Conservative<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mo mathvariant="bold">+</mml:mo><mml:mn>1</mml:mn></mml:math>general relativistic variable Eddington tensor radiation transport equations

Cardall, Christian Y.; Endeve, Eirik; Mezzacappa, Anthony

doi:10.1103/physrevd.87.103004

Cited by 71 publications

(107 citation statements)

References 60 publications

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“…(We caution that the use of the base symbol ℓ in Ref. [35] differs from its use here.) Having discussed the interpretation of…”

Section: B Tetrad Decompositionmentioning

confidence: 99%

“…(This served us well in Ref. [35] on a moments approach to radiation transport.) The unit normal n µ to a spacelike slice-which is also the four-velocity of an 'Eulerian observer'-has lab frame coordinate basis components …”

Section: A Geometry Descriptionmentioning

confidence: 99%

“…(A14) of Ref. [35], with the substitution T µν → L µμ L νν pμpνf . In the momentum equation, we have…”

Section: E Lepton Number and Four-momentum Reconciliationmentioning

confidence: 99%

“…(59), (63)-(65) in mind, and regard hatted indices likeμ only as labels identifying a particular vector in the tetrad in such instances. In a moments approach to radiation transport [35], the only comoving basis vector we had to deal with was L µ0 = u µ , and we found it useful to consider its Eulerian decomposition into parts orthogonal and tangent to the spacelike slice:…”

Section: B Tetrad Decompositionmentioning

confidence: 99%

“…These have been implemented in simplified, energy-integrated ('grey') form in the 3D position space simulations of Kuroda et al [34]. In order to more fully address simultaneous energy and lepton number conservation in moments formalisms, the energy derivative term in the Shibata et al [33] equations was more fully elaborated into a useful 3+1 form by Cardall et al [35], who also considered in detail the termby-term cancellations that must occur for consistency between conservative four-momentum transport equations and the conservative number transport equation; see also the partially relativistic limits discussed by Endeve et al [30].…”

Section: Introductionmentioning

confidence: 99%

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Conservative3+1general relativistic Boltzmann equation

2013

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We present a new derivation of the conservative form of the general relativistic Boltzmann equation and specialize it to the 3+1 metric. The resulting transport equation is intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry. The independent variables are lab frame coordinate basis spacetime position components and comoving frame curvilinear momentum space coordinates. With an eye towards astrophysical applicationssuch as core-collapse supernovae and compact object mergers-in which the fluid includes nuclei and/or nuclear matter at finite temperature, and in which the transported particles are neutrinos, we examine the relationship between lepton number and four-momentum exchange between neutrinos and the fluid.

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“…(We caution that the use of the base symbol ℓ in Ref. [35] differs from its use here.) Having discussed the interpretation of…”

Section: B Tetrad Decompositionmentioning

confidence: 99%

Section: A Geometry Descriptionmentioning

confidence: 99%

“…(A14) of Ref. [35], with the substitution T µν → L µμ L νν pμpνf . In the momentum equation, we have…”

Section: E Lepton Number and Four-momentum Reconciliationmentioning

confidence: 99%

Section: B Tetrad Decompositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Conservative3+1general relativistic Boltzmann equation

2013

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Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

Mezzacappa

Endeve

Messer

2020

Living Rev Comput Astrophys

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The proposal that core collapse supernovae are neutrino driven is still the subject of active investigation more than 50 years after the seminal paper by Colgate and White. The modern version of this paradigm, which we owe to Wilson, proposes that the supernova shock wave is powered by neutrino heating, mediated by the absorption of electron-flavor neutrinos and antineutrinos emanating from the proto-neutron star surface, or neutrinosphere. Neutrino weak interactions with the stellar core fluid, the theory of which is still evolving, are flavor and energy dependent. The associated neutrino mean free paths extend over many orders of magnitude and are never always small relative to the stellar core radius. Thus, neutrinos are never always fluid like. Instead, a kinetic description of them in terms of distribution functions that determine the number density of neutrinos in the six-dimensional phase space of position, direction, and energy, for both neutrinos and antineutrinos of each flavor, or in terms of angular moments of these neutrino distributions that instead provide neutrino number densities in the four-dimensional phase-space subspace of position and energy, is needed. In turn, the computational challenge is twofold: (i) to map the kinetic equations governing the evolution of these distributions or moments onto discrete representations that are stable, accurate, and, perhaps most important, respect physical laws such as conservation of lepton number and energy and the Fermi–Dirac nature of neutrinos and (ii) to develop efficient, supercomputer-architecture-aware solution methods for the resultant nonlinear algebraic equations. In this review, we present the current state of the art in attempts to meet this challenge.

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Neutrino transport in general relativistic neutron star merger simulations

Foucart

2023

Living Rev Comput Astrophys

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Numerical simulations of neutron star–neutron star and neutron star–black hole binaries play an important role in our ability to model gravitational-wave and electromagnetic signals powered by these systems. These simulations have to take into account a wide range of physical processes including general relativity, magnetohydrodynamics, and neutrino radiation transport. The latter is particularly important in order to understand the properties of the matter ejected by many mergers, the optical/infrared signals powered by nuclear reactions in the ejecta, and the contribution of that ejecta to astrophysical nucleosynthesis. However, accurate evolutions of the neutrino transport equations that include all relevant physical processes remain beyond our current reach. In this review, I will discuss the current state of neutrino modeling in general relativistic simulations of neutron star mergers and of their post-merger remnants. I will focus on the three main types of algorithms used in simulations so far: leakage, moments, and Monte-Carlo scheme. I will review the advantages and limitations of each scheme, as well as the various neutrino–matter interactions that should be included in simulations. We will see that the quality of the treatment of neutrinos in merger simulations has greatly increased over the last decade, but also that many potentially important interactions remain difficult to take into account in simulations (pair annihilation, oscillations, inelastic scattering).

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Conservative3+1general relativistic variable Eddington tensor radiation transport equations

Cited by 71 publications

References 60 publications

Conservative3+1general relativistic Boltzmann equation

Conservative3+1general relativistic Boltzmann equation

Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

Neutrino transport in general relativistic neutron star merger simulations

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