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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. 

The solution of compressible flow equations is of interest with many aerospace engineering applications. Past literature has focused primarily on the solution of Computational Fluid Dynamics (CFD) problems with low-order finite element and finite volume methods. High-order methods are more the norm nowadays, in both a finite element and a finite volume setting. In this paper, inviscid compressible flow of an ideal gas is solved with high-order spectral/hp stabilized formulations using uniform high-order spectral element methods. The Euler equations are solved with high-order spectral element methods. Traditional definitions of stabilization parameters used in conjunction with traditional low-order bilinear Lagrange-based polynomials provide diffused results when applied to the high-order context. Thus, a revision of the definitions of the stabilization parameters was needed in a high-order spectral/hp framework. We introduce revised stabilization parameters, τsupg, with low-order finite element solutions. We also reexamine two standard definitions of the shock-capturing parameter, δ: the first is described with entropy variables, and the other is the YZβ parameter. We focus on applications with the above introduced stabilization parameters and analyze an array of problems in the high-speed flow regime. We demonstrate spectral convergence for the Kovasznay flow problem in both L1 and L2 norms. We numerically validate the revised definitions of the stabilization parameter with Sod’s shock and the oblique shock problems and compare the solutions with the exact solutions available in the literature. The high-order formulation is further extended to solve shock reflection and two-dimensional explosion problems. Following, we solve flow past a two-dimensional step at a Mach number of 3.0 and numerically validate the shock standoff distance with results obtained from NASA Overflow 2.2 code. Compressible flow computations with high-order spectral methods are found to perform satisfactorily for this supersonic inflow problem configuration. We extend the formulation to solve the implosion problem. Furthermore, we test the stabilization parameters on a complex flow configuration of AS-202 capsule analyzing the flight envelope. The proposed stabilization parameters have shown robustness, providing excellent results for both simple and complex geometries.

 

Early researchers applied visualization techniques based on smoke and dye injections in order to describe coherent structures in turbulent flows. Generally speaking, visualization techniques have substantially evolved in the last few decades, spanning all disciplines. In recent times, Virtual Reality (VR) has revolutionized the way that visualization is carried out. In this study, we are performing fully immersive visualization of high-fidelity numerical results of supersonic spatially-developing turbulent boundary layers (SDTBL) under strong concave and concave curvatures and Mach = 2.86. The selected numerical tool is Direct Numerical Simulation (DNS) with high spatial/temporal resolution. The comprehensive DNS information sheds important light on the transport phenomena inside turbulent boundary layers subject to strong deceleration or Adverse Pressure Gradient (APG) caused by concave walls as well as to strong acceleration or Favorable Pressure Gradient (FPG) caused by convex walls at different wall thermal conditions (i.e., cold, adiabatic and hot walls). Another fluid dynamics example to be discussed is the high-speed crossflow-jet problem. We are extracting vortex core iso-surfaces via the Q-criterion to convert them to a file format readable by the HTC Vive VR and Varjo toolkit. Amidst the backdrop of cutting-edge progressions in both capabilities and User Interface (UI) enhancements of the VWT, researchers are now poised to delve into a realm of comprehensive understanding concerning SDTBL. Within this dynamic, fully immersive environment, the intricacies of flow development unfold before their eyes. The elevated UI refinements have bestowed users with remarkable freedom of movement across six directions and database selection, effectively amplifying their capacity for meticulous observation and incisive analysis of the animated flow phenomena 

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. 

This paper focuses on the laminar boundary layer startup process (momentum and thermal) in incompressible flows. The unsteady boundary layer equations can be solved via similarity analysis by normalizing the stream-wise (x), wall-normal (y) and time (t) coordinates by a variable η and τ, respectively. The resulting ODEs are solved by a finite difference explicit algorithm. This can be done for two cases: flat plate flow where the change in pressure are zero (Blasius solution) and wedge or Falkner-Skan flow where the changes in pressure can be favorable (FPG) or adverse (APG). In addition, transient passive scalar transport is examined by setting several Prandtl numbers in the governing equation at two different wall thermal conditions: isothermal and isoflux. Numerical solutions for the transient evolution of the momentum and thermal boundary layer profiles are compared with analytical approximations for both small times (unsteady flow) and large (steady-state flow) times. 

Direct Numerical Simulation (DNS) of spatially-developing turbulent boundary layers (SDTBL) is performed over isothermal/adiabatic flat plates for incompressible and compressible-subsonic (M∞ = 0.5 and 0.8) flow regimes. Similar low Reynolds numbers are considered in all cases with the purpose of assessing modest flow compressibility on low/high order flow statistics of Zero Pressure Gradient (ZPG) flows. The considered molecular Prandtl number is 0.72. Additionally, temperature is regarded as a passive scalar in the incompressible SDTBL with the purpose to examine differences in the thermal transport phenomena of subsonic flows, i.e., passive vs. active scalar. It was found that the Van Driest transform and Morkovin scaling are able to collapse incompressible and subsonic quantities very well. 

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.

 

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. 

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.