Multi-group Radiative Transfer Research Articles

A maximum principle preserving implicit Monte Carlo method for frequency-dependent radiative transfer equations

In this paper, we develop a maximum principle preserving Monte Carlo method for the frequency-dependent (multi-group) radiative transfer equations. In order to deal with the nonlinear coupling between the radiation intensity and background material, Newton's iteration is involved into the discretization of the nonlinear system. We employ the maximum principle of the material temperature as the stopping criterion of the nonlinear iterations. The classical implicit Monte Carlo method can be regarded as one iteration of the new iterative method. We demonstrate that if the nonlinear iteration of the new method converges, it will become a fully implicit discretization of the multi-group radiative transfer equations. Moreover, the radiation temperature will also satisfy the maximum principle under certain conditions. Several frequency-dependent radiative transfer examples are given to show the effectiveness of the new method.

Chromospheric extension of the MURaM code

Context. Detailed numerical models of the chromosphere and corona are required to understand the heating of the solar atmosphere. An accurate treatment of the solar chromosphere is complicated by the effects arising from non-local thermodynamic equilibrium (NLTE) radiative transfer. A small number of strong, highly scattering lines dominate the cooling and heating in the chromosphere. Additionally, the recombination times of ionised hydrogen are longer than the dynamical timescales, requiring a non-equilibrium (NE) treatment of hydrogen ionisation. Aims. We describe a set of necessary additions to the MURaM code that allow it to handle some of the important NLTE effects. We investigate the impact on solar chromosphere models caused by NLTE and NE effects in radiation magnetohydrodynamic simulations of the solar atmosphere. Methods. The MURaM code was extended to include the physical process required for an accurate simulation of the solar chromosphere, as implemented in the Bifrost code. This includes a time-dependent treatment of hydrogen ionisation, a scattering multi-group radiation transfer scheme, and approximations for NLTE radiative cooling. Results. The inclusion of NE and NLTE physics has a large impact on the structure of the chromosphere; the NE treatment of hydrogen ionisation leads to a higher ionisation fraction and enhanced populations in the first excited state throughout cold inter-shock regions of the chromosphere. Additionally, this prevents hydrogen ionisation from buffering energy fluctuations, leading to hotter shocks and cooler inter-shock regions. The hydrogen populations in the ground and first excited state are enhanced by 102–103 in the upper chromosphere and by up to 109 near the transition region. Conclusions. Including the necessary NLTE physics leads to significant differences in chromospheric structure and dynamics. The thermodynamics and hydrogen populations calculated using the extended version of the MURaM code are consistent with previous non-equilibrium simulations. The electron number and temperature calculated using the non-equilibrium treatment of the chromosphere are required to accurately synthesise chromospheric spectral lines.

A Study of Low-Temperature Neutron Star Atmospheres

We present a study of how a low-temperature accreted atmosphere influences the emitted X-ray spectrum of a neutron star. The atmosphere models and spectra were computed with Zcode, a multigroup radiation transfer code developed at the Los Alamos National Laboratory. Though the underlying hot neutron star behaves as a blackbody, the atmosphere shifts the peak of spectrum away from a blackbody and toward higher energies, producing an emitted spectrum similar to a dilute blackbody. Quantifying the effects of this atmosphere will remove a source of uncertainty in X-ray observations and better constrain the mass-radius relation for neutron stars and thus the equation of state of dense matter. We present a suite of these atmospheres with varying compositions and temperatures as well as the resulting spectra.

Multilevel quasidiffusion method with mixed-order time discretization for multigroup thermal radiative transfer problems

In this paper we present a numerical method for solving multigroup thermal radiative transfer (TRT) problems in 2D Cartesian geometry. It is based on the Quasidiffusion (aka Variable Eddington Factor) method and defined by the multilevel system of multigroup high-order radiative transfer (RT) equations and multigroup and grey low-order equations for moments of the intensity with the exact closures. We apply time integration schemes of different orders of accuracy to approximate the high-order and low-order equations. The first-order scheme is used for the high-order RT equations. The second-order scheme is applied to the low-order equations. This improves the accuracy of the TRT solution while using robust and relatively inexpensive scheme for the high-order RT equations. The solution of the low-order equations is non-monotonic because the hyperbolic low-order Quasidiffusion (QD) equations are discretized by the second-order scheme. To reduce non-monotonicity of the low-order solution we apply a monotonization procedure to the discretized time-dependent low-order equations based on the Limited-Trapezoidal method. Numerical results of the Fleck-Cummings test are presented to demonstrate performance of the developed mixed-order time integration scheme for the multilevel system of high-order and low-order QD equations. We use this TRT test problem to analyze the convergence in time of the mixed-order scheme.

Investigations on the hohlraum radiation in the first shaped laser pulse implosion experiment at the SGIII laser facility

The first 0.1 MJ scale shaped pulse implosion experiment was performed at the Shenguang-III laser facility in 2016. The hohlraum radiation of three representative shots with troughs of 1.0 ns, 1.5 ns, and 2.5 ns is analysed using the two-dimensional code LARED with the multi-group radiation transfer model. It is found that the simulated multi-angle radiation temperatures are generally in good agreement with the measurements within ∼3%. However, our simulations underestimate the peak radiation temperature at 64° by ∼6% for the shot with the 2.5 ns trough, due to the much smaller laser entrance hole in our calculations. In addition, we simulate the time-integrated M-band (2–4 keV) x-ray image at the view angle of 20° for the shot with the 1.0 ns trough. The simulated laser spot positions are consistent with the measurement. But the relative brightness between the inner beams and the outer beams is larger than the experimental result, which may be caused by the overestimation of the plasma density at the edge of the bubbles in our simulation. With the bubble contribution approximately removed, the simulated relative brightness between the inner beams and the outer beams approaches the experimental result.

An improved random walk algorithm for the implicit Monte Carlo method

In this work, we introduce a modified Implicit Monte Carlo (IMC) Random Walk (RW) algorithm, which increases simulation efficiency for multigroup radiative transfer problems with strongly frequency-dependent opacities.To date, the RW method has only been implemented in “fully-gray” form; that is, the multigroup IMC opacities are group-collapsed over the full frequency domain of the problem to obtain a gray diffusion problem for RW. This formulation works well for problems with large spatial cells and/or opacities that are weakly dependent on frequency; however, the efficiency of the RW method degrades when the spatial cells are thin or the opacities are a strong function of frequency.To address this inefficiency, we introduce a RW frequency group cutoff in each spatial cell, which divides the frequency domain into optically thick and optically thin components. In the modified algorithm, opacities for the RW diffusion problem are obtained by group-collapsing IMC opacities below the frequency group cutoff. Particles with frequencies above the cutoff are transported via standard IMC, while particles below the cutoff are eligible for RW. This greatly increases the total number of RW steps taken per IMC time-step, which in turn improves the efficiency of the simulation. We refer to this new method as Partially-Gray Random Walk (PGRW).We present numerical results for several multigroup radiative transfer problems, which show that the PGRW method is significantly more efficient than standard RW for several problems of interest. In general, PGRW decreases runtimes by a factor of ∼2–4 compared to standard RW, and a factor of ∼3–6 compared to standard IMC. While PGRW is slower than frequency-dependent Discrete Diffusion Monte Carlo (DDMC), it is also easier to adapt to unstructured meshes and can be used in spatial cells where DDMC is not applicable. This suggests that it may be optimal to employ both DDMC and PGRW in a single simulation.

An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations

This paper presents an extension of previous work (Sun et al., 2015 [22]) of the unified gas kinetic scheme (UGKS) for the gray radiative transfer equations to the frequency-dependent (multi-group) radiative transfer system. Different from the gray radiative transfer equations, where the optical opacity is only a function of local material temperature, the simulation of frequency-dependent radiative transfer is associated with additional difficulties from the frequency-dependent opacity. For the multiple frequency radiation, the opacity depends on both the spatial location and the frequency. For example, the opacity is typically a decreasing function of frequency. At the same spatial region the transport physics can be optically thick for the low frequency photons, and optically thin for high frequency ones. Therefore, the optical thickness is not a simple function of space location. In this paper, the UGKS for frequency-dependent radiative system is developed. The UGKS is a finite volume method and the transport physics is modeled according to the ratio of the cell size to the photon's frequency-dependent mean free path. When the cell size is much larger than the photon's mean free path, a diffusion solution for such a frequency radiation will be obtained. On the other hand, when the cell size is much smaller than the photon's mean free path, a free transport mechanism will be recovered. In the regime between the above two limits, with the variation of the ratio between the local cell size and photon's mean free path, the UGKS provides a smooth transition in the physical and frequency space to capture the corresponding transport physics accurately. The seemingly straightforward extension of the UGKS from the gray to multiple frequency radiation system is due to its intrinsic consistent multiple scale transport modeling, but it still involves lots of work to properly discretize the multiple groups in order to design an asymptotic preserving (AP) scheme in all regimes. The current scheme is tested in a few frequency-dependent radiation problems, and the results are compared with the solutions from the well-defined implicit Monte Carlo (IMC) method. The UGKS is much more efficient than IMC, and the computational times of both schemes for all test cases are listed. The UGKS seems to be the first discrete ordinate method (DOM) for the accurate capturing of multiple frequency radiative transport physics from ballistic particle motion to the diffusive wave propagation.

Angular distribution of the hohlraum radiation temperature in indirect drive fusion

Hohlraum radiation flux is the source of the capsule implosion in the indirect drive fusion, which strongly affects the capsule compression properties. It is very important to study the angular distribution of the hohlraum radiation temperature in order to understand the radiation properties inside the hohlraum. In this work, the angular distribution of the hohlraum radiation temperature is studied through theoretical analysis and multi-group radiation transfer simulations with LARED. It is found that the angular distribution of the radiation temperature is mainly determined by the ratio of the radiation flux between the hot spot and non-spot region, the ratio of the hot spot area in the detected line of sight, and the component of the volume emission. The theoretical analysis agrees very well with the LARED simulation in the two dimensional laser cone case. It is found that the two dimensional LARED simulation can be effectively used to study the angular distribution of the radiation temperature in the SGIII-P hohlraum experiments with three dimensional laser spot structures. An improved method is proposed to measure the angular distribution of the radiation temperature with more significant variation of the radiation temperature.

X-ray conversion efficiency and radiation non-uniformity in the hohlraum experiments at Shenguang-III prototype laser facility

The hohlraum radiation properties are studied experimentally by the Shenguang-III prototype laser facility and numerically by the two-dimensional code LARED with the multi-group radiation transfer model. The measured radiation temperature is consistent with the prediction of the simulations in a wide laser energy range, suggesting that the x-ray conversion efficiency is around 75% at the peak radiation temperature. The delicate hohlraum experiments further show that the radiation intensity inside the hohlraum is significantly non-uniform. The measured radiation flux of the hot spot region is over twice higher than that of the re-emitted wall region. Good agreements between the experiments and simulations further demonstrate the validity of the LARED code to study the hohlraum radiation properties.

Characterizing the hohlraum radiation via one-end driven experiments

A new experiment is designed and performed on the Shenguang III laser facility with the first eight available beams to characterizing the hohlraum radiation, in which the hohlraum with laser entrance holes on both ends is driven through one-end only. The experiment enables us to identify the x-ray radiations originated from the hohlraum reemission wall and high-Z bubble plasmas utilizing their position and spectral characters, which provides a better test on the associated hohlraum models. The total and M-band x-ray radiation fluxes are measured with the flat response x-ray detectors and the filtered M-band x-ray detectors, respectively. Numerical simulations are conducted with the two-dimensional radiation hydrodynamic code LARED-INTEGRATION using the multi-group radiation transfer and/or diffusion models. It is found that the experimentally measured temporal profiles and angular distributions of hohlraum radiation are in good agreement with the predictions of simulation using radiation transfer models, but differ significantly from the results obtained with the multi-group radiation diffusion calculations. We thus note that to accurately represent the hohlraum radiation, a true radiation transfer model is essential.

Two-dimensional radiative transfer calculations of the laser-target hohlraum

High non-LTE issue of ionization and radiative transfer are important physical characteristics of the laser-target hohlraum. Detailed multi-group transport approximation under non-LTE atomic physics is necessary for precisely describing radiation transfer and its interaction with matter. Using the recently developed LARED-integration code, we have accomplished multi-group radiative transfer calculations of the laser-target experimental hohlraum in 2D. Numerical results reflect the radiative illumination ununiformity inside the hohlraum. The ratio of X-ray intensity of the laser spot versus other regions along the gold wall agrees well with that of the experimental result, meanwhile the measured and simulated fuel shape resembles each other closely.

Ramses-rt: radiation hydrodynamics in the cosmological context

We present a new implementation of radiation hydrodynamics (RHD) in the adaptive mesh refinement (AMR) code RAMSES. The multi-group radiative transfer (RT) is performed on the AMR grid with a first-order Godunov method using the M1 closure for the Eddington tensor, and is coupled to the hydrodynamics via non-equilibrium thermochemistry of hydrogen and helium. This moment-based approach has the large advantage that the computational cost is independent of the number of radiative sources - it can even deal with continuous regions of emission such as bound-free emission from gas. As it is built directly into RAMSES, the RT takes natural advantage of the refinement and parallelization strategies already in place. Since we use an explicit advection solver for the radiative transport, the time step is restricted by the speed of light - a severe limitation that can be alleviated using the so--called "reduced speed of light" approximation. We propose a rigorous framework to assess the validity of this approximation in various conditions encountered in cosmology and galaxy formation. We finally perform with our newly developed code a complete suite of RHD tests, comparing our results to other RHD codes. The tests demonstrate that our code performs very well and is ideally suited for exploring the effect of radiation on current scenarios of structure and galaxy formation.

The influence of frequency-dependent radiative transfer on the structures of radiative shocks

Radiative shocks are shocks in a gas where the radiative energy and flux coming from the very hot post-shock material are non-negligible in the shock's total energy budget, and are often large enough to heat the material ahead of the shock. Many simulations of radiative shocks, both in the contexts of astrophysics and laboratory experiments, use a grey treatment of radiative transfer coupled to the hydrodynamics. However, the opacities of the gas show large variations as a function of frequency and this needs to be taken into account if one wishes to reproduce the relevant physics. We have performed radiation hydrodynamics simulations of radiative shocks in Ar using multigroup (frequency dependent) radiative transfer with the heracles code. The opacities were taken from the odalisc database. We show the influence of the number of frequency groups used on the dynamics and morphologies of subcritical and supercritical radiative shocks in Ar gas, and in particular on the extent of the radiative precursor. We find that simulations with even a low number of groups show significant differences compared to single-group (grey) simulations, and that in order to correctly model such shocks, a minimum number of groups is required. Results appear to eventually converge as the number of groups increases above 50. We were also able to resolve in our simulations of supercritical shocks the adaptation zones which connect the cooling layer to the final post-shock state and the precursor. Inside these adaptation zones, we find that the radiative flux just ahead of the shock in one or several high-opacity groups can heat the gas to a temperature higher than the post-shock temperature. Through the use of Hugoniot curves, we have checked the consistency of our radiation hydrodynamics scheme by showing that conservation of mass, momentum and energy (including radiative flux) holds throughout the computational domain for all our simulations. We conclude that a minimum number of frequency groups are required to correctly simulate radiating flows in gases whose opacities present large variations as a function of frequency.

Synthetic light curves of shocked dense circumstellar shells

We numerically investigate light curves (LCs) of shocked circumstellar shells which are suggested to reproduce the observed LC of superluminous SN 2006gy analytically. In the previous analytical model, the effects of the recombination and the bolometric correction on LCs are not taken into account. To see the effects, we perform numerical radiation hydrodynamic calculations of shocked shells by using STELLA, which can numerically treat multigroup radiation transfer with realistic opacities. We show that the effects of the recombination and the bolometric correction are significant and the analytical model should be compare to the bolometric LC instead of a single band LC. We find that shocked circumstellar shells have a rapid LC decline initially because of the adiabatic expansion rather than the luminosity increase and the shocked shells fail to explain the LC properties of SN 2006gy. However, our synthetic LCs are qualitatively similar to those of superluminous SN 2003ma and SN 1988Z and they may be related to shocked circumstellar shells.

Coupling of matter and radiation at supernova shock breakout

Some features of the physics of radiation-dominated shock waves are discussed with emphasis on the peculiarities which are important for correct numerical modeling of shock breakouts in supernova. With account of those peculiarities, a number of models for different supernova types is constructed based on multigroup radiation transfer coupled to hydrodynamics. We describe the implementation of a new algorithm RADA, designed for modeling photon transfer at extremely-relativistic motions of matter, into our older code STELLA. The results of numerical simulations of light curves, and continuum spectra are presented. The influence of effects of photon scattering on electrons, of thermalization depth and of special relativity in transfer equation is considered. Some cases are demonstrated, when the appearance of hard X-ray emission is possible at the shock breakout. The necessary refinements in numerical algorithms for radiative transfer and hydrodynamics are pointed out. Prospects for using the results of numerical simulation to analyze and interpret available and future data from space observatories are discussed.

Development of our laser fusion integration simulation

In the target design of the Inertial Confinement Fusion (ICF) program, it is common practice to apply radiation hydrodynamics code to study the key physical processes happening in ICF process, such as hohlraum physics, radiation drive symmetry, capsule implosion physics in the radiation-drive approach of ICF. Recently, many efforts have been done to develop our 2D integrated simulation capability of laser fusion with a variety of optional physical models and numerical methods. In order to effectively integrate the existing codes and to facilitate the development of new codes, we are developing an object-oriented structured-mesh parallel code-supporting infrastructure, called JASMIN. Based on two-dimensional three-temperature hohlraum physics code LARED-H and two-dimensional multi-group radiative transfer code LARED-R, we develop a new generation two-dimensional laser fusion code under the JASMIN infrastructure, which enable us to simulate the whole process of laser fusion from the laser beams' entrance into the hohlraum to the end of implosion. In this paper, we will give a brief description of our new-generation two-dimensional laser fusion code, named LARED-Integration, especially in its physical models, and present some simulation results of holhraum.

Multigroup radiative transfer in supernova shock breakout models

The physical peculiarities of supernova shock breakout are discussed. A number of models for various types of supernovae have been constructed based on multigroup radiative transfer by taking these peculiarities into account. The results of numerical simulations and the influence of the effects of photon scattering by electrons and the thermalization depth on them are considered. It is shown under which conditions the appearance of hard X-ray emission is possible at shock breakout. It is pointed out what refinements are necessary in the computational algorithms for radiative transfer and hydrodynamics.

A numerical model for multigroup radiation hydrodynamics

We present in this paper a multigroup model for radiation hydrodynamics to account for variations of the gas opacity as a function of frequency. The entropy closure model ( M 1) is applied to multigroup radiation transfer in a radiation hydrodynamics code. In difference from the previous grey model, we are able to reproduce the crucial effects of frequency-variable gas opacities, a situation omnipresent in physics and astrophysics. We also account for the energy exchange between neighbouring groups which is important in flows with strong velocity divergence. These terms were computed using a finite volume method in the frequency domain. The radiative transfer aspect of the method was first tested separately for global consistency (reversion to grey model) and against a well-established kinetic model through Marshak wave tests with frequency-dependent opacities. Very good agreement between the multigroup M 1 and kinetic models was observed in all tests. The successful coupling of the multigroup radiative transfer to the hydrodynamics was then confirmed through a second series of tests. Finally, the model was linked to a database of opacities for a Xe gas in order to simulate realistic multigroup radiative shocks in Xe. The differences with the previous grey models are discussed.

The light curves and spectra of supernova explosions: multi-dimensional time-dependent Monte Carlo radiative transfer calculations

While the disruption of a star in a supernova explosion lasts only seconds, the ejected stellar material, much of it newly radioactive, continues to shine brightly for several months. Multi-physics simulations of supernova are now illuminating the physics of the stellar explosion itself, but further post-processing of models with a radiative transfer code is needed to predict the visible emission and compare directly to astronomical observations. Here we discuss Monte Carlo techniques for addressing multi-group time-dependent radiative transfer in 3-dimensional, rapidly expanding atmospheres. We have developed the SEDONA code, which calculates detailed angle dependent light curves, spectra, and polarization, and have applied it to study the nature and cosmological utility of supernovae. The code is scalable and is typically run on high-performance computers using 1024 processors.

Secondary Maximum in the Near‐Infrared Light Curves of Type Ia Supernovae

We undertake a theoretical study of the near-infrared (NIR) light curves of Type Ia supernovae (SNe Ia). In these bands, the light curves are distinguished by a secondary maximum occurring roughly 20-30 days after the initial one. Using time-dependent multigroup radiative transfer calculations, we calculate the UBVRIJHK-band light curves of model SN Ia ejecta structures. Our synthetic NIR light curves show distinct secondary maxima and provide favorable fits to observed SNe Ia. We offer a detailed explanation of the origin of the NIR secondary maximum, which is shown to relate directly to the ionization evolution of iron group elements in the ejecta. This understanding provides immediate insight into the dependence of the NIR light curves on the physical properties of the ejecta and in particular explains why brighter supernovae have a later and more prominent secondary maximum. We demonstrate the dependence of the NIR light curves on the mass of 56Ni, the degree of 56Ni mixing, the mass of electron capture elements, the progenitor metallicity, and the abundance of intermediate-mass elements (especially calcium). The secondary maximum is shown to be a valuable diagnostic of these important physical parameters. The models further confirm that SNe Ia should be excellent standard candles in the NIR, with a dispersion of 0.2 mag even when the physical properties of the ejecta are varied widely. This study emphasizes the consummate value of NIR observations in probing the structure of SNe Ia and in furthering their cosmological utility.