Fast iterative methods for discrete-ordinates particle transport calculations

We present a formulation for multigroup radiation hydrodynamics that is correct to order O(v/c) using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system, implemented in the compressible astrophysics code, CASTRO. CASTRO uses a Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. In our multigroup radiation solver, the system is split into three parts: one part that couples the radiation and fluid in a hyperbolic subsystem, another part that advects the radiation in frequency space, and a parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem and the frequency space advection are solved explicitly with high-order Godunov schemes, whereas the parabolic part is solved implicitly with a first-order backward Euler method. Our multigroup radiation solver works for both neutrino and photon radiation.

Castro: a new compressible astrophysical solver. iii. multigroup radiation hydrodynamics

The anaerobic pyrolysis of wood material used to palletize commodities is studied in a Fire Propagation Apparatus (FPA) for a range of heating conditions relevant to fires. The data collected, consisting of mass loss rate, cumulative mass loss, and surface temperature, are used to determine model-specific material properties using inverse modeling and optimization methodologies previously developed in our laboratory. However, in this study, considerable effort is placed on determining the radiation environment that characterizes the FPA tests as well as how the radiation interacts with the samples. This is done on the basis of the recognition that boundary conditions have a pronounced effect on the output of a given pyrolysis model and, thus, the optimization results. The spectral radiance from the FPA heaters as well as the absorptivity/emissivity of the material surface are measured herein. The spectral features of the surface indicate that markedly different effective emissivities and absorptivities can be exhibited by the material depending on the spectral distribution of incident radiation. These effects are included in the pyrolysis model used to extract model-specific material properties so that the optimization process can, in a sense, be decoupled from boundary conditions. Therefore, it is expected that the approach described in this study can ensure that the derived model-specific properties can be applied to practical scenarios that are characterized by radiation environments that differ from those in bench-scale test apparatuses such as the FPA.

/pdf/spectral-aspects-of-bench-scale-flammability-testing-278a8nd9f8.pdf

Spectral Aspects of Bench-Scale Flammability Testing: Application to Hardwood Pyrolysis

We present a formulation for multigroup radiation hydrodynamics that is correct to order $O(v/c)$ using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system, implemented in the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically-rectangular variable-sized grids with simultaneous refinement in both space and time. In our multigroup radiation solver, the system is split into three parts, one part that couples the radiation and fluid in a hyperbolic subsystem, another part that advects the radiation in frequency space, and a parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem and the frequency space advection are solved explicitly with high-order Godunov schemes, whereas the parabolic part is solved implicitly with a first-order backward Euler method. Our multigroup radiation solver works for both neutrino and photon radiation.

CASTRO: A New Compressible Astrophysical Solver. III. Multigroup Radiation Hydrodynamics

A new method based on the polylogarithm function is used to derive an exact expression for the fractional emissive power of a blackbody in any arbitrary spectral band. Compared to all previously used methods the polylogarithm based method is unsurpassed in its simplicity. Displacement laws for the centroid of blackbody radiation in the linear wavelength and frequency spectral representations that make use of the polylogarithm based approach are also given.

Blackbody radiation functions and polylogarithms

Computing multigroup radiation integrals using polylogarithm-based methods

Publisher Summary Radiation hydrodynamics treats the interactions of thermal radiation with matter. Thermal radiation is taken to mean electromagnetic radiation of atomic origin, obtained from the processes of scattering, absorption, and thermal emission. The radiation field is described by an equation of transfer, which is a Boltzmann transport equation for photons. From a computational viewpoint, time-dependent radiative transfer problems in emitting media are difficult to solve. In general, their solution involves an equation with seven independent variables for the radiation field, along with the additional equations describing the mass, momentum, and energy balance of the underlying medium. This chapter describes new numerical methods for solving such problems. It also discusses three aspects of the solution method: the time dependence, the intimate coupling between the radiation field and the medium, and the iteration acceleration of the equation of transfer. The time dependence is treated implicitly, that is, the equation of transfer is written in terms of the dependent variables evaluated at the advanced time.

The Diffusion-Synthetic Acceleration of Transport Iterations, with Application to a Radiation Hydrodynamics Problem

A new three-point nonlinear difference scheme for diffusion synthetic acceleration (DSA) of the radiation transport equation is described. The new scheme is compared with the standard one-point met...

Nonlinear Diffusion Synthetic Acceleration Difference Schemes for Radiative Transfer Applications

Two enhancements to the Fleck implicit Monte Carlo method for radiative transport are described, for use in transparent and opaque media, respectively. The first introduces a spectral mean cross section, which applies to pseudoscattering in transparent regions with a high frequency incident spectrum. The second provides a simple Monte Carlo random walk method for opaque regions, without the need for a supplementary diffusion equation formulation.

/pdf/implicit-monte-carlo-methods-and-non-equilibrium-marshak-2ayk81lizn.pdf

Bradley A. Clark

Papers

Computing multigroup radiation integrals using polylogarithm-based methods

The Diffusion-Synthetic Acceleration of Transport Iterations, with Application to a Radiation Hydrodynamics Problem

Nonlinear Diffusion Synthetic Acceleration Difference Schemes for Radiative Transfer Applications

Implicit Monte-Carlo Methods and Non-Equilibrium Marshak Wave Radiative Transport