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Mathematics > Numerical Analysis

arXiv:2409.15805 (math)
[Submitted on 24 Sep 2024]

Title:Bound Preserving Lax-Wendroff Flux Reconstruction Method for Special Relativistic Hydrodynamics

Authors:Sujoy Basak, Arpit Babbar, Harish Kumar, Praveen Chandrashekar
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Abstract: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.
Subjects: Numerical Analysis (math.NA)
MSC classes: 65M60
ACM classes: G.1.8
Cite as: arXiv:2409.15805 [math.NA]
  (or arXiv:2409.15805v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2409.15805

Submission history

From: Sujoy Basak [view email]
[v1] Tue, 24 Sep 2024 07:07:29 UTC (5,836 KB)
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