Efficient Hybrid WENO Schemes for Special Relativistic Hydrodynamics with Adaptive Characteristic Reconstruction
Abstract
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.
Related
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BibTeX
@misc{kumar2026efficient,
title = {{Efficient Hybrid WENO Schemes for Special Relativistic Hydrodynamics with Adaptive Characteristic Reconstruction}},
author = {Rakesh Kumar and Biswarup Biswas and Asha Kumari Meena and Harish Kumar},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29776},
eprint = {2608.29776},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29776},
}
RIS
TY - UNPB
TI - Efficient Hybrid WENO Schemes for Special Relativistic Hydrodynamics with Adaptive Characteristic Reconstruction
AU - Rakesh Kumar
AU - Biswarup Biswas
AU - Asha Kumari Meena
AU - Harish Kumar
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29776
UR - https://arxiv.org/abs/2608.29776
AB - 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.
ER -