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Register a new user3D B_2 Model for Radiative Transfer Equation Part I: Modelling
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We extend to three-dimensional space the approximate M_2 model for the slab geometry studied in our previous paper. The B_2 model therein, as a special case of the second order extended quadrature method of moments (EQMOM), is proved to be globally hyperbolic. The model we proposed here extends EQMOM to multiple dimensions following the idea to approximate the maximum entropy closure for the slab geometry case. Like the M_2 closure, the ansatz of the new model has the capacity to capture both isotropic and beam-like solutions, while the new model has fluxes in closed-form, thus is applicable to practical numerical simulations. The rotational invariance, realizability, and hyperbolicity of the model are studied.
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Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient and accurate numerical resolution lies in the high dimensionality of the physical and velocity/angular variables and the fact that the problem is multiscale in nature. Leveraging the existence of a hidden low-rank structure hinted by the diffusive limit, in this work, we design and test the angular-space reduced order model for the linear radiative transfer equation, the first such effort based on the celebrated reduced basis method (RBM). Our method is built upon a high-fidelity solver employing the discrete ordinates method in the angular space, an asymptotic preserving upwind discontinuous Galerkin method for the physical space, and an efficient synthetic accelerated source iteration for the resulting linear system. Addressing the challenge of the parameter values (or angular directions) being coupled through an integration operator, the first novel ingredient of our method is an iterative procedure where the macroscopic density is constructed from the RBM snapshots, treated explicitly and allowing a transport sweep, and then updated afterwards. A greedy algorithm can then proceed to adaptively select the representative samples in the angular space and form a surrogate solution space. The second novelty is a least-squares density reconstruction strategy, at each of the relevant physical locations, enabling the robust and accurate integration over an arbitrarily unstructured set of angular samples toward the macroscopic density. Numerical experiments indicate that our method is highly effective for computational cost reduction in a variety of regimes.
The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering. It is an integro-differential equation involving time, space and angular variables and contains an integral term in angular directions while being hyperbolic in space. The challenges for its numerical solution include the needs to handle with its high dimensionality, the presence of the integral term, and the development of discontinuities and sharp layers in its solution along spatial directions. Its numerical solution is studied in this paper using an adaptive moving mesh discontinuous Galerkin method for spatial discretization together with the discrete ordinate method for angular discretization. The former employs a dynamic mesh adaptation strategy based on moving mesh partial differential equations to improve computational accuracy and efficiency. Its mesh adaptation ability, accuracy, and efficiency are demonstrated in a selection of one- and two-dimensional numerical examples.
Investigating the dust heating mechanisms in galaxies provides a deeper understanding of how the internal energy balance drives their evolution. Over the last decade, radiative transfer simulations based on the Monte Carlo method have underlined the role of the various stellar populations heating the diffuse dust. Beyond the expected heating through ongoing star formation, both older stellar population (> 8Gyr) and even AGN can contribute energy to the infrared emission of diffuse dust. Here, we examine how the radiation of an external heating source, like the less massive galaxy NGC5195, in the M51 interacting system, could affect the heating of the diffuse dust of its parent galaxy, NGC5194, and vice versa. To quantify the exchange of energy between the two galaxies we use SKIRT, a state-of-the-art Monte Carlo radiative transfer code. In the interest of modelling, the assumed centre-to-centre distance separation between the two galaxies is 10kpc. Our model reproduces the global SED of the system, and it closely matches the observed images. In total, 40.7% of the intrinsic stellar radiation of the combined system is absorbed by dust. Furthermore, we quantify the contribution of the various dust heating sources in the system, and find that the young stellar population of NGC5194 is the predominant dust-heating agent, with a global heating fraction of 71.2%. Another 23% is provided by the older stellar population of the same galaxy, while the remaining 5.8% has its origin in NGC5195. Locally, we find that the regions of NGC5194 closer to NGC5195 are significantly affected by the radiation field of the latter, with the absorbed energy fraction rising up to 38%. The contribution of NGC5195 remains under the percentage level in the outskirts of the disc of NGC5194. This is the first time that the heating of the diffuse dust by a companion galaxy is quantified in a nearby interacting system.
New mathematical and numerical results are given for the coupling of the temperature equation of a fluid with Radiative Transfer: existence and uniqueness and a convergent monotone numerical scheme. The technique is shown to be feasible for studying the temperature of lake Leman heated by the sun and for the earth atmosphere to study the effects of greenhouse gases.
Context: Dust in late-type galaxies in the local Universe is responsible for absorbing approximately one third of the energy emitted by stars. It is often assumed that dust heating is mainly attributable to the absorption of UV and optical photons emitted by the youngest (<= 100 Myr) stars. Consequently, thermal re-emission by dust at FIR wavelengths is often linked to the star-formation activity of a galaxy. However, several studies argue that the contribution to dust heating by much older stars might be more significant. Advances in radiation transfer (RT) simulations finally allow us to actually quantify the heating mechanisms of diffuse dust by the stellar radiation field. Aims: As one of the main goals in the DustPedia project, we have constructed detailed 3D stellar and dust RT models for nearby galaxies. We analyse the contribution of the different stellar populations to the dust heating in four face-on barred galaxies: NGC1365, M83, M95, and M100. We aim to quantify the fraction directly related to young stars, both globally and on local scales, and to assess the influence of the bar on the heating fraction. Results: We derive global attenuation laws for each galaxy and confirm that galaxies of high sSFR have shallower attenuation curves and weaker UV bumps. On average, 36.5% of the bolometric luminosity is absorbed by dust. We report a clear effect of the bar structure on the radial profiles of the dust-heating fraction by the young stars, and the dust temperature. We find that the young stars are the main contributors to the dust heating, donating, on average ~59% of their luminosity to this purpose throughout the galaxy. This dust-heating fraction drops to ~53% in the bar region and ~38% in the bulge region where the old stars are the dominant contributors to the dust heating. We also find a strong link between the heating fraction by the young stars and the sSFR.
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