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1. A GPU-Accelerated Particle Advection Methodology for 3D Lagrangian Coherent Structures in High-Speed Turbulent Boundary Layers

   Lagares C. and Araya G. (May 2023, Preprints)

   In this work, we introduce a scalable and efficient GPU-accelerated methodology for volumetric particle advection and finite-time Lyapunov exponent (FTLE) calculation, focusing on the analysis of Lagrangian Coherent Structures (LCS) in large-scale Direct Numerical Simulation (DNS) datasets across incompressible, supersonic, and hypersonic flow regimes. LCS play a significant role in turbulent boundary layer analysis, and our proposed methodology offers valuable insights into their behavior in various flow conditions. Our novel owning-cell locator method enables efficient, constant-time cell search, and the algorithm draws inspiration from classical search algorithms and modern multi-level approaches in numerical linear algebra. The proposed method is implemented for both multi-core CPUs and Nvidia GPUs, demonstrating strong scaling up to 32,768 CPU cores and up to 62 Nvidia V100 GPUs. By decoupling particle advection from other problems, we achieve modularity and extensibility, resulting in consistent parallel efficiency across different architectures. Our methodology was applied to calculate and visualize the FTLE on four turbulent boundary layers at different Reynolds and Mach numbers, revealing that coherent structures grow more isotropic proportional to the Mach number, and their inclination angle varies along the streamwise direction. We also observed increased anisotropy and FTLE organization at lower Reynolds numbers, with structures retaining coherency along both spanwise and streamwise directions. Additionally, we demonstrated the impact of lower temporal frequency sampling by upscaling with an efficient linear upsampler, preserving general trends with only 10% of the required storage. In summary, we present a particle search scheme for particle advection workloads in the context of visualizing LCS via FTLE that exhibits strong scaling performance and efficiency at scale. Our proposed algorithm is applicable across various domains requiring efficient search algorithms in large structured domains. While this manuscript focuses on the methodology and its application to LCS, an in-depth study of the physics and compressibility effects in LCS candidates will be explored in a future publication. 

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2. Aquila-LCS: GPU/CPU-Accelerated Particle Advection Schemes for Large-Scale Simulations

   Christian Lagares and Guillermo Araya (March 2024, Software X)

   We introduce Aquila-LCS, GPU and CPU optimized object-oriented, in-house codes for volumetric particle advection and 3D Finite-Time Lyapunov Exponent (FTLE) and Finite-Size Lyapunov Exponent (FSLE) computations. The purpose is to analyze 3D Lagrangian Coherent Structures (LCS) in large Direct Numerical Simulation (DNS) data. Our technique uses advanced search strategies for quick cell identification and efficient storage techniques. This solver scales effectively on both GPUs (up to 62 Nvidia V100 GPUs) and multi-core CPUs (up to 32,768 CPU cores), tracking up to 8-billion particles. We apply our approach to four turbulent boundary layers at different flow regimes and Reynolds numbers. 

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3. Lagrangian coherent structures and heat transport in compressible flows

   Lagares C. and Araya G. (September 2023, International Conference of Numerical Analysis and Applied Mathematics)

   In this study, we delve into the intricate relation between Lagrangian Coherent Structures (LCS), primarily represented by the finite-time Lyapunov exponent (FTLE), and instantaneous temperature in turbulent wall-bounded flow scenarios. Turbulence, despite its chaotic facade, houses coherent structures vital to understanding the dynamical behavior of fluid flows. Recognizing this, we leverage high-fidelity Direct Numerical Simulation (DNS) to investigate compressible flows, focusing on the attracting manifolds in FTLE and their correlation with instantaneous temperature. The consequent insights into the coupling between fluid dynamics and thermodynamics reveal the profound influence of vortex stretching, shearing, and compression on local thermodynamic characteristics. Notably, the interplay of instantaneous static temperature and fluid properties, along with the cascading nature of energy in turbulent flows, underpins the observed correlation. Furthermore, we leveraged a high-performance, scalable volumetric particle advection scheme for LCS determination in subsonic (M∞ = 0.8) and supersonic (M∞ = 1.6) turbulent boundary layers over adiabatic flat plates. 

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4. Direct numerical simulation of hypersonic turbulent boundary layers: effect of spatial evolution and Reynolds number

   https://doi.org/10.1017/jfm.2022.80  

   Huang, Junji; Duan, Lian; Choudhari, Meelan M. (April 2022, Journal of Fluid Mechanics)

   Direct numerical simulations (DNS) are performed to investigate the spatial evolution of flat-plate zero-pressure-gradient turbulent boundary layers over long streamwise domains ( $${>}300\delta _i$$ , with $$\delta _i$$ the inflow boundary-layer thickness) at three different Mach numbers, $2.5$ , $4.9$ and $10.9$ , with the surface temperatures ranging from quasiadiabatic to highly cooled conditions. The settlement of turbulence statistics into a fully developed equilibrium state of the turbulent boundary layer has been carefully monitored, either based on the satisfaction of the von Kármán integral equation or by comparing runs with different inflow turbulence generation techniques. The generated DNS database is used to characterize the streamwise evolution of multiple important variables in the high-Mach-number, cold-wall regime, including the skin friction, the Reynolds analogy factor, the shape factor, the Reynolds stresses, and the fluctuating wall quantities. The data confirm the validity of many classic and newer compressibility transformations at moderately high Reynolds numbers (up to friction Reynolds number $$Re_\tau \approx 1200$$ ) and show that, with proper scaling, the sizes of the near-wall streaks and superstructures are insensitive to the Mach number and wall cooling conditions. The strong wall cooling in the hypersonic cold-wall case is found to cause a significant increase in the size of the near-wall turbulence eddies (relative to the boundary-layer thickness), which leads to a reduced-scale separation between the large and small turbulence scales, and in turn to a lack of an outer peak in the spanwise spectra of the streamwise velocity in the logarithmic region. 

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5. Direct simulation of a Mach-5 turbulent spatially-developing boundary layer

   https://doi.org/10.2514/6.2019-3340  

   Araya, Guillermo; Lagares, Christian; Jansen, Kenneth E. (June 2019, 49th AIAA Fluid Dynamics Conference, AIAA AVIATION Forum, (AIAA 3131876) 17 - 21 June, Dallas, TX, 2019.)

   Direct Numerical Simulation (DNS) of turbulent spatially-developing boundary layers is performed over an isothermal flat plate at several flow regimes: incompressible, supersonic (Mach 2.5), and hypersonic (Mach 5). Similar low Reynolds numbers are considered in all cases with the purpose of assessing flow compressibility on low/high order flow statistics and on the dynamics of coherent structures of Zero Pressure Gradient (ZPG) flows. Turbulent inflow information is generated by following the concept of the rescaling-recycling approach introduced by Lund et al. (J. Comp. Phys. 140, 233-258, 1998); although, the proposed methodology is extended to high-speed flows. Furthermore, a dynamic approach is employed to connect the friction velocities at the inlet and recycle stations (i.e., there is no need of an empirical correlation as in Lund et al.). The Mach number effect has been mainly identified as significant changes in peak values of the streamwise velocity fluctuations. The vertical transport of Reynolds shear stresses is slightly away from the wall in the near wall region for the hypersonic case. Zones of low speed fluid exhibits a much more elongated shape in incompressible flow as compared with the compressible counterpart. Furthermore, low speed streaks exhibit a contorted, twisted and stretched form in incompressible flow while they are shorter and more isotropic in the supersonic flow. 

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