arXiv subjects

Parv Khurana

Publications and source records attributed to Parv Khurana.

3 recordsLinked to original sources

arXiv2026

Low-Order Refined Preconditioning for Spectral/hp Element Method for Complex, 3D Geometries

Low-order refined (LOR) preconditioning replaces a high-order operator with a low-order discretisation on a refined nodal mesh. For tensor-product elements, the two operators are spectrally equivalent with bounds independent of the polynomial order $P$, but the construction does not extend directly to simplex and mixed-element discretisations. This work makes two contributions: it extends LOR preconditioning to simplex and mixed-element discretisations, including triangular, tetrahedral, and prismatic elements, and establishes a generalised Vandermonde transformation linking the modal and nodal LOR formulations, showing that the resulting preconditioned spectra and Krylov convergence are independent of the high-order basis. Numerical experiments show controlled iteration growth on triangular meshes despite increasing condition number, and controlled iteration counts up to $P=6$ on tetrahedral, prismatic, and mixed-element meshes. A single algebraic multigrid V-cycle per outer iteration gives the best balance of iteration count and cost. The method is applied to a production incompressible Navier-Stokes simulation of a race-car front-wing and wheel configuration, discretised on a mesh of $2.87\times10^6$ mixed prismatic and tetrahedral elements giving $32.2\times10^6$ pressure degrees of freedom at $P=3$. LOR reduces the mean pressure conjugate gradient (CG) iteration count from $235.3$ to $5.5$, and the pressure-solve time over 1000 timesteps by 16.1%, relative to the default production static-condensation diagonal preconditioner in Nektar++. The one-time cost of constructing the LOR preconditioner is amortised over the production simulation.

math.NA↗

arXiv2026

Flow behind the Imperial Front Wing: comparison of results from volumetric PTV experiment and Nektar++ simulations

High-fidelity simulations are increasingly adopted, due to advances in computational power and methods such as Direct Numerical Simulation (DNS) and hybrid Large-Eddy Simulation (LES). These approaches are particularly valuable for unsteady flows around complex geometries at high Reynolds numbers; however they still require careful experimental validation. Planar and stereo Particle Image Velocimetry (PIV) are widely used for measurements but limited by measurement-plane selection and their ability to capture vortices shapes and trajectories. This motivates the growing interest in volumetric techniques, historically difficult to implement in industrial settings. Recent advances in Particle Tracking Velocimetry (PTV) for measuring flows over large volumes make this approach suitable for validating numerical simulations of complex flows.This study compares volumetric PTV measurements against high-fidelity LES to assess the capabilities and limitations for industrial flows. The aim is to establish a benchmark PTV dataset for motorsport aerodynamics using the Shake-The-Box algorithm. The experiment was carried out in the 10x5 wind tunnel at Imperial College London equipped with a rolling road for ground effect simulation and capable of testing up to 50% scale F1 model. Volumetric PTV measurements were performed downstream of the open-source Imperial Front Wing (IFW) at Re=74896. Results are compared with planar PIV studies and implicit LES simulation using spectral h/p elements in Nektar++. This work addresses open questions in the literature concerning the wake of the IFW. Good quantitative agreement is observed in the wake topology. A previously unreported vortex is identified which has the key role of preventing the merging of other dominant structures. These results demonstrate the suitability of PTV and STB for industrial applications while providing a benchmark dataset for the IFW.

physics.flu-dyn↗

arXiv2025

Industrialisation of spectral/hp element method for incompressible, transitional flow around Formula 1 geometries

This study applies the high-fidelity spectral/hp element method using the open-source Nektar++ framework to simulate the unsteady, transitional flow around complex 3D geometries representative of the Formula 1 industry. This study extends the work on a previously investigated industrial benchmark, the Imperial Front Wing (IFW), derived from the McLaren MP4-17D race car's front wing and endplate design. A combined configuration of the IFW with a wheel in contact with a moving ground in a rolling state is considered, representing the first instance of such a configuration being simulated using higher-order methods. The rolling wheel combined with the IFW (IFW-W) provides the most realistic industrial configuration until now. The spectral/hp element method is applied to this test case to solve the incompressible Navier-Stokes equations, simulating the flow at a Reynolds number of $\mathbf{2.2 \times 10^5}$. Time-averaged results from the unsteady simulation are compared to experimental Particle Image Velocimetry (PIV) data to assess the model's fidelity, offering insights into its reliability for accurately representing key flow characteristics. This research addresses the challenges and requisites associated with achieving diverse levels of flow resolution using the under-resolved DNS/implicit LES approach.

physics.flu-dyn↗