Simulating magnetized neutron stars with discontinuous Galerkin methods

Deppe, Nils; Hébert, François; Kidder, Lawrence E.; Throwe, William; Anantpurkar, Isha; Armaza, Cristóbal; Bonilla, Gabriel S.; Boyle, Michael; Chaudhary, Himanshu; Duez, Matthew D.; Fischer, Nils; Foucart, François; Giesler, Matthew; Guo, Jason S.; Kim, Yoonsoo; Kumar, P.; Legred, Isaac; Li, Dongjun; Lovelace, Geoffrey; Ma, Sizheng; Macedo, Alexandra Lorandi; Melchor, D. A.; Morales, Marlo; Moxon, Jordan; Nelli, Kyle C.; O’Shea, E.; Pfeiffer, H. P.; Ramirez, T. D.; Rüter, Hannes R.; Sanchez, J. H.; Scheel, Mark A.; Thomas, Sierra; Vieira, D.; A., Wittek, Nikolas; Wlodarczyk, T.; Teukolsky, Saul A.

doi:10.1103/physrevd.105.123031

Cited by 7 publications

(25 citation statements)

References 82 publications

(111 reference statements)

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“…Unless stated otherwise, the second-order reconstruction scheme is monotonized central [36]. See [45] for details of the implementation in SpECTRE and [46][47][48] for more detailed discussions of the GRMHD system. All simulations are performed using SpECTRE [49] with the implementation of the algorithms described being publicly available.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…We perform simulations of both magnetized and non-magnetized TOV stars. We adopt the same configuration as in [32,45,70]. Specifically, we use a polytropic equation of state,…”

Section: Tolman-oppenheimer-volkoff (Tov) Starmentioning

confidence: 99%

“…the spacetime is static. We use a cube [−13, 13] 3 in geometric units, which is slightly higher resolution than was used in [32,45,70]. We convert grid spacing to meters assuming a maximum mass of the neutron star of M max = 2M ⊙ .…”

Section: Tolman-oppenheimer-volkoff (Tov) Starmentioning

confidence: 99%

“…As a final challenging 3d test case, we simulate a uniformly rotating neutron star with a ratio of polar to equatorial radii of 0.7, as in [32,45] and similar to [73]. The initial data is constructed using the RotNS code described in [74,75].…”

Section: Rotating Neutron Starmentioning

confidence: 99%

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A positivity-preserving adaptive-order finite-difference scheme for GRMHD

Deppe,

Kidder,

Teukolsky

et al. 2023

Class. Quantum Grav.

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We present an adaptive-order positivity-preserving conservativefinite-difference scheme that allows a high-order solution away from shocksand discontinuities while guaranteeing positivity and robustness atdiscontinuities. This is achieved by monitoring the relative power in thehighest mode of the reconstructed polynomial and reducing the order when thepolynomial series no longer converges. Our approach is similar to themultidimensional optimal order detection (MOOD) strategy, but differs inseveral ways. The approach is a priori and so does not requireretaking a time step. It can also readily be combined withpositivity-preserving flux limiters that have gained significant traction incomputational astrophysics and numerical relativity. This combinationultimately guarantees a physical solution both during reconstruction and timestepping. We demonstrate the capabilities of the method using a standard suiteof very challenging 1d, 2d, and 3d general relativistic magnetohydrodynamicstest problems.

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Section: Numerical Resultsmentioning

confidence: 99%

“…We perform simulations of both magnetized and non-magnetized TOV stars. We adopt the same configuration as in [32,45,70]. Specifically, we use a polytropic equation of state,…”

Section: Tolman-oppenheimer-volkoff (Tov) Starmentioning

confidence: 99%

Section: Tolman-oppenheimer-volkoff (Tov) Starmentioning

confidence: 99%

Section: Rotating Neutron Starmentioning

confidence: 99%

See 2 more Smart Citations

A positivity-preserving adaptive-order finite-difference scheme for GRMHD

Deppe,

Kidder,

Teukolsky

et al. 2023

Class. Quantum Grav.

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“…Since the TCI may trigger in smooth regions, ideally the limiting procedure does not flatten local extrema when applied in such regions. In a companion paper [53] we have experimented with the (admittedly quite dated but very robust) minmod family of limiters [3,4,54], the hierarchical limiter of Krivodonova [55,56], the simple WENO limiter [57], and the Hermite WENO (HWENO) limiter [58]. While this does not include every limiter applicable to structured meshes, it covers the common ones.…”

Section: Overview Of Existing Dg Limitersmentioning

confidence: 99%

A high-order shock capturing discontinuous Galerkin–finite difference hybrid method for GRMHD

Deppe¹,

Hébert²,

Kidder³

et al. 2022

Class. Quantum Grav.

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We present a discontinuous Galerkin (DG)–finite difference (FD) hybrid scheme that allows high-order shock capturing with the DG method for general relativistic magnetohydrodynamics. The hybrid method is conceptually quite simple. An unlimited DG candidate solution is computed for the next time step. If the candidate solution is inadmissible, the time step is retaken using robust FD methods. Because of its a posteriori nature, the hybrid scheme inherits the best properties of both methods. It is high-order with exponential convergence in smooth regions, while robustly handling discontinuities. We give a detailed description of how we transfer the solution between the DG and FD solvers, and the troubled-cell indicators necessary to robustly handle slow-moving discontinuities and simulate magnetized neutron stars. We demonstrate the efficacy of the proposed method using a suite of standard and very challenging 1D, 2D, and 3D relativistic magnetohydrodynamics test problems. The hybrid scheme is designed from the ground up to efficiently simulate astrophysical problems such as the inspiral, coalescence, and merger of two neutron stars.

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