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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

MOOSE-based Tritium Migration Analysis Program, Version 8 (TMAP8) for advanced open-source tritium transport and fuel cycle modeling

Tritium management is critical for the safety, sustainability, and economics of fusion energy systems, and advanced and reliable modeling tools help accelerate the development of tritium technologies. This paper presents the Tritium Migration Analysis Program, Version 8 (TMAP8), an open-source, MOOSE-based application developed to provide state-of-the-art tritium transport and fuel cycle modeling capabilities. TMAP8 aims to expand the capabilities of previous versions (i.e., TMAP4 and TMAP7) by leveraging modern computational techniques, ensuring high software quality assurance standards (key to building trust), and enabling multispecies, multiscale, and multiphysics simulations for integrated tritium transport modeling in complex geometries. This paper outlines TMAP8’s scope and rigorous development practices, emphasizing its transparency, accessibility, modularity, and reliability. We present the current suite of verification and validation cases based on those from TMAP4, demonstrating TMAP8’s accuracy and reliability against analytical solutions and experimental data. Additionally, the paper showcases TMAP8’s integrated fuel cycle modeling capabilities, highlighting its applicability at various scales and levels. The TMAP8 code and documentation are openly available, promoting collaborative development and widespread adoption within the fusion community. Future work will soon expand TMAP8’s verification and validation suite to include those from TMAP7 and other recent experimental studies for validation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Construction of 3D MHD pressure drop correlation and flow characterization in the contraction region of a fusion blanket manifold

Inlet and outlet manifolds are typical components of liquid metal (LM) blanket designs of a fusion power reactor to be used to distribute the LM flow into breeding channels and collect it at the exit of the blanket. High pressure loss in the magnetohydrodynamic (MHD) flows featuring abrupt geometrical changes is one of the main feasibility issues of such designs. Recently, optimization studies were conducted to construct 3D MHD pressure drop correlations for a LM flow in an electrically insulating manifold with gradual expansion. Here, the 3D computational approach developed in that study is applied to the outlet manifold featuring gradual contraction. A systematic analysis was performed with a total number of 135 flow cases computed with COMSOL Multiphysics for Hartmann numbers 1000 < Ha < 10,000, Reynolds numbers 100 < Re < 12,000, and contraction angles 45° < θ < 75° for a fixed contraction ratio of 4. The effects of Ha, Re and θ on the flow recirculation, development length and the total pressure drop were carefully examined. A linear regression analysis was used to determine the power rule of pressure drop coefficient k related to Ha and Re, demonstrating a good match with the Ludford layer theory. Eventually, a correlation for the 3D MHD pressure drop coefficient was constructed as a function of Ha, Re and θ. Further, the results were compared against the inlet manifold. It was found that the flow in the inlet manifold exhibits larger recirculation zones. In the investigated range of Ha, Re and θ, the pressure drop coefficient k of the LM MHD flow in the gradual contraction is only slightly lower (< 8 %) than that in the gradual expansion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Evaluation of accuracy and convergence of numerical coupling approaches for poroelasticity benchmark problems

Accurate modeling of subsurface flow and transport processes is vital as the prevalence of subsurface activities such as carbon sequestration, geothermal recovery, and nuclear waste disposal increases. Computational modeling of these problems leverages poroelasticity theory, which describes coupled fluid flow and mechanical deformation. Although fully coupled monolithic schemes are accurate for coupled problems, they can demand significant computational resources for large problems. In this work, a fixed stress scheme is implemented into the Sandia Sierra Multiphysics toolkit. Two implementation methods, along with the fully coupled method, are verified with one-dimensional (1D) Terzaghi, 2D Mandel, and 3D Cryer sphere benchmark problems. The impact of a range of material parameters and convergence tolerances on numerical accuracy and efficiency was evaluated. Overall the fixed stress schemes achieved acceptable numerical accuracy and efficiency compared to the fully coupled scheme. However, the accuracy of the fixed stress scheme tends to decrease with low permeable cases, requiring the finer tolerance to achieve a desired numerical accuracy. For the fully coupled scheme, high numerical accuracy was observed in most of cases except a low permeability case where an order of magnitude finer tolerance was required for accurate results. Finally, a two-layer Terzaghi problem and an injection–production well system were used to demonstrate the applicability of findings from the benchmark problems for more realistic conditions over a range of permeability. Simulation results suggest that the fixed stress scheme provides accurate solutions for all cases considered with the proper adjustment of the tolerance. Furthermore, this work clearly demonstrates the robustness of the fixed stress scheme for coupled poroelastic problems, while a cautious selection of numerical tolerance may be required under certain conditions with low permeable materials.

58 GEOSCIENCES↗
DOE OSTI2018

Computational examination of two-phase microchannel heat transfer correlations with conjugate heat spreading

Microchannel flow boiling is an attractive thermal management strategy for ever-growing volumetric heat dissipation demands associated with electronic systems. Due to difficulties related to measurement at the microscales, the majority of researchers have chosen to study relatively simple situations with uniform heat flux. However, many applications involve local hotspots which give rise to highly non-uniform heat flux and temperature gradients due to heat spreading. This necessitates the consideration of conjugate heat transfer for accurate analysis. The current work is aimed at investigating conjugate heat transfer in a two-phase microchannel array. Experimental data was collected on R134a flow boiling heat transfer for very small hydraulic diameter (<100 µm) silicon microchannels with very high heat fluxes (>1 kW cm -2 ) applied via platinum strip heaters with a footprint size of 1 cm × 1 mm. The collected experimental data was then combined with detailed computational modeling utilizing finite element modeling with COMSOL Multiphysics and MATLAB to examine the applicability of five published heat transfer correlations for use in determining local heat transfer coefficients. A two-phase correlation from Agostini and Bontemps, developed for markedly different test parameters, provided the best computational agreement with an RMS temperature difference from experiment of 3.3 °C and a predicted peak perimeter-averaged heat transfer coefficient of 116 MW m -2 K -1 . Modeling confirms the presence of highly non-uniform local heat flux and correspondingly non-uniform local heat transfer coefficient. Finally, the results of this study make clear the need for better micro-scale two-phase correlations developed to predict local heat transfer coefficients at these small scales and high local heat fluxes.

42 ENGINEERING↗
DOE OSTI2021

Prediction of PbLi fluid flow and temperature field in a thermal convection loop for qualification of fusion materials

Two modeling tools, a thermohydraulics code and a computational model in COMSOL Multiphysics, have been developed, tested and then applied to the analysis of fluid flow and heat transfer in a thermal convection loop (TCL). Such a device has recently been used to experimentally evaluate corrosion compatibility of APMT (Fe–21Cr–5Al–3Mo) steel with high-temperature molten eutectic lead-lithium (PbLi) alloy at Oak Ridge National Lab, TN, USA. Here, the 1-D thermohydraulics code allows for rapid calculations of the loop parameters as a function of the applied heat flux. The supplemental COMSOL finite-element computations provide detailed 3-D velocity and temperature field data but are much more time consuming. Both modelling tools demonstrate an excellent agreement in the computed circulation velocity as well as maximum and minimum temperatures. The performed TCL analysis focuses on flow development in the “hot” and “cold” legs, formation of Dean vortices in corner regions, blocking effect of the immersed samples, and radiative and convective cooling effects under the experiment-relevant conditions for Prandtl number Pr = 0.015, Grashof numbers Gr ~10 7 , and Reynolds numbers Re ~10 4 .

36 MATERIALS SCIENCE↗
DOE OSTI2021

Thermal-striping analysis methodology for sodium-cooled reactor design

Computational fluid dynamics simulations have been performed to study the applicability of engineering CFD methods for thermals striping analysis. Thermal striping is the fluctuating temperature profile in a solid caused by fluctuating fluid temperature, and the resulting fluctuating thermal stresses cause high cycle fatigue and eventual material failure. Here this study presents the methodology for thermal striping analysis that including a transient conjugate heat transfer RANS model and benchmark the results against a sodium triple jet experiment. The multiphysics calculations are implemented to analyze the thermal stresses in the solid domain caused by the coupled heat transfer between the fluid and solid domains. Validation data from a liquid sodium triple jet experiment include time-averaged temperature measurements and power spectra of the temperature signal. The numerical results agree well with these experimental measures, demonstrating key features such as the dominant frequency of temperature fluctuations. The applicability of a low-cost wall treatment method is demonstrated, enabling key computational savings. Finally, the performance of two finite element stress analysis software packages is compared, and the validity of the lower-cost method is confirmed. These results demonstrate the applicability of engineering methods for computational thermal striping calculations, enabling thermal striping estimations in large fluid systems such as the core of a Sodium-cooled nuclear reactor.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Cooling performance of an active-passive hybrid composite phase change material (HcPCM) finned heat sink: Constant operating mode

Here, the present study explores a hybrid thermal management technology based on air cooling and hybrid composite phase change material (HcPCM) filled finned heat sink for cooling performance of lower to medium heat flux dissipating electronic devices. Two-dimensional numerical simulations are conducted to study the conjugate heat transfer effects of three types of finned heat sink: air-cooled finned heat sink, HcPCM-cooled finned heat sink, and hybrid (air-HcPCM) cooled finned heat sink. A heat sink with a constant volume faction of plate-fins is designed in all cases and simultaneous effects of hybrid nanoparticles and air are investigated to keep the heat sink temperature at safe operating conditions between 40–60°C. The effect of air is incorporated into the heat sink by applying the convective heat transfer coefficient of h c = 10–100W /m 2 .K which tends to create the natural convection and forced convection heat transfer characteristics. The heat flux is varied from 25–40kW /m 2 in the current study. The hybrid nanoparticles of carbon additives (GO and MWCNTs) are dispersed into the RT-35HC, used as a PCM, with a volume fraction of 0% to 6%. Transient simulations are carried out using COMSOL Multiphysics to solve the governing equations for PCM based conjugate heat transfer model. The results showed that forced convection heat transfer improved the cooling performance of the hybrid heat sink compared to natural convection heat transfer. The addition of nanoparticles further enhanced thermal enhancement and uniform melting distribution of PCM inside the finned heat sink. The h c between 30 to 50W/m 2 .K shows optimized values for forced convection heat transfer operating conditions. The volume fraction of 2% of GO+MWCNTs nanoparticles in recommended or optimum concentration for uniform melting of PCM inside the finned heat sink.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Modeling the performance and faradaic efficiency of solid oxide electrolysis cells using doped barium zirconate perovskite electrolytes

Y-doped BaZrO 3 (BaZr 1 x Y x O 3 δ , or “BZY”), a proton-conducting ceramic featuring high bulk conductivity and good chemical stability, is a promising electrolyte material for solid oxide electrolysis cells. Further doping with Ce and/or Yb (creating materials “BCZY” and “BCZYYb”) can improve conductivity and sintering properties, but at significant penalty to cells’ faradaic efficiency (FE). Studies have proposed that reduction of lattice Ce can occur in the hydrogen electrode, which consumes some hydrogen produced by the hydrogen evolution reaction, leading to decreased FE. Despite studies suggesting this phenomenon, the mechanism is largely unknown. In this work, we developed a multiphysics model to study the transport of multiple defect species and the performance of BZY, BCZY, and BCZYYb, capturing the tradeoff between enhanced performance at the cost of FE for BCZY and BCZYYb electrolytes compared to BZY. We also found that increasing the water content of the anode gas supply lowers the current output of the cell but results in better FE. The model, which uses several parameters previously unavailable in the literature, was validated to experiments varying temperature, steam water content, and electrolyte material, as well as two performance metrics (performance curves and FE). Results verify and explain observed trends, informing future work on Ce-doped BZY electrolytes.

08 HYDROGEN↗
DOE OSTI2021

Mathematical modeling of novel porous transport layer architectures for proton exchange membrane electrolysis cells

Thin foil based porous transport layers (PTLs) that contain highly structured pore arrays have shown promise as anode PTLs in proton exchange membrane electrolysis cells. These novel PTLs, fabricated with advanced manufacturing techniques, produce thin, tunable, multifunctional layers with reduced flow and interfacial resistances and high thermal and electric conductivities. To further optimize their design, it is important to understand their fundamental impact on the transport of protons, electrons, and liquid/vapor mixtures in the electrode. In this work, we develop a two-dimensional multiphysics model to simulate the coupled electrochemistry and multiphase transport in an electrolysis cell operated with the novel PTL architecture. The results show that larger pores improve access of water to the anode catalyst layer, which is beneficial for both the oxygen evolution reaction and membrane hydration. Larger pore sizes also improve oxygen gas transport from the catalyst layer, because generated oxygen gas is forced to travel in-plane through the anode catalyst layer until it reaches a pore opening that is connected to a channel. The discussed results confirm that the proposed thin foil based PTLs are fundamentally different from conventional PTLs, such as felts or layered meshes. The model developed in this work also provides generalizable insight into fundamental PEMEC phenomena, such as the competition between liquid and gas phase transport, membrane hydration and water management, and nonuniform electrochemical reactions, which are processes relevant to all PEMEC designs.

25 ENERGY STORAGE↗
DOE OSTI2025

Development, validation, and verification of multi-pass thermo-mechanical welding simulations using the open-source MOOSE framework: NeT TG4 benchmark weldment

This study develops and validates a sequentially coupled thermo-mechanical welding simulation for the three-pass 316L stainless steel NeT TG4 benchmark weldment using the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) and the Nuclear Engineering Material model Library (NEML). A diffused ellipsoidal heat source was calibrated against thermocouple data and weld macrographs to accurately model the fusion zone geometry and transient thermal fields. Material hardening is represented using the Lemaitre-Chaboche mixed isotropic-kinematic hardening model, while four annealing models - no annealing, single-stage at 1050 °C and 1300 °C, and two-stage at 800 °C/1300 °C - were implemented to assess the impact of annealing models on the accuracy of the predicted welding-induced plasticity, distortions, and residual stresses. The predictions were validated against experimental measurements and benchmarked against results from commercial software, demonstrating that thermo-mechanical MOOSE welding simulations achieve comparable accuracy with enhanced computational efficiency. This work highlights the potential of using open-source finite element frameworks like MOOSE for advanced manufacturing simulations.

Ji, Wendy [Australian Nuclear Science and Technolo↗
DOE OSTI2015

AETHER: A simulation platform for inductively coupled plasma

An in-house code is developed to simulate the inductively coupled plasma (ICP). The model comprises the fluid, electromagnetic and transformer submodels. Fluid equations are solved to evaluate the plasma flow parameters, including the plasma and neutral densities, ion and neutral velocities, electron flux, electron temperature, and electric potential. The model relies on the ambipolar approximation and offers the evaluation of plasma parameters without solving the sheath region. The electromagnetic model handles the calculation of the electric and magnetic fields using the magnetic vector potential. The transformer model captures the effect of the matching circuit utilized in laboratory experiments for RF power deposition. The continuity and momentum equations are solved using finite volume method. The energy, electric potential, and magnetic vector potential equations are solved using finite difference method. The resulting linear systems of equations are solved with iterative solvers including Jacobi and GMRES. The code is written using the C++ programming language, it works in parallel and has graphical user interface. The model is applied to study ICP characteristics of a plasma confined within a cylindrical chamber with dielectric walls for two different power deposition cases. The results obtained from the developed model are verified using the plasma module of COMSOL Multiphysics. The model is also applied to a plasma source configuration, and it is demonstrated that there is an overall increase in the plasma potential when current is extracted from ICP with a biased wall electrode.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Entropy-based artificial viscosity stabilization for non-equilibrium Grey Radiation-Hydrodynamics

The entropy viscosity method is extended to the non-equilibrium Grey Radiation-Hydrodynamic equations. The method employs a viscous regularization to stabilize the numerical solution. The artificial viscosity coefficient is modulated by the entropy production and peaks at shock locations. The added dissipative terms are consistent with the entropy minimum principle. A new functional form of the entropy residual, suitable for the Radiation-Hydrodynamic equations, is derived. We demonstrate that the viscous regularization preserves the equilibrium diffusion limit. The equations are discretized with a standard Continuous Galerkin Finite Element Method and a fully implicit temporal integrator within the MOOSE multiphysics framework. The method of manufactured solutions is employed to demonstrate second-order accuracy in both the equilibrium diffusion and streaming limits. Several typical 1-D radiation-hydrodynamic test cases with shocks (from Mach 1.05 to Mach 50) are presented to establish the ability of the technique to capture and resolve shocks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as well as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Modeling and simulation challenges pursued by the Consortium for Advanced Simulation of Light Water Reactors (CASL)

The Consortium for the Advanced Simulation of Light Water Reactors (CASL), the first Energy Innovation Hub of the Department of Energy, was established in 2010 with the goal of providing modeling and simulation (M&S) capabilities that support and accelerate the improvement of nuclear energy's economic competitiveness and the reduction of spent nuclear fuel volume per unit energy, and all while assuring nuclear safety. To accomplish this requires advances in M&S capabilities in radiation transport, thermal-hydraulics, fuel performance and corrosion chemistry. To focus CASL's R&D, industry challenge problems have been defined, which equate with long standing issues of the nuclear power industry that M&S can assist in addressing. To date CASL has developed a multi-physics “core simulator” based upon pin-resolved radiation transport and subchannel (within fuel assembly) thermal-hydraulics, capitalizing on the capabilities of high performance computing. CASL's fuel performance M&S capability can also be optionally integrated into the core simulator, yielding a coupled multi-physics capability with untapped predictive potential. Material models have been developed to enhance predictive capabilities of fuel clad creep and growth, along with deeper understanding of zirconium alloy clad oxidation and hydrogen pickup. Understanding of corrosion chemistry (e.g., CRUD formation) has evolved at all scales: micro, meso and macro. CFD R&D has focused on improvement in closure models for subcooled boiling and bubbly flow, and the formulation of robust numerical solution algorithms. For multiphysics integration, several iterative acceleration methods have been assessed, illuminating areas where further research is needed. Finally, uncertainty quantification and data assimilation techniques, based upon sampling approaches, have been made more feasible for practicing nuclear engineers via R&D on dimensional reduction and biased sampling. Industry adoption of CASL's evolving M&S capabilities, which is in progress, will assist in addressing long-standing and future operational and safety challenges of the nuclear industry. - Highlights: • Complexity of physics based modeling of light water reactor cores being addressed. • Capability developed to help address problems that have challenged the nuclear power industry. • Simulation capabilities that take advantage of high performance computing developed.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Conservative tightly-coupled simulations of stochastic multiscale systems

Multiphysics problems often involve components whose macroscopic dynamics is driven by microscopic random fluctuations. The fidelity of simulations of such systems depends on their ability to propagate these random fluctuations throughout a computational domain, including subdomains represented by deterministic solvers. When the constituent processes take place in nonoverlapping subdomains, system behavior can be modeled via a domain-decomposition approach that couples separate components at the interfaces between these subdomains. Its coupling algorithm has to maintain a stable and efficient numerical time integration even at high noise strength. We propose a conservative domain-decomposition algorithm in which tight coupling is achieved by employing either Picard's or Newton's iterative method. Coupled diffusion equations, one of which has a Gaussian white-noise source term, provide a computational testbed for analysis of these two coupling strategies. Fully-converged (“implicit”) coupling with Newton's method typically outperforms its Picard counterpart, especially at high noise levels. This is because the number of Newton iterations scales linearly with the amplitude of the Gaussian noise, while the number of Picard iterations can scale superlinearly. At large time intervals between two subsequent inter-solver communications, the solution error for single-iteration (“explicit”) Picard's coupling can be several orders of magnitude higher than that for implicit coupling. Increasing the explicit coupling's communication frequency reduces this difference, but the resulting increase in computational cost can make it less efficient than implicit coupling at similar levels of solution error, depending on the communication frequency of the latter and the noise strength. This trend carries over into higher dimensions, although at high noise strength explicit coupling may be the only computationally viable option.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A hybrid incremental projection method for thermal-hydraulics applications

In this paper, a new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya–Babuška–Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie–Chow interpolation or by using a Petrov–Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes, and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

On the use of reverse Brownian motion to accelerate hybrid simulations

Multiscale and multiphysics simulations are two rapidly developing fields of scientific computing. Efficient coupling of continuum (deterministic or stochastic) constitutive solvers with their discrete (stochastic, particle-based) counterparts is a common challenge in both kinds of simulations. We focus on interfacial, tightly coupled simulations of diffusion that combine continuum and particle-based solvers. The latter employs the reverse Brownian motion (rBm), a Monte Carlo approach that allows one to enforce inhomogeneous Dirichlet, Neumann, or Robin boundary conditions and is trivially parallelizable. We discuss numerical approaches for improving the accuracy of rBm in the presence of inhomogeneous Neumann boundary conditions and alternative strategies for coupling the rBm solver with its continuum counterpart. Numerical experiments are used to investigate the convergence, stability, and computational efficiency of the proposed hybrid algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A Variable Eddington Factor method for the 1-D grey radiative transfer equations with discontinuous Galerkin and mixed finite-element spatial differencing

The purpose of this paper is to present a Variable Eddington Factor (VEF) method for the 1-D grey radiative transfer equations that uses a lumped linear discontinuous Galerkin spatial discretization for the Sequations together with a constant-linear mixed finite-element discretization for the VEF moment and material temperature equations. The use of independent discretizations can be particularly useful for multiphysics applications such as radiation-hydrodynamics. The VEF method is quite old, but to our knowledge, this particular combination of differencing schemes has not been previously investigated for radiative transfer. We define the scheme and present computational results. As expected, the scheme exhibits second-order accuracy for the directionally-integrated intensity and material temperature, and behaves well in the thick diffusion limit. An important focus of this study is the treatment of the strong temperature dependence of the opacities and the spatial dependence of the opacities within each cell, which are not explicitly defined by the basic discretization schemes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗