Bound Preserving Lax-Wendroff Flux Reconstruction Method for Special Relativistic Hydrodynamics
<|reference_start|>Bound Preserving Lax-Wendroff Flux Reconstruction Method for Special Relativistic Hydrodynamics: Lax-Wendroff flux reconstruction (LWFR) schemes have high order of accuracy in both space and time despite having a single internal time step. Here, we design a Jacobian-free LWFR type scheme to solve the special relativistic hydrodynamics equations. We then blend the scheme with a first-order finite volume scheme to control the oscillations near discontinuities. We also use a scaling limiter to preserve the physical admissibility of the solution after ensuring the scheme is admissible in means. A particular focus is given to designing a discontinuity indicator model to detect the local non-smoothness in the solution of the highly non-linear relativistic hydrodynamics equations. Finally, we present the numerical results of a wide range of test cases with fourth and fifth-order schemes to show their robustness and efficiency.<|reference_end|>
@article{basak2024bound,
    title={Bound Preserving Lax-Wendroff Flux Reconstruction Method for Special
  Relativistic Hydrodynamics},
    author={Sujoy Basak, Arpit Babbar, Harish Kumar, Praveen Chandrashekar},
    journal={arXiv preprint arXiv:2409.15805},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.15805},
    primaryClass={math.NA cs.NA}
}