arXiv subjects

Narsimha Reddy Rapaka

Publications and source records attributed to Narsimha Reddy Rapaka.

3 recordsLinked to original sources

arXiv2026

Stable, Compact, and Direct Ghost-Cell Reconstruction: A Non-Iterative Approach for Embedded-Boundary Methods

A direct, analytical, non-iterative ghost-cell reconstruction framework is developed for Cartesian-grid embedded-boundary methods. Analytical expressions impose Dirichlet and Neumann boundary conditions directly at the embedded boundary, eliminating intermediate image-point reconstruction, matrix inversion, and precomputation or storage of geometry-dependent reconstruction weights. For the Cartesian stencil considered, dependencies among neighboring ghost cells form a directed acyclic graph. A topological ordering partitions ghost cells into dependency levels, permitting level-by-level reconstruction without iterative updates. The formulation is combined with hybrid ghost cells (HGC), whose centers may lie on either side of the embedded boundary. This placement satisfies the linear reconstruction-stability criterion previously derived for scalar advection while retaining a compact nearest-neighbour Cartesian stencil. An extended-stencil classical ghost-cell formulation (CGC_ES) serves as a stability-preserving reference, distinguishing the effects of reconstruction stability and stencil compactness. The same analytical relations provide solution values and spatial gradients directly on the embedded boundary, enabling evaluation of pressure forces, wall stresses, drag, and lift without separate surface reconstruction or filtering. Simulations of flow past a circular cylinder and an airfoil show that the linear criterion remains a useful indicator of reconstruction stability for the nonlinear incompressible Navier-Stokes cases considered. Classical ghost-cell reconstruction develops spurious oscillations when the criterion is violated, whereas CGC_ES and HGC remain stable. HGC additionally satisfies the stability requirement with a compact nearest-neighbour stencil.

physics.flu-dyn↗

arXiv2026

Ultimate regime in Rayleigh-Darcy Convection

DNS of Rayleigh-Darcy convection in a 3D porous domain is performed at Ra $\in [10^3, 10^6]$ to investigate heat-transfer scaling, thermal boundary-layer dynamics, and flow-structure evolution in the unexplored ultimate regime. The Nu exhibits an approximately linear dependence on Ra throughout the investigated range. However, a distinct change in slope is observed at $Ra \approx 4\times10^5$, indicating the onset of the ultimate regime. For $Ra \leq 2.5\times10^5$, our scaling is 6.25% lower than that reported by \cite{hewitt2014high}, while for $Ra \geq 4\times10^5$ our results are within 1.24% of the extrapolated ultimate-regime prediction of \cite{pirozzoli2021towards}. Analysis of thermal structure reveals formation of near-wall protoplumes that merge into large-scale columnar megaplumes. With increasing Ra, the size of the protoplumes decreases, whereas the numbers increase, thus enhancing boundary-layer convection and heat transport. The thermal boundary-layer thickness scales as ~ Ra^{-1} and ~ Nu^{-1}, corroborating the persistence of linear heat-transfer scaling in the ultimate regime. The thermal dissipation is found to be increasingly shifting from the boundary layer to the bulk with increasing $Ra$, further indicating that the finer protoplumes efficiently transport heat from walls to bulk. The flow structures are quantified using the dominant length scale using the mean wavenumber ($\overline{k}$). It exhibits linear variation with $Ra$ for near-wall structures, with a higher slope in the ultimate regime, signifying finer protoplumes. At the mid-plane, a weaker scaling suggests that the megaplumes also become finer with increasing $Ra$ in the ultimate regime, thus leading to efficient heat transport in the bulk.

physics.flu-dyn↗

arXiv2025

Generalized Fourier Series: An N log2(N) extension for aperiodic functions that eliminates Gibbs oscillations

This article introduces the Generalized Fourier Series (GFS), a novel spectral method that extends the clas- sical Fourier series to non-periodic functions. GFS addresses key challenges such as the Gibbs phenomenon and poor convergence in non-periodic settings by decomposing functions into periodic and aperiodic com- ponents. The periodic part is represented using standard Fourier modes and efficiently computed via the Fast Fourier Transform (FFT). The aperiodic component employs adaptive, low-rank sinusoidal functions with non-harmonic modes, dynamically tuned to capture discontinuities and derivative jumps across domain boundaries. Unlike conventional Fourier extension methods, GFS achieves high accuracy without requiring compu- tational domain extensions, offering a compact and efficient representation of non-periodic functions. The adaptive low-rank approach ensures accuracy while minimizing computational overhead, typically involving additional complex modes for the aperiodic part. Furthermore, GFS demonstrates a high-resolution power, with degrees of freedom comparable to FFT in periodic domains, and maintains N log2(N) computational complexity. The effectiveness of GFS is validated through numerical experiments, showcasing its ability to approximate functions and their derivatives in non-periodic domains accurately. With its robust framework and minimal computational cost, GFS holds significant potential for advancing applications in numerical PDEs, signal processing, machine learning, and computational physics by providing a robust and efficient tool for high-accuracy function approximations.

math.NA↗