Multidimensional Radiation Transport Research Articles

Type Ia supernova explosion models are inherently multidimensional

Theoretical and observational approaches to settling the important questions surrounding the progenitor systems and the explosion mechanism of normal Type Ia supernovae have thus far failed. With its unique capability to obtain continuous spectra through the near- and mid-infrared, JWST now offers completely new insights into Type Ia supernovae. In particular, observing them in the nebular phase allows us to directly see the central ejecta and thereby constrain the explosion mechanism. We aim to understand and quantify differences in the structure and composition of the central ejecta of various Type Ia supernova explosion models. We examined the currently most popular explosion scenarios using self-consistent multidimensional explosion simulations of delayed-detonation and pulsationally assisted, gravitationally confined delayed detonation Chandrasekhar-mass models and double-detonation sub-Chandrasekhar-mass and violent merger models. We find that the distribution of radioactive and stable nickel in the final ejecta, both observable in nebular spectra, are significantly different between different explosion scenarios. Therefore, comparing synthetic nebular spectra with JWST observations should allow us to distinguish between explosion models. We show that the explosion ejecta are inherently multidimensional for all models, and the Chandrasekhar-mass explosions simulated in spherical symmetry in particular lead to a fundamentally unphysical ejecta structure. Moreover, we show that radioactive and stable nickel cover a significant range of densities at a fixed velocity of the homologously expanding ejecta. Any radiation transfer postprocessing has to take these variations into account to obtain faithful synthetic observables; this will likely require multidimensional radiation transport simulations.

Lagrange Discrete Ordinates: A New Angular Discretization for the Three-Dimensional Linear Boltzmann Equation

The classical Sn equations of Carlson and Lee have been a mainstay in multidimensional radiation transport calculations. In this paper, an alternative to the Sn equations, the “Lagrange Discrete Ordinates” (LDO) equations, are derived. These equations are based on an interpolatory framework for functions on the unit sphere in three dimensions. While the LDO equations retain the formal structure of the classical Sn equations, they have a number of important differences. The LDO equations naturally allow the angular flux to be evaluated in directions other than those found in the quadrature set. To calculate the scattering source in the LDO equations, no spherical harmonic moments are needed—only values of the angular flux. Moreover, the LDO scattering source preserves the eigenstructure of the continuous scattering operator. The formal similarity of the LDO equations with the Sn equations should allow easy modification of mature three-dimensional Sn codes such as PARTISN or PENTRAN to solve the LDO equations. Numerical results are shown that demonstrate the spectral convergence (in angle) of the LDO equations for smooth solutions and the ability to mitigate ray effects by increasing the angular resolution of the LDO equations.

A new spherical harmonics scheme for multi-dimensional radiation transport I. Static matter configurations

Recent work by McClarren and Hauck (2010) [31] suggests that the filtered spherical harmonics method represents an efficient, robust, and accurate method for radiation transport, at least in the two-dimensional (2D) case. We extend their work to the three-dimensional (3D) case and find that all of the advantages of the filtering approach identified in 2D are present also in the 3D case. We reformulate the filter operation in a way that is independent of the timestep and of the spatial discretization. We also explore different second- and fourth-order filters and find that the second-order ones yield significantly better results. Overall, our findings suggest that the filtered spherical harmonics approach represents a very promising method for 3D radiation transport calculations.

A hybrid (Monte Carlo/deterministic) approach for multi-dimensional radiation transport

A novel hybrid Monte Carlo transport scheme is demonstrated in a scene with solar illumination, scattering and absorbing 2D atmosphere, a textured reflecting mountain, and a small detector located in the sky (mounted on a satellite or a airplane). It uses a deterministic approximation of an adjoint transport solution to reduce variance, computed quickly by ignoring atmospheric interactions. This allows significant variance and computational cost reductions when the atmospheric scattering and absorption coefficient are small. When combined with an atmospheric photon-redirection scheme, significant variance reduction (equivalently acceleration) is achieved in the presence of atmospheric interactions.

Multi-dimensional radiation transport for modeling axisymmetric Z pinches: Ray tracing compared to Monte Carlo solutions for a two-level atom

Radiation plays a critical role in the dynamical evolution and energetics of Z pinches and a dominant role for those loads designed as radiation sources in the keV photon energy region. Therefore, in modeling such plasmas it is essential to employ an accurate and realistic calculation of radiation generation and transport. This study presents a straightforward method to carry out three-dimensional radiation transport calculations in an azimuthally symmetric cylindrical geometry for use in magnetohydrodynamic simulations of high energy Z-pinch plasma radiation sources. The present approach is based on the integral solution of the radiative transfer equation using long characteristics with equal weight angular quadratures, and uses either a multifrequency grid or probability-of-escape-based zone-to-zone coupling. Using previously published Monte Carlo calculations of a two-level atom in cylindrical geometry as a benchmark, the accuracy of the approach is assessed as a function of the frequency grid, number of rays employed, and spatial grid. An analytic expression for the frequency averaged escape probability of an emission line is found to be as accurate for the population kinetics as the multifrequency method. While the escape probability description sacrifices information on the line profile, it is far more computationally efficient yet sufficiently accurate for line dominated plasmas such as Z-pinch radiation sources.

An efficient tabulated collisional radiative equilibrium radiation transport model suitable for multidimensional hydrodynamics calculations

A computationally efficient method for transporting radiation in multidimensional plasmas has been developed and evaluated. The basis of this method is a uniform plasma approximation that allows one to utilize existing escape probability techniques that are successfully used in one-dimensional (1D) calculations to approximately solve the multidimensional radiation transport problem. This method is superior to diffusion methods because (1) the probability of escape technique insures that the plasma goes to the correct optically thin and thick limits, (2) the effects of line absorption due to photoexcitations are modeled, and (3) this method uses source functions that are based on a self-consistent nonlocal thermodynamic equilibrium calculation, not an ad hoc assumption that the source functions are Planckian. This method is highly efficient because equation of state information from 1D calculations is tabulated as a function of plasma internal energy, ion density, and the line probability of escape from a uniform plasma, and then used in multidimensional calculations. Given the internal energy and ion density, and by calculating the line probability of escape from a zone of the multidimensional plasma, the equation of state, including emissivities and absorption coefficients, of the zone is determined from the table. Total radiative power, K-shell radiative power, total radiative yield, K-shell radiative yield, and plasma density and temperature profiles obtained from 1D Z-pinch calculations employing this method are in good agreement with the same powers, yields, and profiles calculated using a full radiation transport model. This method has been implemented in the 2D plasma radiating imploding source model code [F. L. Cochran et al., Phys. Plasmas 2, 2765 (1995)] to determine the influence of radiation transport in argon Z-pinch experiments performed on the Z machine [R. B. Spielman et al., Phys. Plasmas 5, 2105 (1998)] at Sandia National Laboratories.

Gravitational effects on sooting diffusion flames

Simulations of a laminar ethylene-air diffusion flame burning in quiescent air are conducted to gain a better understanding of the effects of buoyancy on the dynamics and behavior of heavily sooting flames under normal-, partial-, micro-, zero-, and negative-gravity conditions and under conditions of gravitational jitter. The simulations solve the time-dependent reactive-flow Navier-Stokes equations coupled with submodels for soot formation and multidimensional radiation transport. Results from the computations follow many of the trends that have been experimentally observed in nonbuoyant diffusion flames. Due to the significant reduction in buoyancy-induced convection, diffusion becomes the dominant mechanism of transport. Microgravity flames are much longer and wider than their earth gravity counterparts due to the reduction in axial velocity and the thicker diffusion layers. In microgravity, flame flicker disappears due to the lack of a buoyancy-induced instability and the entire sooting region is much larger. The reduction in the axial velocity results in significantly longer residence times, allowing more time for soot particle surface growth, and resulting in greatly enhanced soot volume fraction. The enhanced soot production results in increased radiative heat losses, resulting in reduced flame temperatures. By tracing the path lines along which a soot parcel travels, the simulations show significant differences in the local environments through which soot passes between earth-gravity and microgravity flames.

Discrete-Ordinate Solutions of the Radiation Transport Equation

Over the past decade, the discrete-ordinate method has been used by a number of researchers to solve multidimensional radiation transport problems in the field of engineering heat transfer. The method is based on a discrete representation for the angular variation in the radiation intensity. The angular quadrature is arbitrary, although restrictions arise from the need to preserve symmetries and invariance properties of the physical system. Moment-matching, completely symmetric quadratures are frequently selected because of their generality. However, some quadratures do not match half-range moments, in particular the half-range first moment which is related to the one-way radiation flux. It is the purpose of this note to point out that low-order discrete-ordinate solutions of the transport equation may be significantly improved when the quadrature is chosen to match the half-range first moment. These improvements are illustrated for the specific case of radiation in a two-dimensional rectangular enclosure, examined recently by Fiveland.

Use of Multidimensional Transport Methodology on Nuclear Logging Problems

A review is made of multidimensional radiation transport techniques that are being used to model nuclear oil well logging measurements. Both Monte Carlo and deterministic methods are employed for this work, and it is found that the realism that can be incorporated into these models has led to greater understanding of all kinds of logging measurements. As a result, models are now used as part of the new logging tool design process in much the same way that they are used to support nuclear reactor and shielding designs. Despite the success so far, there is still room to improve both Monte Carlo and especially deterministic methods for logging applications. Monte Carlo codes, impressive as they are, are still expensive computations for many logging problems. Although improvements in basic Monte Carlo can still be made, it seems that the next significant improvement in the efficiency of Monte Carlo will come from computer architecture in the form of multiprocessor machines. On the other hand, the prinicipal limitation of deterministic calculations centers mainly on the lack of accurate, practical, three-dimensional transport capabilities. With this in mind, some recent work to extend a nodal, discrete ordinates method to three dimensions for logging applications ismore » reviewed.« less

Approximate and exact technique for multidimensional radiation transport in a plane parallel atmosphere; Application to the 4.3 μm auroral arc

We develop an integral equation formulation for the solution of multidimensional radiation transport problems in a plane-parallel atmosphere. The formulation is applied to a nominal case of a 4.3 μm auroral arc. The accuracy of a computation-saving, approximate method is investigated.