Hybrid Discrete Ordinates Solver for the Radiative Transport Equation using Second Order Finite Volume and Discontinuous Galerkin

Heningburg, Vincent

doi:10.2172/1467230

Cited by 3 publications

(4 citation statements)

References 32 publications

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“…The DG method has been used to develop structure-preserving methods in a range of applications; see for example Zhang and Shu (2010b) and Wu and Tang (2016) for physical-constraint-preserving methods for the non-relativistic and relativistic Euler equations, respectively, Li and Xing (2018) for a steady-state preserving method for the Euler equations with gravitation, and Juno et al (2018) for an energy-conserving DG method for kinetic plasma simulations. We also mention the work of Heningburg and Hauck (2020), where DG and finite-volume methods are combined to a hybrid transport scheme that captures the diffusion limit and is more efficient in terms of memory usage and computational time than the corresponding DG-only scheme.…”

Section: Newtonian-gravity O(v/c) Finite-volume Implementationmentioning

confidence: 99%

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

Mezzacappa,

Endeve,

Messer

et al. 2020

Preprint

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The proposal that core collapse supernovae are neutrino driven is still the subject of active investigation more than fifty 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 protoneutron 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

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Section: Newtonian-gravity O(v/c) Finite-volume Implementationmentioning

confidence: 99%

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

Mezzacappa,

Endeve,

Messer

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Remark 3.2. As demonstrated in [18], the inversion of the block L 00 in (3.22), rather than the full matrix L in (2.14), results in a significant savings in terms of floating point operations (and hence time-to-solution). This savings will be partially offset by the need to invert the matrix B 11 in (3.20).…”

Section: Low-memory Schemementioning

confidence: 99%

“…In this paper, we apply the reconstruction suggested in [18] to recover slopes for simplicity, although in general other upwind approaches can also be used 7 . For illustration, we consider a uniform Cartesian mesh on [0, 1] × [0, 1] × [0, 1].…”

Section: Reconstructed Low-memory Schemementioning

confidence: 99%

Low-memory, discrete ordinates, discontinuous Galerkin methods for radiative transport

Sun¹,

Hauck²

2019

Preprint

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The discrete ordinates discontinuous Galerkin (S N -DG) method is a well-established and practical approach for solving the radiative transport equation. In this paper, we study a lowmemory variation of the upwind S N -DG method. The proposed method uses a smaller finite element space that is constructed by coupling spatial unknowns across collocation angles, thereby yielding an approximation with fewer degrees of freedom than the standard method. Like the original S N -DG method, the low memory variation still preserves the asymptotic diffusion limit and maintains the characteristic structure needed for mesh sweeping algorithms. While we observe second-order convergence in scattering dominated, diffusive regime, the low-memory method is in general only first-order accurate. To address this issue, we use upwind reconstruction to recover second-order accuracy. For both methods, numerical procedures based on upwind sweeps are proposed to reduce the system dimension in the underlying Krylov solver strategy.

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mentioning

confidence: 99%

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

Mezzacappa

Endeve

Messer

2020

Living Rev Comput Astrophys

View full text Add to dashboard Cite

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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Hybrid Discrete Ordinates Solver for the Radiative Transport Equation using Second Order Finite Volume and Discontinuous Galerkin

Cited by 3 publications

References 32 publications

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

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

Low-memory, discrete ordinates, discontinuous Galerkin methods for radiative transport

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

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