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1. Reconstructing Turbulent Flows Using Physics-Aware Spatio-Temporal Dynamics and Test-Time Refinement

   Shengyu Chen, Tianshu Bao (April 2023, arXivorg)

   Simulating turbulence is critical for many societally important applications in aerospace engineering, environmental science, the energy industry, and biomedicine. Large eddy simulation (LES) has been widely used as an alternative to direct numerical simulation (DNS) for simulating turbulent flows due to its reduced computational cost. However, LES is unable to capture all of the scales of turbulent transport accurately. Reconstructing DNS from low-resolution LES is critical for many scientific and engineering disciplines, but it poses many challenges to existing super-resolution methods due to the spatio-temporal complexity of turbulent flows. In this work, we propose a new physics-guided neural network for reconstructing the sequential DNS from low-resolution LES data. The proposed method leverages the partial differential equation that underlies the flow dynamics in the design of spatio-temporal model architecture. A degradation-based refinement method is also developed to enforce physical constraints and further reduce the accumulated reconstruction errors over long periods. The results on two different types of turbulent flow data confirm the superiority of the proposed method in reconstructing the high-resolution DNS data and preserving the physical characteristics of flow transport. 

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2. Physics guided neural networks for spatio-temporal super-resolution of turbulent flows

   Tianshu Bao, Shengyu Chen (August 2022, Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR)

   Direct numerical simulation (DNS) of turbulent flows is computationally expensive and cannot be applied to flows with large Reynolds numbers. Low-resolution large eddy simulation (LES) is a popular alternative, but it is unable to capture all of the scales of turbulent transport accurately. Reconstructing DNS from low-resolution LES is critical for large-scale simulation in many scientific and engineering disciplines, but it poses many challenges to existing super-resolution methods due to the complexity of turbulent flows and computational cost of generating frequent LES data. We propose a physics-guided neural network for reconstructing frequent DNS from sparse LES data by enhancing its spatial resolution and temporal frequency. Our proposed method consists of a partial differential equation (PDE)-based recurrent unit for capturing underlying temporal processes and a physics-guided super-resolution model that incorporates additional physical constraints. We demonstrate the effectiveness of both components in reconstructing the Taylor-Green Vortex using sparse LES data. Moreover, we show that the proposed recurrent unit can preserve the physical characteristics of turbulent flows by leveraging the physical relationships in the Navier-Stokes equation. 

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3. PeleLM-FDF large eddy simulator of turbulent reacting flows

   A. AITZHAN, S. SAMMAK (June 2023, Combustion theory and modelling)

   Taylor and Francis (Ed.)

   A new computational methodology, termed ‘PeleLM-FDF’ is developed and utilised for high fidelity large eddy simulation (LES) of complex turbulent combustion systems. This methodology is constructed via a hybrid scheme combining the Eulerian PeleLM base flow solver with the Lagrangian Monte Carlo simulator of the filtered density func- tion (FDF) for the subgrid scale reactive scalars. The resulting methodology is capable of simulating some of the most intricate physics of complex turbulence-combustion interactions. This is demonstrated by LES of a non-premixed CO/H2 temporally evolv- ing jet flame. The chemistry is modelled via a skeletal kinetics model, and the results are appraised via a posteriori comparisons against direct numerical simulation (DNS) data of the same flame. Excellent agreements are observed for the time evolution of various statistics of the thermo-chemical quantities, including the manifolds of the multi-scalar mixing. The new methodology is capable of capturing the complex phe- nomena of flame-extinction and re-ignition at a 1/512 of the computational cost of the DNS. The high fidelity and the computational affordability of the new PeleLM-FDF solver warrants its consideration for LES of practical turbulent combustion systems. 

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4. Implicit Subgrid-Scale Modeling of a Mach 2.5 Spatially Developing Turbulent Boundary Layer

   https://doi.org/10.3390/e24040555  

   Araya, Guillermo; Lagares, Christian (April 2022, Entropy)

   We employ numerically implicit subgrid-scale modeling provided by the well-known streamlined upwind/Petrov–Galerkin stabilization for the finite element discretization of advection–diffusion problems in a Large Eddy Simulation (LES) approach. Whereas its original purpose was to provide sufficient algorithmic dissipation for a stable and convergent numerical method, more recently, it has been utilized as a subgrid-scale (SGS) model to account for the effect of small scales, unresolvable by the discretization. The freestream Mach number is 2.5, and direct comparison with a DNS database from our research group, as well as with experiments from the literature of adiabatic supersonic spatially turbulent boundary layers, is performed. Turbulent inflow conditions are generated via our dynamic rescaling–recycling approach, recently extended to high-speed flows. Focus is given to the assessment of the resolved Reynolds stresses. In addition, flow visualization is performed to obtain a much better insight into the physics of the flow. A weak compressibility effect is observed on thermal turbulent structures based on two-point correlations (IC vs. supersonic). The Reynolds analogy (u′ vs. t′) approximately holds for the supersonic regime, but to a lesser extent than previously observed in incompressible (IC) turbulent boundary layers, where temperature was assumed as a passive scalar. A much longer power law behavior of the mean streamwise velocity is computed in the outer region when compared to the log law at Mach 2.5. Implicit LES has shown very good performance in Mach 2.5 adiabatic flat plates in terms of the mean flow (i.e., Cf and UVD+). iLES significantly overpredicts the peak values of u′, and consequently Reynolds shear stress peaks, in the buffer layer. However, excellent agreement between the turbulence intensities and Reynolds shear stresses is accomplished in the outer region by the present iLES with respect to the external DNS database at similar Reynolds numbers. 

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5. Deep learning closure models for large-eddy simulation of flows around bluff bodies

   https://doi.org/10.1017/jfm.2023.446  

   Sirignano, Justin; MacArt, Jonathan F. (July 2023, Journal of Fluid Mechanics)

   Near-wall flow simulation remains a central challenge in aerodynamics modelling: Reynolds-averaged Navier–Stokes predictions of separated flows are often inaccurate, and large-eddy simulation (LES) can require prohibitively small near-wall mesh sizes. A deep learning (DL) closure model for LES is developed by introducing untrained neural networks into the governing equations and training in situ for incompressible flows around rectangular prisms at moderate Reynolds numbers. The DL-LES models are trained using adjoint partial differential equation (PDE) optimization methods to match, as closely as possible, direct numerical simulation (DNS) data. They are then evaluated out-of-sample – for aspect ratios, Reynolds numbers and bluff-body geometries not included in the training data – and compared with standard LES models. The DL-LES models outperform these models and are able to achieve accurate LES predictions on a relatively coarse mesh (downsampled from the DNS mesh by factors of four or eight in each Cartesian direction). We study the accuracy of the DL-LES model for predicting the drag coefficient, near-wall and far-field mean flow, and resolved Reynolds stress. A crucial challenge is that the LES quantities of interest are the steady-state flow statistics; for example, a time-averaged velocity component $$\langle {u}_i\rangle (x) = \lim _{t \rightarrow \infty } ({1}/{t}) \int _0^t u_i(s,x)\, {\rm d}s$$ . Calculating the steady-state flow statistics therefore requires simulating the DL-LES equations over a large number of flow times through the domain. It is a non-trivial question whether an unsteady PDE model with a functional form defined by a deep neural network can remain stable and accurate on $$t \in [0, \infty )$$ , especially when trained over comparatively short time intervals. Our results demonstrate that the DL-LES models are accurate and stable over long time horizons, which enables the estimation of the steady-state mean velocity, fluctuations and drag coefficient of turbulent flows around bluff bodies relevant to aerodynamics applications. 

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