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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 article 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. 

Lossy compression techniques are ubiquitous in many fields including imagery and video; however, the incursion of such lossy compression techniques in the computational fluid dynamics community has not advanced to the same extent in decades. In this work, the lossy compression of high-fidelity direct numerical simulation (DNS) is evaluated to assess the impact on various parameters of engineering interest. A Mach 2.5, spatially developing turbulent boundary layer (SDTBL) at a moderately high Reynolds number has been selected as the subject of the study. The ZFP compression scheme was chosen as the core driving algorithm for this study as it was carefully crafted for scientific, floating point data. The resilience of spectral quantities as well as two-point correlations is highlighted. Notwithstanding, we also noted that point-wise values calculated in the physical domain were prone to quantization errors at high compression ratios. Further, we have also presented the impact on higher order statistics. In summary, we have demonstrated that high fidelity results are within reach while achieving 1.45x to 9.82x reductions in required storage over single precision, IEEE 754-compliant data values. 

High-speed, spatially-evolving turbulent boundary layers are of great importance across civilian and military applications. Furthermore, compressible boundary layers present additional challenges for energy and active scalar transport. Understanding transport phenomena is critical to efficient high-speed vehicle designs. Although at any instantaneous point in time a flow field may seem random, regions within the flow can exhibit coherency across space and time. These coherent structures play a key role in momentum and energy transport within the boundary layer. The two main categories for coherent structure identification are Eulerian and Lagrangian approaches. In this video, we focus on 4D (3D+Time) Lagrangian Coherent Structure (LCS), and the effect of wall curvature/temperature on these structures. We present the finite-time Lyapunov exponent (FTLE) for three wall thermal conditions (cooling, quasi-adiabatic and heating) for a concave wall curvature that builds on the experimental study by Donovan et al. (J. Fluid Mech., 259, 1-24, 1994). The flow is subject to a strong concave curvature (δ/R ~ -0.083, R is the curvature radius) followed by a very strong convex curvature (δ/R = 0.17). A GPU-accelerated particle simulation forms the basis for the 3-D FTLE where particles are advected over flow fields obtained via Direct Numerical Simulation (DNS) with high spatial/temporal resolution. We also show the cross-correlation between Q2 events (ejections) and the FTLE. The video is available at: https://gfm.aps.org/meetings/dfd-2022/63122e0e199e4c2da9a946a0