arXiv subjects

Rakesh Kumar

Publications and source records attributed to Rakesh Kumar.

3 recordsLinked to original sources

arXiv2026

Constraint Preserving AFD-WENO Schemes for Relativistic Hydrodynamics with General Equations of State

We develop a high-order physical-constraint-preserving (PCP) alternative finite difference weighted essentially non-oscillatory (AFD-WENO) scheme for the special relativistic hydrodynamics equations with general equations of state. The proposed scheme comprises two key limiters: a state limiter, which acts after the WENO state interpolation step, and a flux limiter, which acts on the final high-order fluxes. The state limiter ensures that the interpolated states are physically admissible, while the flux limiter ensures that the numerical fluxes are physically admissible. The resulting scheme is rigorously proved to satisfy the physical constraints. Incorporating multiple WENO interpolation techniques, including an improved adaptive-order formulation (WENO-AOI), the method is validated through extensive one- and two-dimensional numerical benchmarks with various equations of state. The numerical results demonstrate high-order accuracy, sharp resolution of discontinuities, and robust stability in extreme relativistic regimes.

math.NA↗

arXiv2026

Efficient Hybrid WENO Schemes for Special Relativistic Hydrodynamics with Adaptive Characteristic Reconstruction

Special relativistic hydrodynamics (SRHD) equations arise in the modeling of high-speed fluid flows encountered in astrophysical phenomena such as jets, supernova explosions, and gamma-ray bursts. Owing to their highly nonlinear hyperbolic nature, solutions often develop strong discontinuities, making the design of stable and accurate numerical schemes challenging. Although Weighted Essentially Non-Oscillatory (WENO) schemes are widely used for such problems, component-wise WENO reconstruction may produce spurious oscillations near discontinuities. On the other hand, characteristic-wise WENO reconstruction provides accurate non-oscillatory solutions for systems of conservation laws, but it involves the computation of eigenvectors in each cell, which leads to high computational cost. In this work, we intend to develop hybrid schemes which maintain the non-oscillatory feature of characteristic-wise WENO while being less costly. We propose three hybrid schemes, namely the H1-WENO, H2-WENO, and H3-WENO schemes, based on a new troubled-cell indicator constructed from the smoothness indicators of the WENO scheme. The proposed troubled-cell indicator effectively distinguishes smooth and discontinuous regions, allowing the hybrid schemes to employ inexpensive reconstructions in smooth regions and the characteristic-wise WENO reconstruction only near discontinuities. Numerical experiments demonstrate that the proposed schemes retain the accuracy and robustness of characteristic-wise WENO methods while significantly reducing the computational cost. In particular, the H1-WENO scheme achieves an approximately 30--40% improvement in computational efficiency compared to the standard WENO scheme in 2D test cases.

math.NA↗

arXiv2026

Ground-to-Satellite Localization in Unconstrained Image Collections for 3D Scene Reconstruction

Ground image localization with respect to satellite imagery is a key enabler for metrically-accurate, geo-localized 3D scene reconstruction from unconstrained image collections. Existing cross-view localization methods have strict requirements such as panoramic imagery or known initial locations, limiting their applicability for in-the-wild reconstruction settings. We propose a robust hierarchical cross-view localization framework that leverages geometric constraints from Structure-from-Motion (SfM) models derived from unconstrained ground image collections. Our method generates coarse-to-fine pose hypotheses through a cross-view matching approach and aggregates noisy predictions across SfM model(s) using Kernel Density Estimation to recover consensus alignments while filtering outliers. Experiments demonstrate reliable localization performance from challenging image collections. Empirically we found satellite-referenced alignment enables accurate metric scale estimation, doppelgänger detection, and merging of disjoint SfM reconstructions, resulting in more complete, geo-localized site models than are possible with SfM alone.

cs.CV↗