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All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Low frequency eddy current finite element model validation and benchmark studies

A finite element method (FEM) model was created to calculate the change in impedance of a coil due to the presence of a notch in a plate. The rectangular notches were created via electrical discharge machining (EDM) in a thick aluminum plate and were positioned at normal and oblique angles (10, 20, and 30 degrees) with respect to the vertical axis of the coil. The FEM method was chosen for this model due to its ability to solve problems in complicated geometries with the use of irregular mesh elements to discretize the solution domain. The change in impedance was calculated from the field variables in the simulation for each probe position along the parallel axis of the plate. The error between the model and the experimental data was approximately 5% for the majority of cases. The validated model was used to investigate more complex problems.

42 ENGINEERING↗
DOE OSTI2026

Comparative Evaluation of Spectral Methods for Robust Reactor Noise Estimation

Reactor noise analysis provides a noninvasive means to determine neutron kinetic parameters from stochastic fluctuations in detector signals. However, standard cross-power spectral density (CPSD) analyses can be sensitive to numerical processing choices, which may introduce processing-dependent systematic shifts in estimates of the prompt neutron decay constant (α) and limit reproducibility. This study uses a hybrid multitaper–Welch spectral estimator to analyze subcritical noise measurements from a fast-spectrum critical assembly. The decay constant α was extracted using three frequency-domain methods: the CPSD, the magnitude-squared coherence (MSC), and the generalized magnitude-squared coherence (GMSC). These coherence-based estimators normalize detector auto-spectral structure and are expected to reduce the sensitivity of fitted α values to processing parameters. A Sobol global sensitivity analysis identified which numerical inputs most strongly influence the fitted values of α. All estimators produced a linear dependence of α on inverse count rate, with delayed-critical extrapolations near 1.7 × 10 4 s −1 , in agreement within 8% of MCNP6.3 KOPTS benchmark calculations. Sensitivity results show that while the CPSD depends on both time-bin width and taper selection, the MSC and GMSC are dominated by time-bin width alone, indicating reduced parameter coupling and greater robustness to processing variability. These findings demonstrate the feasibility and practical value of coherence-based spectral estimators for extracting α from reactor noise and support their broader application to multi-detector and irregular datasets in subcritical system characterization.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Ab initio investigation of a hypersonic double cone experiment

This article presents a direct molecular simulation (DMS) of a reactive Mach 8.2 oxygen flow over a double cone geometry. The free stream conditions and article configuration generate a flow with thermal and chemical nonequilibrium, which are common attributes of hypersonic flight. This scenario was first studied experimentally at Calspan University of Buffalo Research Center’s test facility. DMS is a particle method that uses quantum mechanically derived interaction potentials to simulate molecular collisions within a flow field. Since these interaction potentials are the only modeling inputs used in the simulation, all flow features can solely be attributed to the ab initio potential energy surfaces. Hence, providing a comparison of a hypersonic ground test and numerical data anchored to quantum mechanics. The fundamental nature of DMS is leveraged to investigate molecular level mechanisms prevalent in the flow, and comparisons with lower fidelity simulations are presented to highlight the role of these first principles calculations as benchmark solutions.

Science & Technology - Other Topics↗
NASA NTRS1985

Orbiter entry aerothermodynamics

The challenge in the definition of the entry aerothermodynamic environment arising from the challenge of a reliable and reusable Orbiter is reviewed in light of the existing technology. Select problems pertinent to the orbiter development are discussed with reference to comprehensive treatments. These problems include boundary layer transition, leeward-side heating, shock/shock interaction scaling, tile gap heating, and nonequilibrium effects such as surface catalysis. Sample measurements obtained from test flights of the Orbiter are presented with comparison to preflight expectations. Numerical and wind tunnel simulations gave efficient information for defining the entry environment and an adequate level of preflight confidence. The high quality flight data provide an opportunity to refine the operational capability of the orbiter and serve as a benchmark both for the development of aerothermodynamic technology and for use in meeting future entry heating challenges.

Ried, R. C.↗
DOE OSTI2014

Complex absorbing potentials within EOM-CC family of methods: Theory, implementation, and benchmarks

A production-level implementation of equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) for electron attachment and excitation energies augmented by a complex absorbing potential (CAP) is presented. The new method enables the treatment of metastable states within the EOM-CC formalism in a similar manner as bound states. The numeric performance of the method and the sensitivity of resonance positions and lifetimes to the CAP parameters and the choice of one-electron basis set are investigated. A protocol for studying molecular shape resonances based on the use of standard basis sets and a universal criterion for choosing the CAP parameters are presented. Our results for a variety of π{sup *} shape resonances of small to medium-size molecules demonstrate that CAP-augmented EOM-CCSD is competitive relative to other theoretical approaches for the treatment of resonances and is often able to reproduce experimental results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

The Phenix ultimate natural convection test

The French sodium cooled fast reactor Phenix was shut down in 2009 after 35 years of operation. Before decommissioning, a final set of tests were performed by the CEA during 9 months. Several topics were involved such as thermal hydraulics, core physics and fuel behaviour. Among these ultimate experiments, two thermal hydraulic tests were performed: an asymmetrical test consisting in a trip of one secondary pump and a natural convection test in the primary circuit. Recognizing the unique opportunity offered by these Phenix ultimate tests, IAEA decided in 2007 to launch a Coordinated Research Project (CRP) devoted to benchmarking analyses with system codes on the Phenix natural convection test. One objective of the natural convection test in Phenix reactor is the assessment of the CATHARE system code for safety studies on future and advanced sodium cooled fast reactors. The aim of this paper is to describe this test, which was performed on June 22-23, 2009, and the associated benchmark specifications for the CRP work. The paper reminds briefly the Phenix reactor with the main physical parameters and the instrumentation used during the natural convection test. After that, the test scenario is described: - initial state at a power of 120 MWth, - test beginning resulting from a manual dry out of the two steam generators, - manual scram, - manual trip on the three primary pumps without back-up by pony motors, - setting and development of natural convection in the primary circuit, in a first phase without significant heat sink in the secondary circuits and in a second phase with significant heat sink in the secondary circuits, by opening the casing of steam generators to create an efficient heat sink, by air natural circulation in the steam generators casing. The benchmark case ends after this second phase, which corresponds to the experimental test duration of nearly 7 hours. The paper presents also the benchmark specifications data supplied by the CEA to all participants of this CRP in order to perform calculations (core, primary circuit, primary pumps, IHX, shutdown system, operating parameters, test scenario and real test conditions). Finally, main test results and analyses are presented including the evolution of the core and of the heat exchangers inlet and outlet temperatures, and some local temperature measurements. The natural convection has been easily set up in the pool type reactor Phenix with different boundary conditions at the secondary side, with or without heat sink. The data obtained during this unique test represent some very useful and precious results for the development of SFR in a wide range of thematic such as numerical methods dedicated to thermal-hydraulics safety analyses (system codes, CFD codes and coupling system and CFD codes) and instrumentation. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Particle Image Velocimetry Measurements in a Wire-Wrapped 61-Pin Hexagonal Fuel Bundle

Liquid metal fast reactor fuel assemblies using sodium as a coolant typically utilize a tightly packed triangular lattice of fuel pins enclosed in a hexagonal duct. The fuel pins are typically wrapped with a helical wire spacer. The primary function of the wire spacers is to maintain a gap between neighboring fuel pins. They also mitigate vortex-induced vibration and enhance sub-channel mixing to increase convective heat transfer. Many experiments have been performed to study thermal-hydraulic characteristics, primarily pressure drops, of the wire-wrapped fuel bundles. Novendstern developed a semi-empirical model to predict pressure losses in a hexagonal array of wire-wrapped pins in the turbulent flow regime. Rehme proposed pressure drop correlations for a wide range of geometrical parameters, such as pitch-to-diameter ratio P/D from 1.125 to 1.417, lead-to-wire diameter ratio H / dm from 6 to 45, and number of pins n from 7 to 61. Cheng and Todreas introduced their hydrodynamic models for subchannel friction factors and mixing parameters in a 37-pin fuel bundle, which covered the laminar, transition and turbulent flow regimes. Computational fluid dynamics (CFD) offers an opportunity to validate the above correlations and investigate the flow characteristics in the subchannels. Several numerical studies of the wire-wrapped fuel bundles have been performed and most of them are Reynolds-Averaged Navier-Stokes (RANS) based simulations with various turbulence models. Ahmad and Kim performed RANS simulations of 7- and 19-pin bundles using the k-omega SST turbulent model, while Gajapathy et al. performed RANS simulations on 7-pin bundles using the k-epsilons model. Recently, Fischer et al. carried out large-eddy simulation (LES) calculations on wire-wrapped fuel bundles to obtain higher-resolution numerical solutions of subchannel behavior. The geometrical complexity of the hexagonal wire-wrapped fuel bundle has limited experimental activities to pressure drop measurements. A database of pressure drops and flow-field measurements in a 61-pin wire-wrapped hexagonal fuel bundle is not available to benchmark the existing correlations and validate the CFD calculations. Texas A and M University is conducting isothermal flow experiments in a wire-wrapped 61-pin hexagonal fuel bundle to support the research on advanced nuclear fuel development sponsored by the Department of Energy (DOE). The purpose of these tests is to perform high spatial and temporal resolution measurements of the flow and pressure measurements at different locations in the fuel bundle. The experimental facility employs matched-index-of-refraction (MIR) techniques and laser diagnostic velocity measurement techniques such as particle image velocimetry (PIV) and laser Doppler velocimetry (LDV). The result of this experimental activity will be an experimental database of pressure and flow-field measurements that will be suitable for validating CFD computer codes. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2019

Coarse grained computational fluid dynamic simulation of sands and biomass fluidization with a hybrid drag

We report the bubbling fluidized bed reactor is widely used in fast pyrolysis of biomass. Discrete simulation of this reactor is challenging due to many sand particles and lack of accurate drag corrections accounting for the interaction of two different solid particles with different properties. In this research, the computational cost is reduced by using the coarse-grained computational fluid dynamic-discrete element method, where many sand particles are lumped into a larger numerical parcel. The Syamlal–O'Brien drag model is used for sand, while Ganser correction coupled with Gidaspow model is used for the nonspherical biomass particles. This hybrid approach shows superior behavior over other drag models using pressure drops as a benchmark. The predicted bed height and pressure fluctuating frequencies compare well with experiment. Finally, the mixing of biomass is close to perfect if the superficial velocity is larger than four times the minimum fluidization velocity.

09 BIOMASS FUELS↗
DOE OSTI2012

Sensitivity of the Properties of Ruthenium “Blue Dimer” to Method, Basis Set, and Continuum Model

The ruthenium “blue dimer” [(bpy)2RuIIIOH2]2O4+ is best known as the first well-defined molecular catalyst for water oxidation. It has been subject to numerous computational studies primarily employing density functional theory. However, those studies have been limited in the functionals, basis sets, and continuum models employed. The controversy in the calculated electronic structure and the reaction energetics of this catalyst highlights the necessity of benchmark calculations that explore the role of density functionals, basis sets, and continuum models upon the essential features of blue-dimer reactivity. In this paper, we report Kohn-Sham complete basis set (KS-CBS) limit extrapolations of the electronic structure of “blue dimer” using GGA (BPW91 and BP86), hybrid-GGA (B3LYP), and meta-GGA (M06-L) density functionals. The dependence of solvation free energy corrections on the different cavity types (UFF, UA0, UAHF, UAKS, Bondi, and Pauling) within polarizable and conductor-like polarizable continuum model has also been investigated. The most common basis sets of double-zeta quality are shown to yield results close to the KS-CBS limit; however, large variations are observed in the reaction energetics as a function of density functional and continuum cavity model employed.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2022

Combining different 3-D global and regional seismic wave propagation solvers towards box tomography in the deep Earth

SUMMARY In previous publications, we presented a general framework, which we called ‘box tomography’, that allows the coupling of any two different numerical seismic wave propagation solvers, respectively outside and inside a target region, or ‘box’. The goal of such hybrid wavefield computations is to reduce the cost of computations in the context of full-waveform inversion for structure within the target region, when sources and/or receivers are located at large distances from the box. Previously, we had demonstrated this approach with sources and receivers outside the target region in a 2-D acoustic spherical earth model, and demonstrated and applied this methodology in the 3-D spherical elastic Earth in a continental scale inversion in which all stations were inside the target region. Here we extend the implementation of the approach to the case of a 3-D global elastic earth model in the case where both sources and stations are outside the box. We couple a global 3-D solver, SPECFEM3D_GLOBE, for the computation of the wavefield and Green’s functions in a reference 3-D model, with a regional 3-D solver, RegSEM, for the computation of the wavefield within the box, by means of time-reversal mirrors. We briefly review key theoretical aspects, showing in particular how only the displacement is needed to be stored at the boundary of the box. We provide details of the practical implementation, including the geometrical design of the mirrors, how we deal with different sizes of meshes in the two solvers, and how we address memory-saving through the use of B-spline compression of the recorded wavefield on the mirror. The proposed approach is numerically efficient but also versatile, since adapting it to other solvers is straightforward and does not require any changes in the solver codes themselves, as long as the displacement can be recovered at any point in time and space. We present benchmarks of the hybrid computations against direct computations of the wavefield between a source and an array of stations in a realistic geometry centred in the Yellowstone region, with and without a hypothetical plume within the ‘box’, and with a 1-D or a 3-D background model, down to a period of 20 s. The ultimate goal of this development is for applications in the context of imaging of remote target regions in the deep mantle, such as, for example, Ultra Low Velocity Zones.

Geochemistry & Geophysics↗
DOE OSTI2014

DOE CALiPER Program Report 21.2: Linear (T8) LED Lamp Performance in Five Types of Recessed Troffers

Although lensed troffers are numerous, there are many other types of optical systems as well. This report looked at the performance of three linear (T8) LED lamps chosen primarily based on their luminous intensity distributions (narrow, medium, and wide beam angles) as well as a benchmark fluorescent lamp in five different troffer types. Also included are the results of a subjective evaluation. Results show that linear (T8) LED lamps can improve luminaire efficiency in K12-lensed and parabolic-louvered troffers, effect little change in volumetric and high-performance diffuse-lensed type luminaires, but reduce efficiency in recessed indirect troffers. These changes can be accompanied by visual appearance and visual comfort consequences, especially when LED lamps with clear lenses and narrow distributions are installed. Linear (T8) LED lamps with diffuse apertures exhibited wider beam angles, performed more similarly to fluorescent lamps, and received better ratings from observers. Guidance is provided on which luminaires are the best candidates for retrofitting with linear (T8) LED lamps.

CALiPER↗
DOE OSTI2014

CALiPER Report 21.2: Linear (T8) LED Lamp Performance in Five Types of Recessed Troffers

Although lensed troffers are numerous, there are many other types of optical systems as well. This report looks at the performance of three linear (T8) LED lamps—chosen primarily based on their luminous intensity distributions (narrow, medium, and wide beam angles)—as well as a benchmark fluorescent lamp in five different troffer types. Also included are the results of a subjective evaluation. Results show that linear (T8) LED lamps can improve luminaire efficiency in K12-lensed and parabolic-louvered troffers, effect little change in volumetric and high-performance diffuse-lensed type luminaires, but reduce efficiency in recessed indirect troffers. These changes can be accompanied by visual appearance and visual comfort consequences, especially when LED lamps with clear lenses and narrow distributions are installed. Linear (T8) LED lamps with diffuse apertures exhibited wider beam angles, performed more similarly to fluorescent lamps, and received better ratings from observers. Guidance is provided on which luminaires are the best candidates for retrofitting with linear (T8) LED lamps.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2019

High Performance Computing to Enable Next-Generation Low-Temperature Waste Heat Recovery

US manufacturing industry fails to recover an estimated 900 trillion BTUs of low-temperature waste heat from its processes each year. A grand research challenge has been to develop waste heat recovery technology that can be applied to industrial manufacturing processes and vehicle operations. The Oak Ridge National Laboratory (ORNL)/Eaton research team performed computational research and development to design an innovative direct-contact heat exchanger (DCHE) technology to deliver low-cost, compact, longer-lifetime, high-efficiency waste heat recovery that is optimized for a low-temperature organic Rankine cycle. ORNL resources and expertise in high performance computing (HPC) and multiphase flows were utilized to realize this goal while advancing the fundamental understanding of two-phase, two-immiscible-fluid turbulent flow heat transfer for heat exchangers. In the first stage of the project, a computational fluid dynamics (CFD) model of a DCHE was developed. Verification and limited validation of the numerical solution were performed using experimental data from published literature. To support efforts in verification and validation, two-dimensional CFD models were also developed with the objective of investigating different boundary conditions to reach converged, steady-state solutions.Based on benchmarking efforts, a baseline industry-grade design of a DCHE was developed, which consists of two horizontal pipes of different cross-sectional areas – joined by a converging-diverging nozzle in the middle and relies on a three-phase system with co-current flows for operation. Evaporation of the cold liquid (n-pentane or methanol) by the hot liquid water occurs in the first pipe. The first pipe contains two inlets for liquid water and liquid pentane (or liquid methanol). The second pipe with the larger cross-sectional area serves as a gravity-driven phase-separator. It contains two outlets that are staggered to avoid entrainment of the liquid water phase by the gas phase. This baseline design resulted from several trial-and-error evaluations using two-dimensional CFD models. Confirmatory three-dimensional CFD models were also run for different mass flow rates and inlet temperatures (inlet water temperature ranging from 50°C to 90°C), and efficiency plots were produced to fully characterize the proposed industrial-grade design of the DCHE.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

BETO 2021 Peer Review - Algal Biofuels Techno-Economic Analysis 1.3.5.200

The objective of NREL's Algal Biofuel Techno-Economic Analysis (TEA) project is to provide process modeling and analysis to support Algae Program activities, utilizing TEA models to relate key process parameters with overall economics for cultivation, processing, and conversion of algal biomass to fuels and coproducts. By quantifying economic implications of key process metrics, TEA models highlight the technical requirements to achieve future program cost goals as well as enabling a means to track progress towards these goals. This project provides high impact and relevance though generation of critical cost data tied to funded research, with our analyses subsequently exercised by BETO to guide program plans, FOA priorities, and other directives. This includes costs for both algal biomass production and downstream conversion, most notably to support BETO's fuel cost targets below $2.5/GGE by 2030. To mitigate a key risk/challenge in constraining our work to academic analyses rooted only in future projections, our work also seeks to provide near-term value to today's algae industry through frequent industry engagement, while maintaining close ties with other BETO collaborators. This project has made numerous accomplishments since the 2019 peer review, including a continued focus on opportunities for value-added products, with related analyses for new pathway opportunities to achieve BETO cost goals and notable State-of-Technology (SOT) improvements over prior cost benchmarks.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2011

C5 Benchmark Problem with Discrete Ordinate Radiation Transport Code DENOVO

The C5 benchmark problem proposed by the Organisation for Economic Co-operation and Development/Nuclear Energy Agency was modeled to examine the capabilities of Denovo, a three-dimensional (3-D) parallel discrete ordinates (S{sub N}) radiation transport code, for problems with no spatial homogenization. Denovo uses state-of-the-art numerical methods to obtain accurate solutions to the Boltzmann transport equation. Problems were run in parallel on Jaguar, a high-performance supercomputer located at Oak Ridge National Laboratory. Both the two-dimensional (2-D) and 3-D configurations were analyzed, and the results were compared with the reference MCNP Monte Carlo calculations. For an additional comparison, SCALE/KENO-V.a Monte Carlo solutions were also included. In addition, a sensitivity analysis was performed for the optimal angular quadrature and mesh resolution for both the 2-D and 3-D infinite lattices of UO{sub 2} fuel pin cells. Denovo was verified with the C5 problem. The effective multiplication factors, pin powers, and assembly powers were found to be in good agreement with the reference MCNP and SCALE/KENO-V.a Monte Carlo calculations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

SU-E-T-270: Diffusion Synthetic Acceleration for Linear Boltzmann Transport Equation

Purpose: Linear Boltzmann transport equation (LBTE) is as accurate as the Monte Carlo method (MC) for dose calculation in photon/particle therapy (LBTE is a deterministic and Eulerian formulation and MC is a statistical and Lagrangian description). An advantage of LBTE is that numerous acceleration techniques can be utilized for acceleration. This work is to explore the acceleration of LBTE via diffusion synthetic acceleration (DSA). Methods: For simplicity, two-dimensional, steady-state, and within-group LBTE is considered with two angular dimensions and two spatial dimensions. The discrete ordinate method is developed for solving this integro-differential equation. The angular variables are discretized using a level-symmetric quadrature set on the unit sphere. The spatial variables are discretized on the structured grid based on the diamond scheme. The source-iteration method (SI) is used to solve the discretized system.Since SI is slow in optically thick and highly scattering regime. DSA is developed to accelerate SI. The motivation for DSA is that diffusion equation (DE) is a good approximation of LBTE in the above regime. However, DE is much cheaper than LBTE computationally since DE only involves spatial variables. Thus, in each DSA iteration, DSA adds to the SI step a computationally-negligible DE step, i.e., to first solve DE with the SI residual as source term, and then compensate the SI solution with DE solution. Results: DSA was benchmarked and compared with SI. The difference between two methods was within 0.12% which verifies the accuracy of DSA, while DSA demonstrated the great advantage in speed, e.g., the reduction of iteration number to 6% and 4% respectively for cases with 100 and 1,000 scattering-absorption ratio that commonly occur in clinical dose calculation. Conclusion: DSA has been developed as one of many possible means for accelerating the numerical solver of LBTE for dose calculation. The authors were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Scalable Implicit Solvers with Dynamic Mesh Adaptation for a Relativistic Drift-Kinetic Fokker–Planck–Boltzmann Model

In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker–Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source. Here, we develop a new scalable fully implicit solver utilizing finite volume and conservative finite difference schemes and dynamic mesh adaptivity. A new data management framework in the PETSc library based on the p4est library is developed to enable simulations with dynamic adaptive mesh refinement (AMR), distributed memory parallelization, and dynamic load balancing of computational work. This framework and the runaway electron solver building on the framework are able to dynamically capture both bulk Maxwellian at the low-energy region and a runaway tail at the high-energy region. To effectively capture features via the AMR algorithm, a new AMR indicator prediction strategy is proposed that is performed alongside the implicit time evolution of the solution. This strategy is complemented by the introduction of computationally cheap feature-based AMR indicators that are analyzed theoretically. Numerical results quantify the advantages of the prediction strategy in better capturing features compared with nonpredictive strategies; and we demonstrate trade-offs regarding computational costs. The robustness with respect to model parameters, algorithmic scalability, and parallel scalability are demonstrated through several benchmark problems including manufactured solutions and solutions of different physics models. We focus on demonstrating the advantages of using implicit time stepping and AMR for runaway electron simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗