In this study, the unsteady Reynolds-averaged Navier-Stokes (URANS) equations are employed in conjunction with the Menter Shear Stress Transport (SST)-Scale-Adaptive Simulation (SAS) turbulence model in compressible flow, unstructured mesh and complex geometry. Whereas, other scale-resolving approaches in space and time, such as Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES), supply more comprehensive information about the turbulent energy spectra of the fluctuating component of the flow; however, previously mentioned avenues imply computationally intensive situations, usually performed over structured meshes and relatively simply geometries. In contrast, the SAS approach is designed according to “physically” prescribed length scales of the flow. More precisely, it operates by locally comparing the length scale of the modelled turbulence to the von Karman length scale (which is prescribed according to local fluid velocity derivatives and depends on the grid point distribution in the computational domain). This length scale ratio allows the flow to dynamically adjust the local eddy viscosity in order to better capture the large scale motions (LSM) in unsteady regions of URANS simulations. While SAS may be constrained to model only low flow frequencies or waivenumbers (i.e., LSM), its versatility and computational low-cost make it attractive to obtain a quick first insight of the flow physics; particularly, in those situations dominated by strong flow unsteadiness. The selected numerical application is the well-known M219 three-dimensional rectangular acoustic cavity from the literature at two different freestream Mach numbers, M∞ (0.85 and 1.35) and a length-to-depth ratio of 5:1. Thus, we consider the “deep configuration" in experiments by Henshaw. The SST-SAS model has demonstrated a satisfactory compromise between simplicity, accuracy and flow physics description.

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.