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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

s-Step Krylov Subspace Methods as Bottom Solvers for Geometric Multigrid

Geometric multigrid solvers within adaptive mesh refinement (AMR) applications often reach a point where further coarsening of the grid becomes impractical as individual sub domain sizes approach unity. At this point the most common solution is to use a bottom solver, such as BiCGStab, to reduce the residual by a fixed factor at the coarsest level. Each iteration of BiCGStab requires multiple global reductions (MPI collectives). As the number of BiCGStab iterations required for convergence grows with problem size, and the time for each collective operation increases with machine scale, bottom solves in large-scale applications can constitute a significant fraction of the overall multigrid solve time. In this paper, we implement, evaluate, and optimize a communication-avoiding s-step formulation of BiCGStab (CABiCGStab for short) as a high-performance, distributed-memory bottom solver for geometric multigrid solvers. This is the first time s-step Krylov subspace methods have been leveraged to improve multigrid bottom solver performance. We use a synthetic benchmark for detailed analysis and integrate the best implementation into BoxLib in order to evaluate the benefit of a s-step Krylov subspace method on the multigrid solves found in the applications LMC and Nyx on up to 32,768 cores on the Cray XE6 at NERSC. Overall, we see bottom solver improvements of up to 4.2x on synthetic problems and up to 2.7x in real applications. This results in as much as a 1.5x improvement in solver performance in real applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Exactly energy conserving semi-implicit particle in cell formulation

We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non-linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conserves energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested. - Highlights: • We present a new fully energy conserving semi-implicit particle in cell (PIC) method based on the implicit moment method (IMM). The new method is called Energy Conserving Implicit Moment Method (ECIMM). • The novelty of the new method is that unlike any of its predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. • The new method is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency. • The new method eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length. • These features are achieved at a reduced cost compared with either previous IMM or fully implicit implementation of PIC.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Sensitivity Analysis of OECD ATLAS A5.1 Test using MARS-KS code

The ATLAS was designed to model a reduced-height primary system of a typical APR1400 which was developed by the Korean Nuclear Industry. The ATLAS has the 1/2-height, 1/144-area and 1/288-volume scales for the APR 1400 and it is scaled for full pressure and temperature conditions. A benchmark test, test A5.1, was performed to analyze and quantify the extent of scaling distortion in the ATLAS, as a part of a OECD-ATLAS project. The SB-CL-32 test which was conducted using the Large Scale Test Facility (LSTF) of the Rig-of-Safety Assessment-V (ROSA-V) Program was selected as the counterpart test to address the scaling issue. The detailed description of the LSTF test facility and the SB-CL-32 test can be found in the literature. The objective of the A5.1 test is to investigate the thermal hydraulic phenomena during cold leg small break LOCA with steam generator secondary side depressurization as the Accident Management action. In addition to that, the scaling effect analysis of ATLAS was performed in the several viewpoints. In this study, sensitivity analysis of A5.1 test was performed using MARS-KS code. Several experimental conditions of A5.1 test were varied to study effects on the reactor coolant system during the SBLOCA transient. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2014

CALiPER Report 20.3: Robustness of LED PAR38 Lamps

Three samples of 40 of the Series 20 PAR38 lamps underwent multi-stress testing, whereby samples were subjected to increasing levels of simultaneous thermal, humidity, electrical, and vibrational stress. The results do not explicitly predict expected lifetime or reliability, but they can be compared with one another, as well as with benchmark conventional products, to assess the relative robustness of the product designs. On average, the 32 LED lamp models tested were substantially more robust than the conventional benchmark lamps. As with other performance attributes, however, there was great variability in the robustness and design maturity of the LED lamps. Several LED lamp samples failed within the first one or two levels of the ten-level stress plan, while all three samples of some lamp models completed all ten levels. One potential area of improvement is design maturity, given that more than 25% of the lamp models demonstrated a difference in failure level for the three samples that was greater than or equal to the maximum for the benchmarks. At the same time, the fact that nearly 75% of the lamp models exhibited better design maturity than the benchmarks is noteworthy, given the relative stage of development for the technology.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Robust implementation of generative modeling with parametrized quantum circuits

Although the performance of hybrid quantum-classical algorithms is highly dependent on the selection of the classical optimizer and the circuit ansätze, a robust and thorough assessment on-hardware of such features has been missing to date. From the optimizer perspective, the primary challenge lies in the solver’s stochastic nature, and their significant variance over the random initialization. Therefore, a robust comparison requires one to perform several training curves for each solver before one can reach conclusions about their typical performance. Since each of the training curves requires the execution of thousands of quantum circuits in the quantum computer, such a robust study remained a steep challenge for most hybrid platforms available today. In this work, we leverage on Rigetti’s Quantum Cloud Services (QCS™) to overcome this implementation barrier, and we study the on-hardware performance of the data-driven quantum circuit learning (DDQCL) for three different state-of-the-art classical solvers, and on two-different circuit ansätze associated to different entangling connectivity graphs for the same task. Additionally, we assess the gains in performance from varying circuit depths. To evaluate the typical performance associated with each of these settings in this benchmark study, we use at least five independent runs of DDQCL towards the generation of quantum generative models capable of capturing the patterns of the canonical Bars and Stripes dataset. In this experimental benchmarking, the gradient-free optimization algorithms show an outstanding performance compared to the gradient-based solver. In particular, one of them had better performance when handling the unavoidable noisy objective function to be minimized under experimental conditions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Development and Validation of a Two-Phase Thermal-Hydraulic CFD Code NEK-2P

A project is underway to develop, verify and validate an advanced two-phase flow modeling capability for the highly-scalable, high-performance Computational Fluid Dynamics (CFD) code NEK5000. The goal of this work is to verify and validate the two-phase version of the NEK5000 code, named NEK-2P, to simulate the two-phase flow and heat transfer phenomena that occur in a Boiling Water Reactor (BWR) fuel bundle under various operating conditions. The NEK-2P two-phase flow models follow the approach used for the Extended Boiling Framework (EBF) previously developed at Argonne but include more fundamental physical models of boiling phenomena and advanced numerical algorithms for improved computational accuracy, robustness, and computational speed. The development of the NEK-2P two-phase solver and the implementation of the Extended Boiling Framework two-phase models were initially supported by Argonne National Laboratory (Argonne) through a Laboratory Directed Research and Development (LDRD) project during FY2014-2016. The development and validation of the two-phase models through analyses of selected two-phase boiling flow experiments was supported by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in FY2017-2020. This report focuses on verification and validation of the water-steam boiling model NEK-2P Two-Phase, CFD code. The NEK-2P was validated with Nuclear Power Engineering Corporation (NUPEC) Pressurized Water Reactor (PWR) Sub-channel and Bundle Test (PSBT) void distribution benchmark. Three different simulations were performed and analyzed for various operating conditions such as wall-heat flux and sub-cooled inlet temperatures. Reasonably good agreement with measured data was obtained in predicting the measured void distributions. Simulations were performed for Virginia Tech. (VT) 3x3 rod bundle geometry with and without spacers. The preliminary results were presented for Simplified Spacer Grid (SSG). In addition, the implementation of interface reconstruction model was tested with one of the Becker benchmark Critical Heat Flux (CHF) experiments.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2015

First Industrial Tests of a Drum Monitor Matrix Correction for the Fissile Mass Measurement in Large Volume Historic Metallic Residues with the Differential Die-away Technique

The fissile mass in radioactive waste drums filled with compacted metallic residues (spent fuel hulls and nozzles) produced at AREVA La Hague reprocessing plant is measured by neutron interrogation with the Differential Die-away measurement Technique (DDT. In the next years, old hulls and nozzles mixed with Ion-Exchange Resins will be measured. The ion-exchange resins increase neutron moderation in the matrix, compared to the waste measured in the current process. In this context, the Nuclear Measurement Laboratory (NML) of CEA Cadarache has studied a matrix effect correction method, based on a drum monitor ({sup 3}He proportional counter inside the measurement cavity). A previous study performed with the NML R and D measurement cell PROMETHEE 6 has shown the feasibility of method, and the capability of MCNP simulations to correctly reproduce experimental data and to assess the performances of the proposed correction. A next step of the study has focused on the performance assessment of the method on the industrial station using numerical simulation. A correlation between the prompt calibration coefficient of the {sup 239}Pu signal and the drum monitor signal was established using the MCNPX computer code and a fractional factorial experimental design composed of matrix parameters representative of the variation range of historical waste. Calculations have showed that the method allows the assay of the fissile mass with an uncertainty within a factor of 2, while the matrix effect without correction ranges on 2 decades. In this paper, we present and discuss the first experimental tests on the industrial ACC measurement system. A calculation vs. experiment benchmark has been achieved by performing dedicated calibration measurement with a representative drum and {sup 235}U samples. The preliminary comparison between calculation and experiment shows a satisfactory agreement for the drum monitor. The final objective of this work is to confirm the reliability of the modeling approach and the industrial feasibility of the method, which will be implemented on the industrial station for the measurement of historical wastes. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2015

‘Wasteaware’ benchmark indicators for integrated sustainable waste management in cities

Highlights: • Solid waste management (SWM) is a key utility service, but data is often lacking. • Measuring their SWM performance helps a city establish priorities for action. • The Wasteaware benchmark indicators: measure both technical and governance aspects. • Have been developed over 5 years and tested in more than 50 cities on 6 continents. • Enable consistent comparison between cities and countries and monitoring progress. - Abstract: This paper addresses a major problem in international solid waste management, which is twofold: a lack of data, and a lack of consistent data to allow comparison between cities. The paper presents an indicator set for integrated sustainable waste management (ISWM) in cities both North and South, to allow benchmarking of a city’s performance, comparing cities and monitoring developments over time. It builds on pioneering work for UN-Habitat’s solid waste management in the World’s cities. The comprehensive analytical framework of a city’s solid waste management system is divided into two overlapping ‘triangles’ – one comprising the three physical components, i.e. collection, recycling, and disposal, and the other comprising three governance aspects, i.e. inclusivity; financial sustainability; and sound institutions and proactive policies. The indicator set includes essential quantitative indicators as well as qualitative composite indicators. This updated and revised ‘Wasteaware’ set of ISWM benchmark indicators is the cumulative result of testing various prototypes in more than 50 cities around the world. This experience confirms the utility of indicators in allowing comprehensive performance measurement and comparison of both ‘hard’ physical components and ‘soft’ governance aspects; and in prioritising ‘next steps’ in developing a city’s solid waste management system, by identifying both local strengths that can be built on and weak points to be addressed. The Wasteaware ISWM indicators are applicable to a broad range of cities with very different levels of income and solid waste management practices. Their wide application as a standard methodology will help to fill the historical data gap.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Polymer Hole Transport Material Functional Group Tuning for Improved Perovskite Solar Cell Performance

As lead halide perovskites (LHPs) continue to achieve success as a light-harvesting material in perovskite solar cells (PSCs), exploring and understanding other materials in the device stack become increasingly important. Particularly, selection of suitable hole transport materials (HTMs) that demonstrate high performance and stability is imperative in the design of P-I-N PSCs. Presented here are a family of 12 structurally related polymers based on either fluorene or carbazole main chains with select aromatic side groups that introduce tunable properties for use in PSCs. How properties such as the highest occupied molecular orbital energy level, conductivity, glass-transition temperature, and wettability of the HTM affect the PSC performance is explored. Devices that incorporate the polymer HTMs perform well relative to PTAA in benchmark P-I-N PSC architectures while exhibiting similar or superior stability under accelerated aging studies. The relative synthetic simplicity and resultant performance of the HTMs in PSCs coupled with the ability to customize properties with different functional groups demonstrates the potential of this family of HTMs for a variety of LHP materials.

14 SOLAR ENERGY↗
DOE OSTI2020

National Criticality Experiments Research Center (NCERC) - capabilities and recent measurements

The National Criticality Experiments Research Center (NCERC) located at the Device Assembly Facility (DAF) at the Nevada National Security Site (NNSS) and operated by Los Alamos National Laboratory (LANL) is home to four critical assemblies which are used to support of range of missions, including nuclear criticality safety and nuclear nonproliferation. Additionally, subcritical systems can also be assembled at NCERC. NCERC is providing critical and subcritical experiments valuable to the nuclear data community and experiments performed at NCERC are often published as benchmarks in the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook. This manuscript will give a broad overview of recent experiments performed at NCERC, upcoming experiments, and why integral measurements are important and useful to the nuclear data community. The four critical assemblies are GODIVA IV, FLATTOP, COMET, and PLANET. GODIVA IV is a cylindrical metal fast burst reactor, the fourth in the GODIVA series that dates back to the 1950’s. FLATTOP is an highly enriched uranium (HEU) or Pu core reflected by natural uranium. COMET and PLANET are vertical lift assemblies, where one half of the reactor can be lifted to the upper half of the reactor to create a critical system. Some recent experiments include various critical intermediate energy assemblies with lead, and subcritical measurements of plutonium reflected by copper, tungsten, and nickel. Work is also underway to make a better measurement of the critical mass of neptunium, using a neptunium sphere surrounded by nickel shells. Additionally, measurements will be performed next year with HEU shells from Rocky Flats. These HEU shells will be stacked together to make larger systems, allowing for a large range of criticality (from subcritical to delayed critical). Other upcoming measurements include an HEU critical assembly sensitive to intermediate energy neutrons.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2014

Local-hybrid functional based on the correlation length

Local-hybrid functionals involve position-dependent mixing of Hartree-Fock and density-functional exchange, which should allow improved performance relative to conventional hybrids by reducing the inherent delocalization error and improving the long-range behaviour. Herein, the same-spin correlation length, obtained from the Fermi-hole radius, is used as the mixing parameter. The performance of the resulting local-hybrid functional is assessed for standard thermochemical and kinetics benchmarks. The local hybrid is shown to perform significantly better than the corresponding global hybrid in almost all cases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

IRIS-MASH: Efficient Multi-device Asynchronous Multi-Stream Heterogeneous Computing

In the rapidly evolving field of high-performance computing (HPC), effectively leveraging heterogeneous devices through asynchronous task programming is paramount. This paper presents a robust asynchronous task programming model tailored for a multi-device, multi-stream execution environment that incorporates a diverse array of heterogeneous computing units, including GPUs from various vendors and other accelerators. Current state-of-the-art task programming models provide methodologies to support asynchronous task executions, but they typically handle homogeneous devices using native programming languages, while support for heterogeneous devices is limited to frameworks like OpenCL. This gap presents significant challenges in abstracting heterogeneous devices to harness their true asynchronous capabilities effectively using their native programming languages. By implementing asynchronous task execution, our model significantly boosts the performance of tiled algorithm task graphs through overlapping data transfers with computation and enabling the simultaneous execution of multiple kernels. We integrate this approach into a heterogeneous Intelligent Runtime System (IRIS) and assess its performance using a suite of tiled algorithm benchmarks from the heterogeneous math kernels library (MatRIS) based on IRIS. Experimental results demonstrate a performance improvement ranging from 1.6 × to 2 × over IRIS without asynchronous support, and a notable 22% performance enhancement compared to established runtime systems such as StarPU and PaRSEC. This approach significantly improves computation efficiency of HPC workflows and provides a solid base for future exploration and development in the area of asynchronous task programming in heterogeneous systems.

Miniskar, Narasinga Rao [ORNL] (ORCID:000000018259↗
DOE OSTI2026

Qualifying LaBr3:Ce+Sr detector performance for the Mu2e experiment at Fermilab Using the ELBE Accelerator

A LaBr3:Ce+Sr detector will be used to measure the stopped muon captures at the Mu2e experiment at Fermilab. It has been benchmarked in a test beam experiment performed at the ELBE electron accelerator located at the Helmholtz-Zentrum Dresden-Rossendorf, Germany. ELBE’s pulsed bremsstrahlung beam line was set to deliver an average γ -ray energy of between 4–5 MeV. The detector response was mapped to match Mu2e beam conditions, including rates up to 1 Mcps, energy flux, and time structure. A radioactive calibration source was used to mimic the characteristic 1808.7 keV γ -ray, emitted during the atomic muon nuclear capture in the Mu2e aluminum stopping target. The detector energy resolution was measured as a function of the average energy flux: up to 1 TeV/s for 0.34 s, the steady-operation beam-on time and up to 4 TeV/s for 5 ms to get a conservative estimate of the effect of high intensity Mu2e beam fluctuations. The PMT gain variation as a function of the beam spill length and average intensity has been parametrized and corrected for. When a PMT gain correction corresponding to the average beam-spill intensity is applied, the residual effect of beam intensity fluctuations around the average degrades the energy resolution, σ E γ /E γ , at 1808.7 keV from 0.66% to 0.83%.

Huang, Shihua [Purdue U., West Lafayette]↗
DOE OSTI2017

Two-Step Analysis of Watts Bar Nuclear 1 Cycle 1 with SCALE/PARCS

A two-step approach to reactor core analysis was performed using SCALE and PARCS. Polaris is a new lattice physics module in SCALE 6.2 that provides light water reactor (LWR) modelling capabilities. The VERA (Virtual Environment for Reactor Applications) benchmark problems have been established by the Consortium of Advanced Simulation of Light Water Reactors (CASL). These benchmark problems were chosen to assess the performance of Polaris and PARCS. Homogenized few-group assembly cross sections were generated using Polaris and used in the United States Nuclear Regulatory Commission (NRC) core simulator PARCS. This paper will provide descriptions of the benchmark problems modelled, discuss the impact of transport cross section approximations in SCALE 6.2.0 and 6.2.1, and present the results obtained from the SCALE/PARCS benchmark calculations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

A 3D dynamic model to assess the impacts of low-mode asymmetry, aneurysms and mix-induced radiative loss on capsule performance across inertial confinement fusion platforms

A simple 3D dynamic model for inertial confinement fusion (ICF) implosions has been developed and used to assess the impacts of low-mode asymmetry, aneurysms and mix-induced radiative loss on capsule performance across ICF platforms. While benchmarked against radiation hydrodynamics simulations, this model benefits from simplicity and speed to allow rapid assessment of possible sources of degradation as well as to help build intuition about the relative importance of different effects. Degradations in the model result from 3D pr areal density perturbations that grow under deceleration from a radial stagnation flow, resulting in reduced convergence, stagnation pressure and temperature. When available, experimental data are used as input to seed 3D perturbations in the model so that the actual observed hotspot and shell areal density asymmetry at stagnation, as well as the radiation loss increase from mix impurities, are accurately reproduced. This model is applied to a broad set of implosion data from the NIF and Omega, including examples from both indirect drive and direct drive. The model matches most experimental observables and explains major performance degradation mechanisms which can result in 30–100-fold reductions in yield. We investigate a modified ignition criterion that accounts for the increase in expansion pdV work, due to the presence of 3D pr perturbations and loss-of-confinement in thin regions of the shell.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Neural Image Compression: Generalization, Robustness, and Spectral Biases

Recent advances in neural image compression (NIC) have resulted in models which are starting to outperform traditional codecs. While this has led to growing excitement about using these methods in real-world applications, the successful adoption of any machine learning system (including NIC) in the wild requires it to generalize (and be robust) to unseen distribution shifts at deployment time. Unfortunately, current research lacks comprehensive datasets and informative tools to evaluate and understand compression performance in real-world settings. To bridge this crucial gap, first, this paper presents a comprehensive benchmark suite to evaluate the out-of-distribution (OOD) performance of image compression methods. Specifically, we design CLIC-C and Kodak-C by introducing 15 common corruptions to popular CLIC and Kodak benchmarks. Next, we propose spectrally inspired introspection tools to gain a deeper understanding of errors introduced by image compression methods as well as their OOD performance. To this end, we carry out a detailed performance comparison of the classical codec with various variants of NIC (e.g., original, variable rate, pruned), revealing intriguing findings that challenge our current understanding of the strengths and limitations of NIC. Finally, we corroborate our empirical findings with theoretical analysis, providing an in-depth view of the OOD performance of NIC. Our benchmarks, spectral introspection tools, and findings provide a crucial bridge to the real-world adoption of NIC. We hope that our work will propel future efforts in designing more robust and generalizable NIC methods.

neural networks, Variational Autoencoder, robustne↗
DOE OSTI2016

Modified Closures in Monte Carlo Algorithms for Diffusive Binary Stochastic Media Transport Problems

In a stochastic medium, the material properties at a given spatial location are known only statistically. The most common approach to solving particle transport problems involving binary stochastic media (BSM) is to use the atomic mix approximation in which the transport problem is solved using homogenized (volume-averaged) material properties. A common deterministic model developed for solving BSM particle transport problems is the Levermore-Pomraning (LP) model. Zimmerman and Adams proposed a Monte Carlo algorithm (Algorithm A) that solves the LP equations and another Monte Carlo algorithm (Algorithm B) that locally preserves the sampled material realization; we refer to these Monte Carlo algorithms as the LP and LPLRP (LP local realization preserving) algorithms, respectively. One-dimensional (1D) planar geometry benchmark studies have shown that the LPLRP algorithm is often significantly more accurate than the LP algorithm for problems with an incident angular flux as well as for problems with an interior source. The LPLRP algorithm implementation in these benchmark comparisons made explicit use of the one-dimensional nature of the problem. The LP model is derived by assuming an 'upwind' closure in the coupling term relating the two materials in a binary stochastic medium. Su and Pomraning developed a modified form of this closure by considering the small correlation length limit and requiring the modified closure to produce the correct exponential decay for a source-free half-line albedo problem in rod geometry. They concluded that the modified closure is generally not inferior to the LP closure and in some cases is significantly better. Brantley investigated the use of the Su-Pomraning (SP) closure in the Monte Carlo LP algorithm (LP-SP) for the suite of benchmark problems and concluded that 1) the LP-SP algorithm was somewhat more accurate overall than the LP algorithm and somewhat less accurate overall than the LPLRP algorithm for an incident angular flux benchmark suite, and 2) the LP-SP algorithm was generally the least accurate of the algorithms for an interior source benchmark suite. Larsen et al. performed an asymptotic analysis of the transport equation in 1D planar geometry for the situation in which the physical system is 1) a random binary stochastic medium with material macroscopic total cross sections and mean slab width values of O(1) or smaller and 2) optically thick with weak absorption and sources at each spatial point and therefore globally diffusive. The asymptotic analysis demonstrates that, under these assumptions, the transport equation limits to the conventional diffusion equation with atomically-mixed (volume-averaged) material properties. Larsen et al. also demonstrate that, under these same assumptions, the LP equations asymptotically limit to an atomically-mixed diffusion equation with a diffusion coefficient that is too large, leading to an unphysical flattening of the ensemble-averaged scalar flux distribution. Vasques and Yadav recently performed an asymptotic analysis of an adjusted Levermore-Pomraning closure in which the Markovian transition functions are rescaled such that the equations asymptotically limit to the correct atomically-mixed diffusion equation; we refer to this model as LP-VY. In this paper, we demonstrate that the adjusted LP closure proposed by Vasques and Yadav is a special case of the SP closure obtained by assuming that the absorption cross sections in the two materials are equal. We further demonstrate that the Su-Pomraning closure has the correct asymptotic limit for the diffusive physical system and is therefore an appropriate closure for these problems. We also describe how to incorporate these various closures into the Monte Carlo LP and LPLRP particle transport algorithms, and we present numerical results comparing the accuracy of the Monte Carlo LP, LP-VY, LP-SP, LPLRP, and LPLRP-SP algorithms for the set of diffusive benchmark problems. We demonstrated that the SP closure has the correct asymptotic limit for the diffusive physical system under investigation in this paper and that the VY closure is a special case of the SP closure obtained by assuming equal absorption in the two materials. Both of these closures are readily implemented in the Monte Carlo LP and LPLRP algorithms for particle transport in BSM. Through numerical comparisons to a diffusive benchmark suite, we confirmed that 1) the LP and LPLRP algorithms do not limit to the appropriate diffusion solution and 2) the LP-VY, LP-SP, and LPLRP-SP algorithms limit to the appropriate diffusion solution and are of comparable accuracy. The LPLRP algorithm has been shown to be generally more accurate than the LP algorithm for non-diffusive problems. However, the numerical results in this paper indicate that the LPLRP algorithm does not limit to the correct diffusion equation for the asymptotic limit under consideration. The work in this paper demonstrates that the SP algorithm does limit to the correct diffusion equation for the asymptotic limit considered. Future work will investigate the possibility of whether the LPLRP-SP algorithm is accurate for both diffusive and non-diffusive problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

In this paper, we address the aircraft conflict resolution problem in air traffic control. We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions. We first examine the two-dimensional aircraft conflict resolution problem with speed and heading control represented as continuous decision variables. We show that the proposed disjunctive linear separation conditions are equivalent to the classical nonlinear conditions for aircraft separation. Further, we characterise conflict-free trajectories based on aircraft velocity bounds and propose a simple pre-processing algorithm to identify aircraft pairs which are either always conflict-free, or which cannot be separated using speed and heading control only. We then incorporate altitude control and propose a lexicographic optimisation formulation that aims to minimise the number of flight level changes before resolving outstanding conflicts via two-dimensional velocity control. The proposed mixed-integer programming formulations are nonconvex, and we propose convex relaxations, decomposition methods and constraint generation algorithms to solve the two-dimensional and lexicographic optimisation formulations to guaranteed optimality. Numerical experiments on four types of conflict resolution benchmarking instances are conducted to test the performance of the proposed mixed-integer formulations. Further, the proposed method is compared against two benchmarks based on state-of-the-art approaches for the aircraft conflict resolution problem. Our numerical results show that the proposed method largely outperforms both benchmarks in terms of runtime and is able to solve significantly more instances to global optimality.

97 MATHEMATICS AND COMPUTING↗