Entropy-limited hydrodynamics: a novel approach to relativistic hydrodynamics

Guercilena, Federico; Radice, David; Rezzolla, Luciano

doi:10.1186/s40668-017-0022-0

Cited by 21 publications

(48 citation statements)

References 76 publications

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“…When shocks form, e.g. during the collision of the stars, even high order -high resolution shock capturing methods lose their high convergence properties [86,110,111]. We further find that the measurement of the remnant's lifetime is less robust for eccentric orbits than for quasicircular ones.…”

Section: Merger Remnantmentioning

confidence: 85%

Gravitational waves and mass ejecta from binary neutron star mergers: Effect of large eccentricities

Chaurasia¹,

Dietrich²,

Johnson-McDaniel³

et al. 2018

Phys. Rev. D

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As current gravitational wave (GW) detectors increase in sensitivity, and particularly as new instruments are being planned, there is the possibility that ground-based GW detectors will observe GWs from highly eccentric neutron star binaries. We present the first detailed study of highly eccentric BNS systems with full (3+1)D numerical relativity simulations using consistent initial conditions, i.e., setups which are in agreement with the Einstein equations and with the equations of general relativistic hydrodynamics in equilibrium. Overall, our simulations cover two different equations of state (EOSs), two different spin configurations, and three to four different initial eccentricities for each pairing of EOS and spin. We extract from the simulated waveforms the frequency of the f-mode oscillations induced during close encounters before the merger of the two stars. The extracted frequency is in good agreement with f-mode oscillations of individual stars for the irrotational cases, which allows an independent measure of the supranuclear equation of state not accessible for binaries on quasicircular orbits. The energy stored in these f -mode oscillations can be as large as 10 −3 M ∼ 10 51 erg, even with a soft EOS. In order to estimate the stored energy, we also examine the effects of mode mixing due to the stars' offset from the origin on the f -mode contribution to the GW signal. While in general (eccentric) neutron star mergers produce bright electromagnetic counterparts, we find that for the considered cases with fixed initial separation the luminosity decreases when the eccentricity becomes too large, due to a decrease of the ejecta mass. Finally, the use of consistent initial configurations also allows us to produce high-quality waveforms for different eccentricities which can be used as a test bed for waveform model development of highly eccentric binary neutron star systems.

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Section: Merger Remnantmentioning

confidence: 85%

Gravitational waves and mass ejecta from binary neutron star mergers: Effect of large eccentricities

Chaurasia¹,

Dietrich²,

Johnson-McDaniel³

et al. 2018

Phys. Rev. D

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“…We note the larger entropy at the star's surface for the low resolution NC model. This entropy production is caused by the surface as discussed, e.g., in Guercilena et al[51]. The entropy production decreases with an increasing resolution and its origin lies in the high-resolution shock-capturing schemes and the use of an artificial atmosphere surrounding the star.…”

mentioning

confidence: 94%

Rotating neutron stars with nonbarotropic thermal profile

et al. 2019

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Neutron stars provide an excellent laboratory for physics under the most extreme conditions. Up to now, models of axisymmetric, stationary, differentially rotating neutron stars were constructed under the strong assumption of barotropicity, where a one-to-one relation between all thermodynamic quantities exists. This implies that the specific angular momentum of a matter element depends only on its angular velocity. The physical conditions in the early stages of neutron stars, however, are determined by their violent birth processes, typically a supernova or in some cases the merger of two neutron stars, and detailed numerical models show that the resulting stars are by no means barotropic. Here, we construct models for stationary, differentially rotating, non-barotropic neutron stars, where the equation of state and the specific angular momentum depend on more than one independent variable. We show that the potential formulation of the relativistic Euler equation can be extended to the non-barotropic case, which, to the best of our knowledge, is a new result even for the Newtonian case. We implement the new method into the XNS code and construct equilibrium configurations for non-barotropic equations of state. We scrutinize the resulting configurations by evolving them dynamically with the numerical relativity code BAM, thereby demonstrating that the new method indeed produces stationary, differentially rotating, non-barotropic neutron star configurations.1 Bardeen [29] explicitly considers a general entropy distribution in the formulation of his variational principle, but does not compute any stellar structure.

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“…It is natural and interesting to explore robust numerical RHD schemes, whose solutions always stay in the invariant region Ω S 0 , i.e., satisfy the minimum entropy principle at the discrete level and also preserve the intrinsic physical constraints (7). Note that, to obtain a well-defined specific entropy for the numerical solution, it is necessary to first guarantee the positivity of pressure and rest-mass density.…”

Section: Introductionmentioning

confidence: 99%

“…The subluminal constraint on the fluid velocity is also crucial for the relativistic causality, because its violation would yield imaginary Lorentz factor. In fact, violating any of the constraints (7) will cause numerical instability and the break down of the computation. Therefore, the preservation of the minimum entropy principle should be considered together with the constraints (7).…”

Section: Introductionmentioning

confidence: 99%

“…In fact, violating any of the constraints (7) will cause numerical instability and the break down of the computation. Therefore, the preservation of the minimum entropy principle should be considered together with the constraints (7). Recent years have witnessed some advances in developing high-order numerical schemes, which provably preserve the constraints (7), for the special RHD [38,28,41] and the general RHD [32].…”

Section: Introductionmentioning

confidence: 99%

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Minimum Principle on Specific Entropy and High-Order Accurate Invariant Region Preserving Numerical Methods for Relativistic Hydrodynamics

Wu¹

2021

Preprint

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This paper first explores Tadmor's minimum entropy principle for the special relativistic hydrodynamics (RHD) equations and incorporates this principle into the design of robust highorder discontinuous Galerkin (DG) and finite volume schemes for RHD on general meshes. The proposed schemes are rigorously proven to preserve numerical solutions in a global invariant region constituted by all the known intrinsic constraints: minimum entropy principle, the subluminal constraint on fluid velocity, the positivity of pressure, and the positivity of restmass density. Relativistic effects lead to some essential difficulties in the present study, which are not encountered in the non-relativistic case. Most notably, in the RHD case the specific entropy is a highly nonlinear implicit function of the conservative variables, and, moreover, there is also no explicit formula of the flux in terms of the conservative variables. In order to overcome the resulting challenges, we first propose a novel equivalent form of the invariant region, by skillfully introducing two auxiliary variables. As a notable feature, all the constraints in the novel form are explicit and linear with respect to the conservative variables. This provides a highly effective approach to theoretically analyze the invariant-region-preserving (IRP) property of numerical schemes for RHD, without any assumption on the IRP property of the exact Riemann solver. Based on this, we prove the convexity of the invariant region and establish the generalized Lax-Friedrichs splitting properties via technical estimates, lying the foundation for our rigorous IRP analyses. It is rigorously shown that the first-order Lax-Friedrichs type scheme for the RHD equations satisfies a local minimum entropy principle and is IRP under a CFL condition. Provably IRP high-order accurate DG and finite volume methods are then developed for the RHD with the help of a simple scaling limiter, which is designed by following the bound-preserving type limiters in the literature. Several numerical examples demonstrate the effectiveness and robustness of the proposed schemes.

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Entropy-limited hydrodynamics: a novel approach to relativistic hydrodynamics

Cited by 21 publications

References 76 publications

Gravitational waves and mass ejecta from binary neutron star mergers: Effect of large eccentricities

Gravitational waves and mass ejecta from binary neutron star mergers: Effect of large eccentricities

Rotating neutron stars with nonbarotropic thermal profile

Minimum Principle on Specific Entropy and High-Order Accurate Invariant Region Preserving Numerical Methods for Relativistic Hydrodynamics

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