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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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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Unfolding Structure Formation in the Dark Universe via Weak Gravitational Lensing: from Pixels to Cosmology in the Dark Energy Survey and Roman Space Telescope

Weak gravitational lensing (deflection of light from distant galaxies due to the gravitational potential of intervening mass) is one of the most exciting probes in cosmology as it is sensitive both to the growth of the large-scale structure and the expansion history of the Universe. We can measure the coherent distortion of galaxy shapes (which we call cosmic shear) and infer the matter distribution. With next-generation imaging surveys such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (Rubin LSST) and the Nancy G. Roman Space Telescope (Roman), there is immense new promise in understanding the fundamental nature of dark matter and dark energy. With datasets from current experiments like the Dark Energy Survey (DES), we see apparent cosmological tensions between experiments that may either be real and indicate new physics or new systematics we do not yet understand. LSST and Roman will increase the number of galaxies we have observed by an order of magnitude, leading to improved constraints on our cosmological model by up to 300%. These experiments will have the potential to prove if these cosmological tensions are real. However, our control of systematic uncertainties must also improve by similar levels to achieve the promise of what these missions can deliver. To achieve these scientific outcomes, the challenges of determining galaxy shapes and redshifts and modeling the impact of astrophysical effects must be solved. My PhD has focused on enabling weak lensing science in DES and Roman. I co-led the shear analysis teams in DES to produce the largest weak lensing galaxy sample, as well as the final DES cosmological analysis of cosmic shear. For Roman, I have led two papers characterizing and mitigating shear-related systematics with image simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Exotic phases in finite-density ℤ 3 theories

Lattice ℤ 3 theories with complex actions share many key features with finite- density QCD including a sign problem and $\mathcal{CK}$ symmetry. Complex ℤ 3 spin and gauge models exhibit a generalized Kramers-Wannier duality mapping them onto chiral ℤ 3 spin and gauge models, which are simulatable with standard lattice methods in large regions of parameter space. The Migdal-Kadanoff real-space renormalization group (RG) preserves this duality, and we use it to compute the approximate phase diagram of both spin and gauge ℤ 3 models in dimensions one through four. Chiral ℤ 3 spin models are known to exhibit a Devil’s Flower phase structure, with inhomogeneous phases that can be thought of as ℤ 3 analogues of chiral spirals. Out of the large class of models we study, we find that only chiral spin models and their duals have a Devil’s Flower structure with an infinite set of inhomogeneous phases, a result we attribute to Elitzur’s theorem. We also find that different forms of the Migdal-Kadanoff RG produce different numbers of phases, a violation of the expectation for universal behavior from a real-space RG. We discuss extensions of our work to ℤ N models, SU(N) models and nonzero temperature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Safety-assured, real-time neural active fault management for resilient microgrids integration

Federated-learning-based active fault management (AFM) is devised to achieve real-time safety assurance for microgrids and the main grid during faults. AFM was originally formulated as a distributed optimization problem. Here, federated learning is used to train each microgrid's network with training data achieved from distributed optimization. The main contribution of this work is to replace the optimization-based AFM control algorithm with a learning-based AFM control algorithm. The replacement transfers computation from online to offline. With this replacement, the control algorithm can meet real-time requirements for a system with dozens of microgrids. By contrast, distributed-optimization-based fault management can output reference values fast enough for a system with several microgrids. More microgrids, however, lead to more computation time with optimization-based method. Distributed-optimization-based fault management would fail real-time requirements for a system with dozens of microgrids. Controller hardware-in-the-loop real-time simulations demonstrate that learning-based AFM can output reference values within 10 ms irrespective of the number of microgrids.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Microsecond-latency feedback at a particle accelerator by online reinforcement learning on hardware

The commissioning and operation of future large-scale scientific experiments will challenge current tuning and control methods. Reinforcement learning (RL) algorithms are a promising solution due to their ability to dynamically adapt to changing environments and consider delayed consequences. In many real-world applications, RL policies must produce actions in real time, often within microseconds to milliseconds, imposing significant constraints on system latency and computational overhead that conventional machine learning libraries are not designed to handle. To control phenomena in real time at these timescales, RL needs to be deployed on-the-edge, namely on dedicated hardware located near the system it controls, without relying on a host CPU or cloud-based inference. In this work we present the design and deployment of an experience accumulator system in a particle accelerator. In this system, deep-RL algorithms run using hardware acceleration and act within a few microseconds, enabling the use of RL for control of phenomena like beam instabilities. The training uses the collected data offline to reduce the number of operations carried out on the acceleration hardware. The proposed architecture was tested in real experimental conditions at the Karlsruhe research accelerator, a synchrotron light source, where the system was used to control artificially induced horizontal betatron oscillations in real-time, with a control loop period of just 2.7 μs. The results showed a performance comparable to the commercial feedback system available at the accelerator, demonstrating the viability and potential of this approach. Due to the self-learning and reconfiguration capability of this implementation, a seamless application to other control problems is possible. Applications range from particle accelerators to large-scale research and industrial facilities.

FPGA↗
DOE OSTI2021

Toward Decoding the Relationship between Domain Structure and Functionality in Ferroelectrics via Hidden Latent Variables

Polarization switching mechanisms in ferroelectric materials are fundamentally linked to local domain structure and the presence of the structural defects, which both can act as nucleation and pinning centers and create local electrostatic and mechanical depolarization fields affecting wall dynamics. However, the general correlative mechanisms between domain structure and polarization dynamics are only weakly explored, precluding insight into the associated physical mechanisms. In this work, the correlation between local domain structures and switching behavior in ferroelectric materials is explored using convolutional encoder–decoder networks, enabling image to spectral (im2spec) and spectral to image (spec2im) translations via encoding of latent variables. The latter reflect the assumption that the relationship between domain structure and polarization switching is parsimonious, i.e., is based upon a small number of local mechanisms. The analysis of latent variables distributions and their real-space representations provides insight into the predictability of the local switching behavior and hence associated physical mechanisms. We further pose that the regions where these correlative relationships are violated, i.e., predictability of the polarization dynamics from domain structure is reduced, represent the obvious target for detailed studies, e.g., in the context of automated experiments. This approach provides a workflow to establish the presence of correlation between local spectral responses and local structure and can be universally applied to spectral imaging techniques such as piezoresponse force microscopy (PFM), scanning tunneling microscopy (STM) and spectroscopy, and electron energy loss spectroscopy (EELS) in scanning transmission electron microscopy (STEM).

36 MATERIALS SCIENCE↗
DOE OSTI2024

Effective rationality for local unitary invariants of mixed states of two qubits

Abstract We calculate the field of rational local unitary invariants for mixed states of two qubits, by employing methods from algebraic geometry. We prove that this field is rational (i.e. purely transcendental), and that it is generated by nine algebraically independent polynomial invariants. We do so by constructing a relative section, in the sense of invariant theory, whose Weyl group is a finite abelian group. From this construction, we are able to give explicit expressions for the generating invariants in terms of the Bloch matrix representation of mixed states of two qubits. We also prove similar rationality results for the local unitary invariants of symmetrically mixed states of two qubits. We also provide a sketch of how to generalize our results to the case of an arbitrary number of qubits. Our results apply to both complex-valued and real-valued invariants.

Physics↗
DOE OSTI2024

HumoNet: A Framework for Realistic Modeling and Simulation of Human Mobility Network

Understanding, analyzing, and predicting human mobility and dynamics are valuable to solving pressing problems, developing effective plans, and prescribing timely remedies. As a computational approach, realistic human mobility simulations allow us to understand, analyze, and predict complex systems, including human societies. Accurate simulations rely on (1) the model that captures interactions and behaviors of myriad entities in our society and (2) the mapping of model instances to real-world entities. Taking this into account, this paper introduces the Human Mobility Network simulation framework (HumoNet), an integrated patterns of life (POL) simulation framework that leverages real-world data layers including transportation networks, points of interest, populations, popularity, and human trajectories. HumoNet is a data informed model in which agents are equipped with activities, locomotion, and planning capabilities. To simulate realistic kinematic maneuvers of individuals in transportation networks, HumoNet harnesses a microscopic traffic simulator that provides interaction among vehicles and traffic objects. In this paper, we describe the framework, outline our methodologies, and discuss the data processing and challenges of each data layer. Through experiments, we demonstrate that our simulations capture key features of human mobility by comparing them to the literature and real data using standard measures of human mobility (i.e., the radius of gyration, number of locations visited, level of exploration) and metrics scoring (i.e., Jensen-Shannon divergence). We envision that the synthetic data produced by HumoNet will serve as a benchmark for analyzing epidemics, deploying EV charging networks, and validating AI/ML tasks such as location prediction.

Kim, Joon-Seok↗
DOE OSTI2023

Investigation of modified uni-traveling carrier photodiode for cryogenic microwave photonic links

Quantum devices present the potential for unparalleled computing and communications capabilities; however, the cryogenic temperatures required to successfully control and read out many qubit platforms can prove to be very challenging to scale. Recently, there has emerged an interest in using microwave photonics to deliver control signals down to ultracold stages via optical fiber, thereby reducing thermal load and facilitating dense wavelength multiplexing. Photodetectors can then convert this optical energy to electrical signals for qubit control. The fidelity of the quantum operations of interest therefore depend heavily upon the characteristics of the photodiode, yet experimental demonstrations of fiber-coupled photodetection systems at low temperatures are relatively few in number, leaving important open questions regarding how specific detectors may perform in real-world cryogenic settings. In this work, we examine a highly linear modified uni-traveling carrier photodiode (MUTC-PD) under C-band illumination (1530–1565 nm) at three temperature regimes (300 K, 80 K, and ∼4 K) and multiple bias conditions. Our findings of reduced responsivity but preserved bandwidth are consistent with previous studies, while our saturation tests suggest a variety of potential applications for MUTC-PDs in cryogenic microwave photonics with and without electrical bias. Overall, our results should provide a valuable foundation for the continued and expanding use of this detector technology in quantum information processing.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Alternating Direction Decomposition with Strong Bounding and Convexification (ADDSBC) for Solving Security Constrained AC Unit Commitment Problems

This project aims to develop efficient and robust computational methods for solving the security-constrained unit commitment and alternating current optimal power flow problem (SC-UC-ACOPF). The SC-UC-ACOPF problem is at the center of the short-term operation of the U.S. Power Grid. It is solved every week, every day, and every 10 minutes to plan for the optimal action of electricity generation and consumption by minimizing the generation cost and maintaining power system reliability against potential disruptions of equipment failures. In mathematical terms, SC-UC-ACOPF is a challenging large-scale mixed-integer nonlinear optimization model. This means that the decisions involve both discrete variables, e.g. the turning on and off of generators and switching of transmission lines and transformers, and continuous decisions, e.g. the amount of energy generated by each generator and the power flows in the power grid. The physics of the power flow is described by nonlinear equations involving real and reactive power and bus voltages. Another key feature is the large number of contingencies, i.e. the system needs to stay reliable in face of failure of any one equipment, such as transmission lines and generators. The U.S. power grids are extremely complicated and large scale with more than 5,000 generators, 50,000 buses, and 100,000 high-voltage transmission lines, making the SC-UC-ACOPF a very large-scale computation challenge. The research developed in this project aims to solve the SC-UC-ACOPF problems in the three timescales, i.e. weekly, daily, and every 10-min. The proposed computational methods are built on a principled algorithmic approach of decomposition and penalization. More specifically, the algorithm develops spatial and temporal decomposition by exploiting the strong temporal coupling and weak spatial coupling of the UC problem and the complementary feature, i.e. weak temporal coupling and strong spatial coupling of the ACOPF problem. The algorithm also leverages recent progresses in strong convex relaxation of ACOPF. A unique feature of the proposed approach is that it generates a valid, global upper bound on the optimal maximum profit. In this way, a global optimality gap is available to measure the quality of the solution. To further speed up computation, the research team has developed a plethora of effective heuristics to strengthen the iterative penalty-based decomposition framework. For instance, a heuristic is developed to construct inner approximations of the time coupling constraints within the time decoupled problems. Contingencies are pre-screened and low-rank matrix computation is exploited to find the almost unique solution to each contingency. A novel heuristic for line switching is proposed and tested with positive impacts on instances where line switching is beneficial. Taking a systematic approach and carefully handling every detail of the problem pays off. The TIM-GO’s performance throughout the trials and the final event was stellar. TIM-GO garnered the second highest total prize money and is ranked in the top three positions across all categories of comparison.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Progress toward Accelogic compression in ROOT

For the last 7 years, Accelogic pioneered and perfected a radically new theory of numerical computing codenamed “Compressive Computing”, which has an extremely profound impact on real-world computer science [1]. At the core of this new theory is the discovery of one of its fundamental theorems which states that, under very general conditions, the vast majority (typically between 70% and 80%) of the bits used in modern large-scale numerical computations are absolutely irrelevant for the accuracy of the end result. This theory of Compressive Computing provides mechanisms able to identify (with high intelligence and surgical accuracy) the number of bits (i.e., the precision) that can be used to represent numbers without affecting the substance of the end results, as they are computed and vary in real time. The bottom-line outcome will be to provide state-of-the-art compression algorithms --and accompanying software libraries-- able to surpass the performance of the compression engines currently available in the ROOT [7] framework. The resulting technology has the capability to enable substantial economic and operational gains (including speedup) for High Energy and Nuclear Physics data storage/analysis. In our initial studies, a factor of nearly x4 (3.9) compression was achieved with RHIC/STAR data where ROOT compression managed only x1.4 [6].As a collaboration of experimental scientists, private industry, and the ROOT Team, our aim is to capitalize on the substantial success delivered by the initial effort and produce a robust technology properly packaged as an open-source tool that could be used by virtually every experiment around the world as means for improving data management and accessibility.In this contribution, we will present our efforts integrating our concepts of “functionally lossless compression” within the ROOT framework implementation, with the purpose of producing a basic solution readily integrated into HENP applications. We will also present our progress applying this compression through realistic examples of analysis from both the STAR and CMS experiments.

Canal, Ph.↗
DOE OSTI2020

Machine learning applied to classifying neutron resonances

The performance of nuclear reactors and other nuclear systems depends on a precise understanding of the neutron interaction cross sections for materials used in these systems. These cross sections exhibit resonance structure whose shape is determined in part by the angular momentum quantum numbers of the resonances. The correct assignment of the quantum numbers of neutron resonances is therefore of paramount importance. In this project, we apply a machine learning technique, namely decision trees, to automate the quantum number assignments. The tree is trained from simulated data generated to mimic the errors found in real data. We explore the use of several physics-motivated features for training our trees, including the nearest neighbor spacing distribution, cumulative level distribution, and channel width distributions. Initial results using random matrix theory motivated fits which demonstrated that we can determine resonance spin groups somewhat reliably. If we use these fits as features in our trees, we can train them to spot outliers corresponding to misassigned resonances. We found that with the large number of features used in this project that the decision tree tended to over t training data resulting in poor performance with respect to the test data. By reducing the number of features, we can achieve nearly perfect assignment of quantum numbers with our training data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

A Data-Driven Framework for Power System Event Type Identification via Safe Semi-Supervised Techniques

Herein this paper investigates the use of phasor measurement unit (PMU) data with deep learning techniques to construct real-time event identification models for transmission networks. Increasing penetration of distributed energy resources represents a great opportunity to achieve decarbonization, as well as challenges in systematic situational awareness. When high-resolution PMU data and sufficient manually recorded event labels are available, the power event identification problem is defined as a statistical classification problem that can be solved by numerous cutting-edge classifiers. However, in real grids, collecting tremendous high-quality event labels is quite expensive. Utilities frequently have a large number of event records without in-depth details (i.e., unlabeled events). To bridge this gap, we propose a novel semi-supervised learning-based method to improve the performance of event classifiers trained with a limited number of labeled events by exploiting the information from massive unlabeled events. In other words, compared to existing data-driven methods, our method requires only a small portion of labeled data to achieve a similar level of accuracy. Meanwhile, this work discusses and addresses the performance degradation caused by class distribution mismatch between the training set and the real applications. Based on the proposed safe learning mechanism, our model does not directly use all unlabeled events during model training, but selectively uses them through a comprehensive evaluation procedure. Numerical studies on a sizable PMU dataset have been used to validate the performance of the proposed method.

42 ENGINEERING↗
DOE OSTI2024

A machine learning decision criterion for reducing scan time for hyperspectral neutron computed tomography systems

We present the first machine learning-based autonomous hyperspectral neutron computed tomography experiment performed at the Spallation Neutron Source. Hyperspectral neutron computed tomography allows the characterization of samples by enabling the reconstruction of crystallographic information and elemental/isotopic composition of objects relevant to materials science. High quality reconstructions using traditional algorithms such as the filtered back projection require a high signal-to-noise ratio across a wide wavelength range combined with a large number of projections. This results in scan times of several days to acquire hundreds of hyperspectral projections, during which end users have minimal feedback. To address these challenges, a golden ratio scanning protocol combined with model-based image reconstruction algorithms have been proposed. This novel approach enables high quality real-time reconstructions from streaming experimental data, thus providing feedback to users, while requiring fewer yet a fixed number of projections compared to the filtered back projection method. In this paper, we propose a novel machine learning criterion that can terminate a streaming neutron tomography scan once sufficient information is obtained based on the current set of measurements. Our decision criterion uses a quality score which combines a reference-free image quality metric computed using a pre-trained deep neural network with a metric that measures differences between consecutive reconstructions. The results show that our method can reduce the measurement time by approximately a factor of five compared to a baseline method based on filtered back projection for the samples we studied while automatically terminating the scans.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Energy Cost Analysis and Operational Range Prediction Based on Medium- and Heavy-Duty Electric Vehicle Real-World Deployments across the United States

While the market for medium- and heavy-duty battery-electric vehicles (MHD EVs) is still nascent, a growing number of these vehicles are being deployed across the U.S. This study used over 2.3 million miles of operational data from multiple types of MHD EVs across various regions and operating conditions to address knowledge gaps in total cost of ownership and operational range. First, real-world energy cost savings were determined: MHD fleets should experience energy cost savings each year from 2021 to 2035, regardless of vehicle platform, with the greatest savings seen in transit buses (up to USD 4459 annually) and HD trucks (up to USD 3284 annually). Second, to help fleets across various geographies throughout the U.S. assess the suitability of EVs for their year-round operating needs, operational range was modeled using the XGBoost algorithm (R2: 70%) given 22 input features relevant to vehicle efficiency. Finally, this paper recommends (1) that MHD fleets apply energy-saving practices to minimize the impacts of cold temperatures and high congestion levels on vehicle efficiency and range, and (2) that local hauling fleets select trucks with a nominal range nearly double the expected maximum daily range to account for range losses under local, urban driving conditions.

Qiu, Yin (ORCID:0009000900948794)↗
DOE OSTI2021

Universal scaling laws of keyhole stability and porosity in 3D printing of metals

Metal three-dimensional (3D) printing includes a vast number of operation and material parameters with complex dependencies, which significantly complicates process optimization, materials development, and real-time monitoring and control. We leverage ultrahigh-speed synchrotron X-ray imaging and high-fidelity multiphysics modeling to identify simple yet universal scaling laws for keyhole stability and porosity in metal 3D printing. The laws apply broadly and remain accurate for different materials, processing conditions, and printing machines. We define a dimensionless number, the Keyhole number, to predict aspect ratio of a keyhole and the morphological transition from stable at low Keyhole number to chaotic at high Keyhole number. Furthermore, we discover inherent correlation between keyhole stability and porosity formation in metal 3D printing. By reducing the dimensions of the formulation of these challenging problems, the compact scaling laws will aid process optimization and defect elimination during metal 3D printing, and potentially lead to a quantitative predictive framework.

42 ENGINEERING↗
DOE OSTI2022

Heavy-Duty Vehicle Activity Updates for MOVES Using NREL Fleet DNA and CE-CERT Data

The U.S. Environmental Protection Agency's (EPA's) Motor Vehicle Emission Simulator (MOVES) is a publicly available tool used by researchers and policymakers to help understand motor vehicle emission sources at a national, county, and project level. Estimates of heavy-duty activity in the most recent version of the model at the time this work was conducted, MOVES2014, was identified as an area in need of improvement. The start activity in MOVES2014 is based on a limited and dated data set. In addition, MOVES2014 relies on drive cycles that represent on-network activity but do not account for idling activity that occurs on off-network roads, such as at a distribution center, while the truck is queuing or during loading and unloading. As a result, MOVES2014 may currently underestimate the number of starts and idle and soak time for heavy-duty trucks in real-world operation. The National Renewable Energy Laboratory (NREL) has previously leveraged its expansive Fleet DNA database of heavy-duty vehicles to idle and start activity for six of the nine heavy-duty vehicle source types of classes in the MOVES model. The data available in Fleet DNA from 416 conventional, diesel-powered vehicles provided activity estimates from more than 120,000 hours of operation throughout 14,682 vehicle days between October 2006 and January 2016. NREL calculated start fraction, starts per day, soak fraction, and idle fraction by hour of the day for each vehicle type, state, and vocation, and provided results in .CSV files that can be translated to MOVES table inputs. The idle and start activity from this initial analysis of Fleet DNA data was used to develop default idle and start data for heavy-duty vehicles in MOVES3. Satisfied with the results from the Fleet DNA data used for MOVES3, the EPA asked NREL to extend this start/soak/idle analysis using additional data from a larger number of vehicles for a potential future update to the MOVES model. Such a data set was achieved from a project led by the University of California at Riverside, College of Engineering, Center for Environmental Research & Technology (CE-CERT) and funded by California Air Resources Board. Specifically, this data set consists of 90 heavy-duty vehicles operated mainly in California, which can be separated into five of the nine heavy-duty vehicle classes in the MOVES model. In addition, the heavy-duty activity database collected by CE-CERT provided activity estimates from more than 44,000 hours of operation throughout 4,724 vehicle days between November 2014 and September 2016. This report details the analysis of the heavy-duty activity database collected from the University of California at Riverside by providing graphical analysis and context for the start, soak, and idle distributions. The comparison of the related results from both the Fleet DNA and CE-CERT data sets are documented as well.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Unveiling the Significance of Correlations in K-Space and Configuration Space for Drift Wave Turbulence in Tokamaks

Turbulence and transport phenomena play a crucial role in the confinement and stability of tokamak plasmas. Turbulent fluctuations in certain physical quantities, such as density or temperature fluctuations, can have a wide range of spatial scales, and understanding their correlation length is important for predicting and controlling the behavior of the plasma. The correlation length in the radial direction is identified as the critical length in real space. The dynamics in real space are of significant interest because transport in configuration space is primarily focused on them. When investigating transport caused by the E×B drift, the correlation length in real space represents the size of E×B whirls. It was numerically discovered that in drift wave turbulence, this length is inversely proportional to the normalized mode number of the fastest growing mode relative to the drift frequency. Considerable time was required before a proper analytical derivation of this condition was accomplished. Therefore, a connection has been established between phenomena occurring in real space and those occurring in k-space. Although accompanied by a turbulent spectrum in k-space with a substantial width, transport in real space is uniquely determined by the correlation length, allowing for accurate transport calculations through the dynamics of a single mode. Naturally, the dynamics are subject to nonlinear effects, with resonance broadening in frequency being the most significant nonlinear effect. Thus, mode number space is once again involved. Resonance broadening leads to the detuning of waves from particles, permitting a fluid treatment. It should be emphasized that the consideration here involves the total electric field, including the induction part, which becomes particularly important at higher beta plasmas.

Weiland, Jan (ORCID:0000000253496025)↗
DOE OSTI2021

A novel energy balance approach for a verifiable and accurate solution of radiation extinction in purely absorbing particle clouds

Here we consider the problem of radiation transport through purely absorbing particle clouds. The gold-standard solution of particle-resolved Monte Carlo ray-tracing method to this problem is computationally expensive and therefore solving the radiation transport equation (specifically, the Beer-Bouguer law (BB-law)) on a Eulerian mesh is often preferred. While the absorption coefficient in the real problem is infinite, the BB-law approximates it to be a finite number in the form of number density through a set of assumptions. For particle clouds that do not obey these assumptions, the BB-law predicts an incorrect exponential decay. Also, when the number density is computed using the nearest-neighbor approach, the BB-law solution diverges when the Eulerian mesh size becomes closer to or smaller than the particle size. This numerical divergence is due to the homogenization error. Although the filtering strategy for number density minimizes the homogenization error, it still converges to an incorrect exponential decay for particle clouds that break the BB-law constraints and the cost of the filtering is equivalent to that of the gold-standard solution. In this study, we develop a novel, highly accurate, verifiable and cost-effective solution to the radiation transport equation on a Eulerian domain using an energy balance approach where we derive an expression for the absorption coefficient as a function of particle and Eulerian mesh sizes. We apply our new method to Poisson and turbulent particle clouds that violate all the BB-law constraints and show that the solution is converging upon the mesh refinement, and eventually, we recover the same gold-standard solution for a much cheaper computational cost.

42 ENGINEERING↗