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A Godunov Method for Multidimensional Radiation Magnetohydrodynamics based on a variable Eddington tensor
High Energy Astrophysical Phenomena · Submitted 11 Jan 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In particular, we find the method is not only substantially more accurate, but often no more expensive than the diffusion approximation for our intended applications.
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The abstract, sentence by sentence
We describe a numerical algorithm to integrate the equations of radiation magnetohydrodynamics in multidimensions using Godunov methods. This algorithm solves the radiation moment equations in the mixed frame, without invoking any diffusion-like approximations. The moment equations are closed using a variable Eddington tensor whose components are calculated from a formal solution of the transfer equation at a large number of angles using the method of short characteristics. We use a comprehensive test suite to verify the algorithm, including convergence tests of radiation-modified linear acoustic and magnetosonic waves, the structure of radiation modified shocks, and two-dimensional tests of photon bubble instability and the ablation of dense clouds by an intense radiation field. These tests cover a very wide range of regimes, including both optically thick and thin flows, and ratios of the radiation to gas pressure of at least 10^{-4} to 10^{4}. Across most of the parameter space, we find the method is accurate. However, the tests also reveal there are regimes where the method needs improvement, for example when both the radiation pressure and absorption opacity are very large. We suggest modifications to the algorithm that will improve accuracy in this case. We discuss the advantages of this method over those based on flux-limited diffusion. In particular, we find the method is not only substantially more accurate, but often no more expensive than the diffusion approximation for our intended applications.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We describe a numerical algorithm to integrate the equations of radiation magnetohydrodynamics in multidimensions using Godunov methods. | contribution 0.88 | 0.92 | 0.06 | asserted 0.99 |
| s1 | This algorithm solves the radiation moment equations in the mixed frame, without invoking any diffusion-like approximations. | method 0.93 | 0.84 | 0.06 | asserted 1.00 |
| s2 | The moment equations are closed using a variable Eddington tensor whose components are calculated from a formal solution of the transfer equation at a large number of angles using the method of short characteristics. | method 1.00 | 0.86 | 0.04 | asserted 1.00 |
| s3 | We use a comprehensive test suite to verify the algorithm, including convergence tests of radiation-modified linear acoustic and magnetosonic waves, the structure of radiation modified shocks, and two-dimensional tests of photon bubble instability and the ablation of dense clouds by an intense radiation field. | method 0.74 | 0.96 | 0.05 | asserted 0.99 |
| s4 | These tests cover a very wide range of regimes, including both optically thick and thin flows, and ratios of the radiation to gas pressure of at least 10^{-4} to 10^{4}. | method 0.58 | 0.85 | 0.07 | asserted 0.99 |
| s5 | Across most of the parameter space, we find the method is accurate. | result 0.99 | 0.96 | 0.38 | asserted 1.00 |
| s6 | However, the tests also reveal there are regimes where the method needs improvement, for example when both the radiation pressure and absorption opacity are very large. | limitation 0.99 | 0.95 | 0.11 | asserted 0.99 |
| s7 | We suggest modifications to the algorithm that will improve accuracy in this case. | future work 0.94 | 0.64 | 0.08 | hedged possibility 0.94 |
| s8 | We discuss the advantages of this method over those based on flux-limited diffusion. | interpretation 0.72 | 0.54 | 0.09 | asserted 0.61 |
| s9 | In particular, we find the method is not only substantially more accurate, but often no more expensive than the diffusion approximation for our intended applications. | result 0.76 | 0.93 | 0.36 | asserted 0.99 |
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Original abstract
We describe a numerical algorithm to integrate the equations of radiation magnetohydrodynamics in multidimensions using Godunov methods. This algorithm solves the radiation moment equations in the mixed frame, without invoking any diffusion-like approximations. The moment equations are closed using a variable Eddington tensor whose components are calculated from a formal solution of the transfer equation at a large number of angles using the method of short characteristics. We use a comprehensive test suite to verify the algorithm, including convergence tests of radiation-modified linear acoustic and magnetosonic waves, the structure of radiation modified shocks, and two-dimensional tests of photon bubble instability and the ablation of dense clouds by an intense radiation field. These tests cover a very wide range of regimes, including both optically thick and thin flows, and ratios of the radiation to gas pressure of at least 10^{-4} to 10^{4}. Across most of the parameter space, we find the method is accurate. However, the tests also reveal there are regimes where the method needs improvement, for example when both the radiation pressure and absorption opacity are very large. We suggest modifications to the algorithm that will improve accuracy in this case. We discuss the advantages of this method over those based on flux-limited diffusion. In particular, we find the method is not only substantially more accurate, but often no more expensive than the diffusion approximation for our intended applications.
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References
How the literature uses it
7 arXiv papers cite this in 12 sentences
Papers citing it · 9 sentences without a confident label
Cites it as background 3 papers
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The RMHD coupled system has been investigated lately [ref] .
A Spatial-Temporal asymptotic preserving scheme for radiation magnetohydrodynamics in the equilibrium and non-equilibrium diffusion limit · Introduction · 0.98
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Moment methods evolve a truncated hierarchy of angular moments [ref] closed by an assumed relation: flux-limited diffusion [ref] , the M1/Minerbo closure [ref] , or a variable Eddington tensor (VET), as in the hybrid Godunov framework of [ref] , with the tensor obtained from a formal short-characteristics solution in [ref] .
Finite-Solid-Angle Boltzmann Radiation Transport on Dynamical Spacetimes in AthenaK · Introduction · 0.83
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We restrict ourselves to analytic closures for simplicity, although more sophisticated treatments of closures have been used for classical radiation transport (e.g., variable Eddington tensor methods [ref] ).
Neutrino fast flavor oscillations with moments: linear stability analysis and application to neutron star mergers · Closure · 0.92
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