A $4^{\rm th}$-order accurate finite volume method for ideal classical and special relativistic MHD based on pointwise reconstructions - IRFU-AIM
Journal Articles J.Comput.Phys. Year : 2024

A $4^{\rm th}$-order accurate finite volume method for ideal classical and special relativistic MHD based on pointwise reconstructions

Vittoria Berta
  • Function : Author
Andrea Mignone
  • Function : Author
Giancarlo Mattia
  • Function : Author

Abstract

We present a novel implementation of a genuinely $4^{\rm th}$-order accurate finite volume scheme for multidimensional classical and special relativistic magnetohydrodynamics (MHD) based on the constrained transport (CT) formalism. The scheme introduces several novel aspects when compared to its predecessors yielding a more efficient computational tool. Among the most relevant ones, our scheme exploits pointwise to pointwise reconstructions (rather than one-dimensional finite volume ones), employs the generic upwind constrained transport averaging and sophisticated limiting strategies that include both a discontinuity detector and an order reduction procedure. Selected numerical benchmarks demonstrate the accuracy and robustness of the method.
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hal-04267752 , version 1 (20-04-2024)

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Vittoria Berta, Andrea Mignone, Matteo Bugli, Giancarlo Mattia. A $4^{\rm th}$-order accurate finite volume method for ideal classical and special relativistic MHD based on pointwise reconstructions. J.Comput.Phys., 2024, 499, pp.112701. ⟨10.1016/j.jcp.2023.112701⟩. ⟨hal-04267752⟩
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