A Collision-Based Hybrid Method for Time-Dependent, Linear, Kinetic Transport Equations

Hauck, Cory D.; McClarren, Ryan G.

doi:10.1137/110846610

Cited by 34 publications

(19 citation statements)

References 49 publications

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“…Recent work on HOLO methods applied to the problem of thermal radiative transfer include applications where the high-order model is solved with continuum methods such as discrete ordinates (e.g., Park et al 2012Park et al , 2013Lou et al 2019) or Monte Carlo methods (e.g., Park et al 2014;Bolding et al 2017). We also point out related work on solving the linear transport equation (i.e., without nonlinear coupling to the material) with HOLO (or hybrid) methods by Hauck and McClarren (2013), Willert et al (2013); Willert et al (2015) and Crockatt et al (2017Crockatt et al ( , 2019Crockatt et al ( , 2020.…”

Section: Hybrid Methodsmentioning

confidence: 99%

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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Section: Hybrid Methodsmentioning

confidence: 99%

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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“…This decomposition has been studied before in neutron transport theory. [13,14,19,20] The decomposition of the radiation flux would be written as follows:…”

Section: Hybrid Transport-diffusion Methodsmentioning

confidence: 99%

“…Remark: In order to adimensionalize the governing equations (4-11), we introduce the following dimensionless parameters:t = cΣ a2 tx = Σ a2 xψ = ψ/(σT 4 in )T = T /T in (13) where σ is the Stephan-Boltzmann coefficient and σT…”

Section: Problem Statementmentioning

confidence: 99%

Using High-Fidelity Radiation Transport Methods to Supplement the Diffusion Approximation at Material Interfaces

Ruiz

Stephey

2013

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Today, many radiation-hydrodynamics simulations use methods that combine hydrodynamics and radiation diffusion algorithms. The diffusion model has been used because it provides faster calculations for the radiation scalar flux than the full radiation transport model. [5, 7, 8] However, it is well-known that diffusion cannot resolve "transport effects" at material interfaces. This could cause erroneous predictions when coupling the radiation results with a material hydrodynamics calculation. In this work, the "transport effects" are thoroughly characterized using IMC and S N transport methods. Based on the information obtained from this study, new models based on diffusion that can capture these effects are developed. These models are subsequently compared with the full radiation transport model. It is hoped that the new models can be used to provide improved predictions in rad-hydro simulations, such as in ICF capsule implosions.

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“…The collisions induce some mathematical structure, which is utilized to design many algorithms. There are domain decomposition methods [2,26,37,38], perturbative methods [4,19,20,21,22,23,43,49], asymptotic preserving (AP) numerical methods [12,33,34,35], and collision-based hybrid algorithms [14,29,31].…”

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confidence: 99%

Solving the linear transport equation by a deep neural network approach

Chen

Liu

2022

DCDS-S

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In this paper, we study linear transport model by adopting deep learning method, in particular deep neural network (DNN) approach. While the interest of using DNN to study partial differential equations is arising, here we adapt it to study kinetic models, in particular the linear transport model. Moreover, theoretical analysis on the convergence of neural network and its approximated solution towards analytic solution is shown. We demonstrate the accuracy and effectiveness of the proposed DNN method in numerical experiments.

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A Collision-Based Hybrid Method for Time-Dependent, Linear, Kinetic Transport Equations

Cited by 34 publications

References 49 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

Using High-Fidelity Radiation Transport Methods to Supplement the Diffusion Approximation at Material Interfaces

Solving the linear transport equation by a deep neural network approach

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