arXiv subjects

Akash Rodhiya

Publications and source records attributed to Akash Rodhiya.

3 recordsLinked to original sources

arXiv2026

The Asymptotic State of Decaying Turbulence

The long-time evolution of decaying homogeneous turbulence is a fundamental building block of the subject. We investigate the problem by using a comprehensive suite of Direct Numerical Simulations. The simulations cover initial Taylor microscale Reynolds numbers $Re_\lambda$ from $30 \text{ to } 145$, with multiple independent realizations obtained at each $Re_{\lambda}$ to ensure statistical robustness. The energy spectrum is initialized with the Birkhoff-Saffman (BS) form (with $E(k)\sim k^2$ for small $k$) in one case, and the Loitsianskii-Kolmogorov-Batchelor (LKB) form (with $E(k)\sim k^4$ for small $k$), in another. Simulations are performed for unprecedented durations, of the order of 200,000 initial eddy-turnover times in some instances. For both BS and LKB, the turbulent kinetic energy $En$ shows, after an initial transient, unambiguous power-law decay, $En\sim t^{-n}$, with nearly constant decay exponents $n$, whose values are consistent with past theoretical results (and thus not universal). We compute various length scales, second-order structure functions, and the spectral form at large wavenumbers; we note that an initially set $-5/3$ slope disappears quickly, while a perceptible $-1$ power region appears. In particular, we compare the present findings with predictions from the recent theory for decaying turbulence developed by Migdal 2026 Philos. Trans. R. Soc. A 384, 20250032. (doi:10.1098/rsta.2025.0032). The agreement for the BS case is excellent except for the large-wavenumber spectrum. A general discussion and assessment of results is provided in terms of the putative universality of energy decay. A main conclusion is that the energy decay is significantly influenced by ``boundary effects", and that universality likely manifests only when those effects are removed. Alternatively, it may be more useful to discuss the universality of enstrophy decay.

physics.flu-dyn↗

arXiv2025

Relative accuracy of turbulence simulations using pseudo-spectral and finite difference solvers

For a single timestep, a spectral solver is known to be more accurate than its finite-difference counterpart. However, as we show in this paper, turbulence simulations using the two methods have nearly the same accuracy. In this paper, we simulate forced hydrodynamic turbulence on a uniform 256$^3$ grid for Reynolds numbers 965, 1231, 1515, and 1994. We show that the two methods yield nearly the same evolution for the total energy and the flow profiles. In addition, the steady-state energy spectrum, energy flux, and probability distribution functions of the velocity and its derivatives are very similar. We argue that within a turbulence attractor, the numerical errors are likely to get cancelled (rather than get added up), which leads to similar results for the finite-difference and spectral methods. These findings are very valuable, considering that a parallel finite-difference simulation is more versatile and efficient (for large grids) than its spectral counterpart.

physics.flu-dyn↗

arXiv2022

A co-kurtosis based dimensionality reduction method for combustion datasets

Principal Component Analysis (PCA) is a dimensionality reduction technique widely used to reduce the computational cost associated with numerical simulations of combustion phenomena. However, PCA, which transforms the thermo-chemical state space based on eigenvectors of co-variance of the data, could fail to capture information regarding important localized chemical dynamics, such as the formation of ignition kernels, appearing as \rev{extreme-valued} samples in a dataset. In this paper, we propose an alternate dimensionality reduction procedure, co-kurtosis PCA (CoK-PCA), wherein the required principal vectors are computed from a high-order joint statistical moment, namely the co-kurtosis tensor, which may better identify directions in the state space that represent stiff dynamics. We first demonstrate the potential of the proposed CoK-PCA method using a synthetically generated dataset that is representative of typical combustion simulations. Thereafter, we characterize and contrast the accuracy of CoK-PCA against PCA for datasets representing spontaneous ignition of premixed ethylene-air in a simple homogeneous reactor and ethanol-fueled homogeneous charged compression ignition (HCCI) engine. Specifically, we compare the low-dimensional manifolds in terms of reconstruction errors of the original thermo-chemical state, and species production and heat release rates computed from the reconstructed state. \rev{The latter -- a comparison of species production and heat release rates -- is a more rigorous assessment of the accuracy of dimensionality reduction.} We find that, even using a simplistic linear reconstruction, the co-kurtosis based reduced manifold represents the original thermo-chemical state more accurately than PCA, especially in the regions where chemical reactions are important.

physics.flu-dyn↗