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1. Physically Consistent Resolving Simulations of Turbulent Flows

   https://doi.org/10.3390/e26121044  

   Heinz, Stefan (December 2024, Entropy)

   Usually applied simulation methods for turbulent flows as large eddy simulation (LES), wall-modeled LES (WMLES), and detached eddy simulation (DES) face significant challenges: they are characterized by improper resolution variations and essential practical simulation problems given by huge computational cost, imbalanced resolution transitions, and resolution mismatch. Alternative simulation methods are described here. By using an extremal entropy analysis, it is shown how minimal error simulation methods can be designed. It is shown that these methods can overcome the typical shortcomings of usually applied simulation methods. A crucial ingredient of this analysis is the identification of a mathematically implied general hybridization mechanism, which is missing in existing methods. Applications to several complex high Reynolds number flow simulations reveal essential performance, functionality, and computational cost advantages of minimal error simulation methods. 

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2. Continuous Eddy Simulation vs. Resolution-Imposing Simulation Methods for Turbulent Flows

   https://doi.org/10.3390/fluids9010022  

   Fagbade, Adeyemi; Heinz, Stefan (January 2024, Fluids)

   The usual concept of simulation methods for turbulent flows is to impose a certain (partial) flow resolution. This concept becomes problematic away from limit regimes of no or an almost complete flow resolution: discrepancies between the imposed and actual flow resolution may imply an unreliable model behavior and high computational cost to compensate for simulation deficiencies. An exact mathematical approach based on variational analysis provides a solution to these problems. Minimal error continuous eddy simulation (CES) designed in this way enables simulations in which the model actively responds to variations in flow resolution by increasing or decreasing its contribution to the simulation as required. This paper presents the first application of CES methods to a moderately complex, relatively high Reynolds number turbulent flow simulation: the NASA wall-mounted hump flow. It is shown that CES performs equally well or better than almost resolving simulation methods at a little fraction of computational cost. Significant computational cost and performance advantages are reported in comparison to popular partially resolving simulation methods including detached eddy simulation and wall-modeled large eddy simulation. Characteristic features of the asymptotic flow structure are identified on the basis of CES simulations. 

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3. From Two-Equation Turbulence Models to Minimal Error Resolving Simulation Methods for Complex Turbulent Flows

   https://doi.org/10.3390/fluids7120368  

   Heinz, Stefan (December 2022, Fluids)

   Hybrid RANS-LES methods are supposed to provide major contributions to future turbulent flow simulations, in particular for reliable flow predictions under conditions where validation data are unavailable. However, existing hybrid RANS-LES methods suffer from essential problems. A solution to these problems is presented as a generalization of previously introduced continuous eddy simulation (CES) methods. These methods, obtained by relatively minor extensions of standard two-equation turbulence models, represent minimal error simulation methods. An essential observation presented here is that minimal error methods for incompressible flows can be extended to stratified and compressible flows, which opens the way to addressing relevant atmospheric science problems (mesoscale to microscale coupling) and aerospace problems (supersonic or hypersonic flow predictions). It is also reported that minimal error methods can provide valuable contributions to the design of consistent turbulence models under conditions of significant modeling uncertainties. 

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4. Large-Eddy Simulation of Flow over Boeing Gaussian Bump Using Multi-Agent Reinforcement Learning Wall Model

   https://doi.org/10.2514/6.2023-3985  

   Zhou, Di; Whitmore, Michael P.; Griffin, Kevin P.; Bae, Hyunji Jane (June 2023, American Institute of Aeronautics and Astronautics)

   We develop a wall model for large-eddy simulation (LES) that takes into account various pressure-gradient effects using multi-agent reinforcement learning. The model is trained using low-Reynolds-number flow over periodic hills with agents distributed on the wall at various computational grid points. It utilizes a wall eddy-viscosity formulation as the boundary condition to apply the modeled wall shear stress. Each agent receives states based on local instantaneous flow quantities at an off-wall location, computes a reward based on the estimated wall-shear stress, and provides an action to update the wall eddy viscosity at each time step. The trained wall model is validated in wall-modeled LES of flow over periodic hills at higher Reynolds numbers, and the results show the effectiveness of the model on flow with pressure gradients. The analysis of the trained model indicates that the model is capable of distinguishing between the various pressure gradient regimes present in the flow. To further assess the robustness of the developed wall model, simulations of flow over the Boeing Gaussian bump are conducted at a Reynolds number of 2 million, based on the free-stream velocity and the bump width. The results of mean skin friction and pressure on the bump surface, as well as the velocity statistics of the flow field, are compared to those obtained from equilibrium wall model (EQWM) simulations and published experimental data sets. The developed wall model is found to successfully capture the acceleration and deceleration of the turbulent boundary layer on the bump surface, providing better predictions of skin friction near the bump peak and exhibiting comparable performance to the EQWM with respect to the wall pressure and velocity field. We also conclude that the subgrid-scale model is crucial to the accurate prediction of the flow field, in particular the prediction of separation. 

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5. An Eulerian two-phase model investigation on wave-induced scour around a vertical circular cylinder

   Benjamin Tsai, Antoine Mathieu (September 2023, International Conference on Scour and Erosion)

   A three-dimensional Eulerian two-phase flow solver, SedFoam, has been developed for various sediment transport applications. The solver has demonstrated success in modeling sheet flow and bedforms driven by oscillatory flows using a Reynolds-averaged Navier–Stokes (RANS) formulation. However, the accuracy of the RANS formulation for more complex flows, such as scour around structures, requires further evaluation. SedFoam has recently been enhanced to incorporate two-phase large-eddy simulation (LES) capability. In this study, RANS and LES approaches are tested via a three-dimensional case of wave-induced local scour around a single vertical circular pile. Two laboratory experiments, one with an erodible bed and the other with a rigid bed, were chosen for simulation, with both experiments having a Keulegan-Carpenter (KC) number of 10. The k-ω turbulence closure was selected for the RANS simulation, and the dynamic Lagrangian subgrid closure was chosen for the LES simulation. Numerical results reveal that both RANS and LES simulations can resolve lee-wake vortices, although the vortices are significantly weaker in the RANS simulation. In comparison with the LES results, the RANS approach fails to predict horseshoe vortex with sufficient intensity, leading to an underestimation of scour hole depth development. Although the scour depths develop at a very similar rate in the early stage, the scour depth predicted by the RANS simulation quickly reaches equilibrium, while the LES simulation follows the measured trend. These findings indicate that a turbulence-resolving methodology, i.e. LES, is necessary for accurate scour simulations. 

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