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The study presents an innovative pipeline for processing, compressing, and remotely visualizing large-scale numerical simulations of fluid dynamics in a virtual wind tunnel (VWT), leveraging Virtual and Augmented Reality (VR/AR) for enhanced analysis and high-end visualization. The workflow addresses the challenges of handling massive databases obtained via Direct Numerical Simulation (DNS) while maintaining visual fidelity, promoting full immersion, and ensuring efficient rendering for user interaction. We are performing fully immersive visualization of high-fidelity numerical results of supersonic spatially-developing turbulent boundary layers (SDTBL) under strong concave/convex curvatures at a freestream Mach number of 2.86 (i.e., supersonic flow). 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). The process begins with .vts file input from DNS, which is visualized using the ParaView software. Multiple iso-contours for parameters such as velocity and temperature are generated, applying custom formulas to create visualizations at various floating-point precisions (16-bit, 32-bit, 64-bit). These visualizations, representing different fluid behaviors based on DNS with high spatial/temporal resolution and millions of “numerical sensors”, are treated as individual time frames and exported in GLTF format. Our approach demonstrates significant improvements in rendering speed and user experience, particularly when dealing with datasets comprising hundreds of high-resolution frames from Computational Fluid Dynamics (CFD) simulations. By utilizing server-side compression and cloud rendering, we overcome the limitations of on-device processing, enabling smooth and responsive interactions even with large, complex fluid dynamics datasets. This pipeline represents a substantial advancement in scientific visualization of fluid dynamics, offering researchers and engineers a powerful tool for exploring and analyzing large-scale CFD simulations in an immersive, intuitive environment. Additionally, we leverage Unity’s Profile Analyzer and Memory Profiling tools with the purpose of identifying major bottlenecks and resource-consuming events during contour running, with a keen focus on enhancing GPU and CPU efficiency. In conclusion, the materials and methods employed in this project were instrumental in systematically collecting, analyzing, and interpreting performance data from DNS databases. Future work will focus on optimizing compression algorithms for fluid-specific data and expanding the range of supported simulation parameters to enhance the pipeline’s versatility across various fluid dynamics applications. 

A transient stability flow analysis is performed using the unsteady laminar boundary layer equations. The flow dynamics are studied via the Navier–Stokes equations. In the case of external spatially developing flow, the differential equations are reduced via Prandtl or boundary-layer assumptions, consisting of continuity and momentum conservation equations. Prescription of streamwise pressure gradients (decelerating and accelerating flows) is carried out by an impulsively started Falkner–Skan (FS) or wedge-flow similarity flow solution in the case of flat plate or a Blasius solution for particular zero-pressure gradient case. The obtained mean streamwise velocity and its derivatives from FS flows are then inserted into the well-known Orr–Sommerfeld equation of small disturbances at different dimensionless times (τ). Finally, the corresponding eigenvalues are dynamically computed for temporal stability analysis. A finite difference algorithm is effectively applied to solve the Orr–Sommerfeld equations. It is observed that flow acceleration or favorable pressure gradients (FPGs) lead to a significantly shorter transient period before reaching steady-state conditions, as the developed shear layer is notably thinner compared to cases with adverse pressure gradients (APGs). During the transient phase (i.e., for τ<1), the majority of the flow modifications are confined to the innermost 20–25% of the boundary layer, in proximity to the wall. In the context of temporal flow stability, the magnitude of the pressure gradient is pivotal in determining the streamwise extent of the Tollmien–Schlichting (TS) waves. In highly accelerated laminar flows, these waves experience considerable elongation. Conversely, under the influence of a strong adverse pressure gradient, the characteristic streamwise length of the smallest unstable wavelength, which is necessary for destabilization via TS waves, is significantly reduced. Furthermore, flows subjected to acceleration (β > 0) exhibit a higher propensity to transition towards a more stable state during the initial transient phase. For instance, the time response required to reach the steady-state critical Reynolds number was approximately 1τ for β = 0.18 (FPG) and τ = 6.8 for β = −0.18 (APG). 

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.