the influence of the power-law index and the excitation parameter on the mixing characteristics. The results indicate that the flow field experiences Faraday instability due to the intense perturbation during transient mixing. This leads to the fluid mixing through the development of large-scale vortex to small-scale vortex. During this process, the frequency components of the flow field are distributed around the working frequency, demonstrating transient and broad frequency characteristics. The steady state then dissipates energy through the viscous dissipation of small-scale vortices and ultimately relies on the single-frequency components such as submultiples and multiples excited by the nonlinear effect to complete the mixing. The mixing effects of NNF and Newtonian fluids (NF) are essentially the same, but they consume energy in different ways. The mixing uniformity and mixing efficiency of NNF increase with increasing vibration acceleration and decrease with increasing vibration frequency. These findings provide new insights into the RAM mechanism of power-law NNF.
... For the turbulent flow at high Reynolds number, where the internal flow is no longer in an organized state, the flow field exhibits irregularities and contains vortices of various scales. Currently, there are three commonly used indirect numerical simulation methods, including Reynolds-averaged Navier-Stokes (RANS) method (Poroseva et al., 2016;Xue et al., 2022), large eddy simulation (LES) method Pendar and Roohi, 2016), and the detached eddy simulation (DES) method (Yin et al., 2015;Barone and Roy, 2006). ...
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This paper presents a study of the oil flow in a vertically arranged FZG gearbox. The splash and churning losses are experimentally evaluated using measurements of the resistance torque. Using high speed imaging, the instantaneous oil splashing inside the gearbox is also presented and compared with Computational Fluid Dynamics (CFD) results from the Lattice-Boltzmann method (LBM), instead of the traditional grid-based finite volume method. Four different configurations, including a spur gear based on the standard FZG geometry and a disc pair wheel-pinion with the same tip diameters of the standard geometries are used. The experiments cover a range from 500 to 3000 rpm and three oil levels are studied. For the CFD simulations, the same oil levels and rotational speeds are used. The experimental results indicate torque differences depending on the oil level and the configuration. The splashing pattern is also different from the standard horizontal FZG case, which is typically studied in the literature. On the other hand, the CFD simulations and flow visualization experiments are in relative agreement with one another. The similarities and differences in the torque values for the different configurations and the splashing pattern for both experiments and CFD simulations are analyzed and discussed.
