A radiative transfer scheme for cosmological reionization based on a local Eddington tensor

A radiative transfer scheme is presented, based on a moment description of the equation of radiative transfer and the so-called ``M1 closure model'' for the Eddington tensor. This model features a strictly hyperbolic transport step for radiation: it has been implemented using standard Godunov--like techniques in a new code called ATON. Coupled to simple models of ionization chemistry and photo-heating, ATON is able to reproduce the results of other schemes on a various set of standard tests such as the expansion of a HII region, the shielding of the radiation by dense clumps and cosmological ionization by multiple sources. Being simple yet robust, such a scheme is intended to be naturally and easily included in grid--based cosmological fluid solvers.Comment: 14 pages, 13 figures, submitted to MNRA

A radiation-hydrodynamics scheme valid from the transport to the diffusion limit

We present in this paper the numerical treatment of the coupling between hydrodynamics and radiative transfer. The fluid is modeled by classical conservation laws (mass, momentum and energy) and the radiation by the grey moment $M_1$ system. The scheme introduced is able to compute accurate numerical solution over a broad class of regimes from the transport to the diffusive limits. We propose an asymptotic preserving modification of the HLLE scheme in order to treat correctly the diffusion limit. Several numerical results are presented, which show that this approach is robust and have the correct behavior in both the diffusive and free-streaming limits. In the last numerical example we test this approach on a complex physical case by considering the collapse of a gas cloud leading to a proto-stellar structure which, among other features, exhibits very steep opacity gradients.Comment: 29 pages, submitted to Journal of Computational physic

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 (M1) 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 M1 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.Comment: 27 pages, 11 figures, Accepted for publication in JQSR

Deterministic Partial Differential Equation Model for Dose Calculation in Electron Radiotherapy

Treatment with high energy ionizing radiation is one of the main methods in modern cancer therapy that is in clinical use. During the last decades, two main approaches to dose calculation were used, Monte Carlo simulations and semi-empirical models based on Fermi-Eyges theory. A third way to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. Starting from these, we derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free-streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on [BerCharDub], that exactly preserves key properties of the analytical solution on the discrete level. Several numerical results for test cases from the medical physics literature are presented.Comment: 20 pages, 7 figure

Flux limiters in the coupling of radiation and hydrodynamic models

AbstractTwo numerical approximations to radiative heat transfer problem based on asymptotic and entropy approaches are proposed for hydrodynamics radiation coupling. We compare the radiative fluxes between the two approaches and we show that the coupling based on the entropy approach is flux limited, while the other approach does not preserve this condition. Relaxation schemes are considered for the hydrodynamic part, and an iterative procedure is used for radiation. The new splitting algorithm avoids the use of Riemann solvers and Newton iterations. Numerical examples are carried out on two and three dimensional problems

ULTRAVIOLET LINEAR DICHROISM STUDIES OF INDENE

Abstract Ultraviolet Linear Dichroism (LD) spectra of the indene molecule in stretched polyethylene (PE) film are reported. Differently polarized electronic transitions are resolved in the LD spectrum. The first electronic transition at λ max = 285 nm, which is hidden by the second one in solution, is clearly isolated in LD spectra and polarized along the long axis of the molecule. The second one which is located at about λ max = 250 nm is polarized along the short axis. The calculated spectrum of indene shows the same trends in complete agreement with experimental findings

Simulations of protostellar collapse using multigroup radiation hydrodynamics. I. The first collapse

Radiative transfer plays a major role in the process of star formation. Many simulations of gravitational collapse of a cold gas cloud followed by the formation of a protostellar core use a grey treatment of radiative transfer coupled to the hydrodynamics. However, dust opacities which dominate extinction show large variations as a function of frequency. In this paper, we used frequency-dependent radiative transfer to investigate the influence of the opacity variations on the properties of Larson's first core. We used a multigroup M1 moment model in a 1D radiation hydrodynamics code to simulate the spherically symmetric collapse of a 1 solar mass cloud core. Monochromatic dust opacities for five different temperature ranges were used to compute Planck and Rosseland means inside each frequency group. The results are very consistent with previous studies and only small differences were observed between the grey and multigroup simulations. For a same central density, the multigroup simulations tend to produce first cores with a slightly higher radius and central temperature. We also performed simulations of the collapse of a 10 and 0.1 solar mass cloud, which showed the properties of the first core to be independent of the initial cloud mass, with again no major differences between grey and multigroup models. For Larson's first collapse, where temperatures remain below 2000 K, the vast majority of the radiation energy lies in the IR regime and the system is optically thick. In this regime, the grey approximation does a good job reproducing the correct opacities, as long as there are no large opacity variations on scales much smaller than the width of the Planck function. The multigroup method is however expected to yield more important differences in the later stages of the collapse when high energy (UV and X-ray) radiation is present and matter and radiation are strongly decoupled.Comment: 9 pages, 5 figures, accepted for publication in A&

Phase appearance or disappearance in two-phase flows

This paper is devoted to the treatment of specific numerical problems which appear when phase appearance or disappearance occurs in models of two-phase flows. Such models have crucial importance in many industrial areas such as nuclear power plant safety studies. In this paper, two outstanding problems are identified: first, the loss of hyperbolicity of the system when a phase appears or disappears and second, the lack of positivity of standard shock capturing schemes such as the Roe scheme. After an asymptotic study of the model, this paper proposes accurate and robust numerical methods adapted to the simulation of phase appearance or disappearance. Polynomial solvers are developed to avoid the use of eigenvectors which are needed in usual shock capturing schemes, and a method based on an adaptive numerical diffusion is designed to treat the positivity problems. An alternate method, based on the use of the hyperbolic tangent function instead of a polynomial, is also considered. Numerical results are presented which demonstrate the efficiency of the proposed solutions