Constraint Preserving AFD-WENO Schemes for Relativistic Hydrodynamics with General Equations of State
Abstract
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.
Related
- Entropy-Stable and Physical-Constraint-Preserving DGSEM for Symmetry-Reduced General-Relativistic Hydrodynamics on Stationary Spacetimes
- Efficient Hybrid WENO Schemes for Special Relativistic Hydrodynamics with Adaptive Characteristic Reconstruction
- Entropy stable finite difference schemes for One-Fluid Two-Temperature Euler Non-equilibrium Hydrodynamics
- Remap for ALE Hydrodynamics via Direct Interpolation and Constraint Optimization
- The causal diamond of relativistic hydrodynamics
BibTeX
@misc{mishra2026constraint,
title = {{Constraint Preserving AFD-WENO Schemes for Relativistic Hydrodynamics with General Equations of State}},
author = {Pramodit Mishra and Shubham Upadhyay and Rakesh Kumar and Biswarup Biswas},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29654},
eprint = {2608.29654},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29654},
}
RIS
TY - UNPB
TI - Constraint Preserving AFD-WENO Schemes for Relativistic Hydrodynamics with General Equations of State
AU - Pramodit Mishra
AU - Shubham Upadhyay
AU - Rakesh Kumar
AU - Biswarup Biswas
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29654
UR - https://arxiv.org/abs/2608.29654
AB - 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.
ER -