Maximum entropy Eddington factors

Minerbo, Gerald

doi:10.1016/0022-4073(78)90024-9

Cited by 285 publications

(318 citation statements)

References 12 publications

Supporting

Mentioning

310

Contrasting

Order By: Relevance

“…We employ the Minerbo closure to interpolate between the optically thick and thin limits of the radiation pressure tensor and third-order radiation moment in the fluid rest frame (Minerbo 1978). This is similar to the approaches discussed in Shibata et al (2011) andCardall et al (2013) and used in Just et al (2015), O'Connor & Couch (2015), and Kuroda et al (2016).…”

Section: Methods and Setupmentioning

confidence: 99%

General-Relativistic Three-Dimensional Multi-Group Neutrino Radiation-Hydrodynamics Simulations of Core-Collapse Supernovae

Roberts

Ott

Haas

et al. 2016

ApJ

187

182

View full text Add to dashboard Cite

We report on a set of long-term general-relativistic three-dimensional (3D) multi-group (energy-dependent) neutrino radiation-hydrodynamics simulations of core-collapse supernovae. We employ a full 3D two-moment scheme with the local M1 closure, three neutrino species, and 12 energy groups per species. With this, we follow the post-core-bounce evolution of the core of a nonrotating - M 27 progenitor in full unconstrained 3D and in octant symmetry for 380 ms. We find the development of an asymmetric runaway explosion in our unconstrained simulation. We test the resolution dependence of our results and, in agreement with previous work, find that low resolution artificially aids explosion and leads to an earlier runaway expansion of the shock. At low resolution, the octant and full 3D dynamics are qualitatively very similar, but at high resolution, only the full 3D simulation exhibits the onset of explosion.

show abstract

Section: Methods and Setupmentioning

confidence: 99%

General-Relativistic Three-Dimensional Multi-Group Neutrino Radiation-Hydrodynamics Simulations of Core-Collapse Supernovae

Roberts

Ott

Haas

et al. 2016

ApJ

187

182

View full text Add to dashboard Cite

show abstract

“…Diffusion [15,12,14,11,9,43,25,38,6,5,31,35,44,46,27,37,1,42,41,28] 3. Spherical Harmonics (P N ) [7,10,40,13] 4.…”

Section: The Approximationsmentioning

confidence: 99%

“…where the Eddington tensor χ is a nonlinear function of E. There are many different closures for χ that have been proposed [38,35,31,44,25,30]. The flux limited diffusion equations are arrived at by further assuming that Eddington factor χ is "isotropic" (χ = χI), that χ varies slowly with space, and that the approximation in Eq.…”

Section: Flux Limited Diffusion and Variable Eddington Factorsmentioning

confidence: 99%

Forms of Approximate Radiation Transport

Brunner

2002

126

View full text Add to dashboard Cite

Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.4

show abstract

“…In order to solve such an undertermined system, one typically closes it by expressing the moment ψ 2 as a function of ψ 0 and ψ 1 . For the present application, the entropy-based closure ( [13]) was prefered as it provides desirable properties (hyperbolicity, entropy decay, correct modelling of beams). This closure, leading to the so-called M 1 closure, consists in defining ψ 2 as the second order moment of the ansatz ψ M 1 minimizing Boltzmann entropy under the following constraints…”

Section: The M 1 Modelmentioning

confidence: 99%

On the Transverse Diffusion of Beams of Photons in Radiation Therapy

Pichard

Dubroca

Brull

et al. 2018

Theory, Numerics and Applications of Hyperbolic Problems II

View full text Add to dashboard Cite

Typical external radiotherapy treatments consist in emitting beams of energetic photons targeting the tumor cells. Those photons are transported through the medium and interact with it. Such interactions affect the motion of the photons but they are typically weakly deflected which is not well modeled by standard numerical methods.The present work deals with the transport of photons in water. The motion of those particles is modeled by an entropy-based moment model, i.e. the M 1 model. The main difficulty when constructing numerical approaches for photon beam modelling emerges from the significant difference of magnitude between the diffusion effects in the forward and transverse directions. A numerical method for the M 1 equations is proposed with a special focus on the numerical diffusion effects.

show abstract

Maximum entropy Eddington factors

Cited by 285 publications

References 12 publications

General-Relativistic Three-Dimensional Multi-Group Neutrino Radiation-Hydrodynamics Simulations of Core-Collapse Supernovae

General-Relativistic Three-Dimensional Multi-Group Neutrino Radiation-Hydrodynamics Simulations of Core-Collapse Supernovae

Forms of Approximate Radiation Transport

On the Transverse Diffusion of Beams of Photons in Radiation Therapy

Contact Info

Product

Resources

About