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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Collaborative Decision Approach for Electricity Pricing-demand Response Stackelberg Game

Demand response programs are considered as a valuable resource in smart grids that provide several advantages of load shifting, peak load reduction, mediating intermittency of renewable energy integration, etc. Flexible price-based incentives have been recognized as a critical strategy in motivating and compensating consumers' load adjustment actions for successful implementation of demand response. Game theoretical approaches, especially Stackelberg games are popularly adopted to model the relationship between electricity price and customers' demand response and solved by the classical centralized backward induction (BI) method. However, the BI method generally requires convexity of the follower's model for necessary optimality conditions, and the computational time of any centralized approach increases sharply with larger problem instances. In this paper, the Stackelberg game of electricity pricing-demand response between a distribution system operator (DSO) and load aggregators (LAs) is decomposed based on a collaborative optimization (CO) framework, where each LA is treated as a discipline with its own domain constraints (e.g. building temperature control), while the DSO at the system level tries to reduce the solution discrepancy and guide the searching towards optimality. Several groups of comparison experiments have demonstrated the effectiveness of the proposed collaborative decision approach in solving the demand response game.

Chen, Yang↗
DOE OSTI2020

Toward DMRG-tailored coupled cluster method in the 4c-relativistic domain

There are three essential problems in computational relativistic chemistry: Electrons moving at relativistic speeds, close lying states, and dynamical correlation. Currently available quantum-chemical methods are capable of solving systems with one or two of these issues. However, there is a significant class of molecules in which all the three effects are present. These are the heavier transition metal compounds, lanthanides, and actinides with open d or f shells. For such systems, sufficiently accurate numerical methods are not available, which hinders the application of theoretical chemistry in this field. In this paper, we combine two numerical methods in order to address this challenging class of molecules. These are the relativistic versions of coupled cluster methods and the density matrix renormalization group (DMRG) method. To the best of our knowledge, this is the first relativistic implementation of the coupled cluster method externally corrected by DMRG. The method brings a significant reduction of computational costs as we demonstrate on the system of TlH, AsH, and SbH.

Brandejs, Jan (ORCID:0000000221073095)↗
DOE OSTI2023

PCAfold 2.0—Novel tools and algorithms for low-dimensional manifold assessment and optimization

We describe an update to our open-source Python package, PCAfold, designed to help researchers generate, analyze and improve low-dimensional data manifolds. In the current version, PCAfold 2.0, we introduce novel tools and algorithms for assessing and optimizing low-dimensional manifolds. This includes a method that generates a “map” of local feature sizes that can help pinpoint researchers to problematic regions on a manifold. We introduce a novel cost function that characterizes the quality of a manifold topology with a single number. We develop two algorithms for feature selection based on principal component analysis (PCA) that use the cost function as an objective function to minimize. We introduce a quantity of interest (QoI)-aware dimensionality reduction strategy where data projections are computed using an artificial neural network and are directly optimized towards representing various projection-independent and projection-dependent QoIs. We also introduce an implementation of partition of unity networks (POUnets) for efficient reconstruction of QoIs from low-dimensional manifolds based on combining neural network classification with localized polynomial regression. Our software can be broadly applicable in all domains of science and engineering that aim to reduce data dimensionality, as well as in the fundamental research on representation learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Correlation of coercivity, microstructure, and surface defects in HDDR-processed Nd-Fe-B powders for bonded magnet applications

Hydrogenation-Disproportionation-Desorption-Recombination (HDDR) is an effective method for producing high coercivity, anisotropic powder from either fresh Nd-Fe-B alloy or recycled Nd-Fe-B magnets for use in bonded magnets. We investigated the impact of surface defects on the coercivity of HDDR-processed Nd-Fe-B using scanning electron microscopy (SEM), magnetic measurements, and micromagnetic simulations. We observed that coercivity decreases as particle size reduces, with SEM revealing surface defects and the detachment of Nd 2 Fe 14 B grains and Nd-rich phases from the particle surface. Micromagnetic simulations indicate that demagnetization initiates at the particle surface, where these defects are most concentrated, leading to reduced coercivity. The reduction in squareness of demagnetization curve, knee point field and coercivity for smaller HDDR particles is attributed to an increased specific surface area, which exhibits reduced nucleation field and weak domain wall pinning field during magnetization reversal. By addressing the role of surface defects in coercivity degradation, this study provides insights for improving both new powder production and recycling strategies, ultimately leading to enhanced performance of bonded magnets and contributing to more sustainable practices in the rare earth supply chain. One potential strategy to enhance the performance of HDDR Nd-Fe-B materials involves reducing the fraction of fine particles ($<$35 µm) and promoting the formation of grain boundary phases on particle surfaces.

Liu, Xubo B. [Ames Laboratory (AMES), Ames, IA (Un↗
DOE OSTI2020

Time-Domain Nuclear Magnetic Resonance Determination of Wettability Alteration: Analysis for Low-Salinity Water

Wettability has been shown to influence oil recovery. This property has become central to low-salinity (LSW) and smart (SWF) water flooding recovery mechanisms research. The challenge lies in the fact that oil recovery results from the combined effects of solid-liquid and liquid-liquid interactions. This demands methods that allow an independent interpretation of wettability alteration contributions. The primary objective of this work is to assess changes in wettability through the application of Time-Domain Nuclear Magnetic Resonance (TD-NMR) T 2 distribution and diffusion coefficient, starting with a well-controlled porous system, that is, glass beads, and then a model rock (Berea), in the presence of one phase, either oil or brine exclusively. Subsequently, two-phase fluid saturation was tested. For the glass beads, dimethyldichlorosilane was used to induce a hydrophobic response, as confirmed by contact angle experiments on slides of the same material. Sodium sulfate was used for its known positive influence on oil recovery during LSW and SWF. In cases where alteration of surface properties was expected, a leftward shift of the average T 2 distribution curve modes, accompanied by a reduction on the diffusion coefficient during the aging process was observed. The results of this work confirm that fluid-solid interactions during LSW and SWF, namely a shift in wettability, take place after the injection of low-salinity water.

42 ENGINEERING↗
DOE OSTI2021

Applying Time-Parallelization to Turbulent Flows

Parallelization of the temporal domain is explored for the solution of turbulent flows. Multigrid reduction-in-time (MGRIT) is used to advance the large-scale fluid dynamics in time sequentially on the coarsest space-time grid but propagate the information in time parallel on all other levels. The goal of this process is to accurately and efficiently resolve the coarse-scale turbulence structure and use that to drive the fine-scales of the turbulent flow. The extra forcing from nonlinear multigrid facilitates the coupling and interaction between fine and coarse scales, through which the multiscale nonlinear physics is properly captured. Adaptive mesh refinement is employed to finely resolve only the regions with strong gradients, which provides further computational efficiency. The underlying computational fluid dynamics solver is a fourth-order finite-volume scheme with the standard 4-stage Runge-Kutta method. An advanced approach is devised and implemented to enable MGRIT to solve highly turbulent flows successfully. Furthermore, the method is applied to solve a Taylor-Green vortex problem and a doubleshear-layer turbulent mixing flow. Results are promising, validating that MGRIT with the filtering approach has the potential to efficiently solve general turbulent flows.

Computational Fluid Dynamics↗
DOE OSTI2024

Synthesis of the land carbon fluxes of the Amazon region between 2010 and 2020

The Amazon is the largest continuous tropical forest in the world and plays a key role in the global carbon cycle. Human-induced disturbances and climate change have impacted the Amazon carbon balance. Here we conduct a comprehensive synthesis of existing state-of-the-art estimates of the contemporary land carbon fluxes in the Amazon using a set of bottom-up methods (i.e., dynamic vegetation models and bookkeeping models) and a top-down inversion (atmospheric inversion model) over the Brazilian Amazon and the whole Biogeographical Amazon domain. Over the whole biogeographical Amazon region bottom-up methodologies suggest a small average carbon sink over 2010-2020, in contrast to a small carbon source simulated by top-down inversion (2010-2018). However, these estimates are not significantly different from one another when accounting for their large individual uncertainties, highlighting remaining knowledge gaps, and the urgent need to reduce such uncertainties. Nevertheless, both methodologies agreed that the Brazilian Amazon has been a net carbon source during recent climate extremes and that the south-eastern Amazon was a net land carbon source over the whole study period (2010-2020). Overall, our results point to increasing human-induced disturbances (deforestation and forest degradation by wildfires) and reduction in the old-growth forest sink during drought.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Local Lagrangian reduced-order modeling for the Rayleigh-Taylor instability by solution manifold decomposition

The Rayleigh-Taylor instability is a classical hydrodynamic instability of great interest in various disciplines of science and engineering, including astrophysics, atmospheric sciences and climate, geophysics, and fusion energy. Analytical methods cannot be applied to explain the long-time behavior of the Rayleigh-Taylor instability, and therefore, numerical simulation of the full problem is required. However, in order to capture the growth of amplitude of perturbations accurately, both the spatial and temporal discretizations need to be extremely fine for traditional numerical methods, and long-time simulation may become prohibitively expensive. In this paper, we propose efficient reduced order model techniques to accelerate the simulation of the Rayleigh-Taylor instability in compressible gas dynamics. Here, we introduce a general framework for decomposing the solution manifold to construct the temporal domain partition and temporally-local reduced order model construction with varying Atwood number. We propose two practical approaches in this framework, namely decomposition by physical time and by penetration distance. Numerical results are presented to examine the performance of the proposed approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Reduced Order Modeling conditioned on monitored features for response and error bounds estimation in engineered systems

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM construction, schemes that allow to retain a portion of the physics tend to enhance the interpretability and generalization of ROMs. However, physics-based techniques can adversely scale when dealing with nonlinear systems that feature parametric dependencies. This study introduces a generative physics-based ROM that is suited for nonlinear systems with parametric dependencies and is additionally able to provide numerical error bounds associated with the respective estimates. A main contribution of this work is the conditioning of these parametric ROMs to features that can be derived from monitoring measurements, feasibly in an online fashion. This is contrary to most existing ROM schemes, which remain restricted to the prescription of the physics-based, and usually a priori unknown, system parameters. Our work utilizes conditional Variational Autoencoders to continuously map the required reduction bases to a feature vector extracted from limited output measurements, while additionally allowing for a probabilistic assessment of the ROM-estimated Quantities of Interest. An auxiliary task using a neural network-based parametrization of suitable probability distributions is introduced to re-establish the link with physical model parameters. We verify the proposed scheme on a series of simulated case studies incorporating effects of geometric and material nonlinearity under parametric dependencies related to system properties and input load characteristics.

Conditional VAEs↗
DOE OSTI2026

HostSub_GP: Precise Galaxy Background Subtraction in Transient Long-slit Spectroscopy with Gaussian Processes

We present a novel host galaxy subtraction technique in long-slit spectroscopy for extragalactic transients. Unlike classic methods which generally estimate the background using simple interpolation of local galaxy flux in the 2D spectrum, our approach leverages multi-band archival images of the host galaxies to model the background emission from the galaxy in the 2D spectrum. Such imaging encodes the wavelength-dependent galaxy profile along the slit, and is readily accessible through wide-field imaging surveys. We construct a smooth prior for the 2D galaxy profile with a Gaussian process (GP) based on these reference images, and use another GP to model the correlated deviations from the prior in the observed spectrum. This enables accurate inference of the galaxy flux blended with the transient. On synthetic long-slit data of a spiral galaxy extracted from a Multi Unit Spectroscopic Explorer hyper-spectral cube, the GP method remains robust as long as the host galaxy is spatially resolved and consistently outperforms classic methods. We apply the method to archival Keck spectra of two real transients, SN 2019eix and AT 2019qiz, to further demonstrate how the method uniquely recovers weak spectral features amid strong galaxy contamination, enabling refined constraints on the properties of both transients. We have released the software implementation, HostSub_GP, a scalable toolkit that leverages JAX, with an MIT license.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Dimensionality reduction of the many-body problem using coupled-cluster subsystem flow equations: classical and quantum computing perspective

We discuss reduced-scaling strategies employing recently introduced sub-system embedding sub-algebras coupled-cluster formalism (SES-CC) to describe many-body systems. These strategies utilize properties of the SES-CC formulations where the equations describing certain classes of sub- systems can be integrated into a computational flows composed coupled eigenvalue problems of reduced dimensionality. Additionally, these flows can be defined at the level of the CC Ansatz defined by selected classes of cluster amplitudes, which define the wave function ”memory” of possible partitionings of the many-body system into constituent sub-systems. One of the possible ways of solving these coupled problems is through implementing procedures, where the information is passed between the sub-systems in a self-consistent manner. As a special case, we consider local flow formulations where the so-called local character of correlation effects can be closely related to properties of sub-system embedding sub-algebras employing localized molecular basis. We also generalize flow equations to the time domain and to downfolding methods utilizing double exponential unitary CC Ansatz (DUCC), where reduced dimensionality of constituent sub-problems offer a possibility of efficient utilization of limited quantum resources in modeling realistic systems.

Electron correlation, quantum chemistry, quantum c↗
DOE OSTI2025

Toward equitable environmental exposure modeling through convergence of data, open, and citizen sciences: an example of air pollution exposure modeling amidst increasing wildfire smoke

Exposure modeling is critical in environmental epidemiology and human health but may face challenges (e.g., skewed data, unequal error, context-insensitive validation, and computational demands). Modeling decisions reflect the intended use of the models and the values that modelers prioritize. We aimed to provide a conceptual framework and machine learning (ML) modeling protocols that address these issues. With 500m-gridded hourly PM 2.5 and O 3 levels in Illinois before, during, and after the 2023 Canadian wildfire season as a motivating example, we conducted modeling experiments to evaluate modeling methods, guided by three domains we propose based on theories of science: 1) Data Diversity, leveraging open and citizen science data to enhance inclusivity, parsimony, and representativeness; 2) Equitable Accuracy, ensuring fairly distributed uncertainties across subpopulations; and 3) Sustainable Modeling, balancing accuracy with reducing computational demands to promote accessibility for under-resourced researchers. Here, we found that ML with publicly available data can achieve high accuracy. Depending on methods, performance may vary substantially, even with identical input data. Large but skewed data may reduce performance. Misuse of cross-validation protocols can underestimate prediction error; although we observed R 2 s of ∼98 %, the modeled estimates varied significantly, indicating the need for careful model validation. By using new modeling protocols including representativeness-considered training and validation data and a new loss function, we achieved high agreement between estimates and ground-based measurements (e.g., R 2 = ∼90 % for PM 2.5 ; ∼80 % for O 3 ), equally distributed errors across sociodemographic strata and urban–rural divides, and reduction in computation time—from several weeks or months to a few days.

Exposure assessment↗
DOE OSTI2025

Experimental confirmation of first-principles thermal conductivity in Zirconium-doped ThO 2

The degradation of thermal conductivity in advanced nuclear fuels due to the accumulation of fission products and irradiation-induced defects is inevitable, and must be considered as part of safety and efficiency analyses of nuclear reactors. Here, this study examines the thermal conductivity of a zirconium-doped ThO 2 crystal, synthesized via the hydrothermal method using a spatial domain thermoreflectance technique. Zirconium is one of the soluble fission products in oxide fuels that can effectively scatter heat-carrying phonons in the crystalline lattice of fuel. Thus, thermal property measurements of zirconium-doped ThO 2 single crystals provide insights into the effects of substitutional zirconium doping, isolated from extrinsic factors such as grain boundary scattering. The experimental results are compared with first-principles calculations of the lattice thermal conductivity of ThO 2 , employing an iterative solution of the Peierls-Boltzmann transport equation. Additionally, the non-perturbative Green's function methodology is utilized to compute phonon-point defect scattering rates, accounting for local distortions around point defects, including mass difference changes, interatomic force constants, and structural relaxation. The congruence between the predicted results from first-principles calculations and the measured temperature-dependent thermal conductivity validates the computational methodology. Furthermore, the methodologies employed in this study enable systematic investigations of thermal conductivity reduction by fission products, potentially leading to the development of more accurate fuel performance codes.

36 - MATERIALS SCIENCE↗
DOE OSTI2024

Unlocking the potential: machine learning applications in electrocatalyst design for electrochemical hydrogen energy transformation

Machine learning (ML) is rapidly emerging as a pivotal tool in the hydrogen energy industry for the creation and optimization of electrocatalysts, which enhance key electrochemical reactions like the hydrogen evolution reaction (HER), the oxygen evolution reaction (OER), the hydrogen oxidation reaction (HOR), and the oxygen reduction reaction (ORR). This comprehensive review demonstrates how cutting-edge ML techniques are being leveraged in electrocatalyst design to overcome the time-consuming limitations of traditional approaches. ML methods, using experimental data from high-throughput experiments and computational data from simulations such as density functional theory (DFT), readily identify complex correlations between electrocatalyst performance and key material descriptors. Leveraging its unparalleled speed and accuracy, ML has facilitated the discovery of novel candidates and the improvement of known products through its pattern recognition capabilities. This review aims to provide a tailored breakdown of ML applications in a format that is readily accessible to materials scientists. Hence, we comprehensively organize ML-driven research by commonly studied material types for different electrochemical reactions to illustrate how ML adeptly navigates the complex landscape of descriptors for these scenarios. We further highlight ML's critical role in the future discovery and development of electrocatalysts for hydrogen energy transformation. Potential challenges and gaps to fill within this focused domain are also discussed. As a practical guide, we hope this work will bridge the gap between communities and encourage novel paradigms in electrocatalysis research, aiming for more effective and sustainable energy solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Salt-Mediated Coarsening in Conversion-Reaction-Synthesized Nanoporous Metals and Nanocomposites Resolved through In Situ Synchrotron Diffraction Studies

High-energy synchrotron X-rays were used to probe the structural and microstructural evolution in Fe, Co, and Cu nanoporous metals (NPMs) and metal/salt nanocomposites (NCs) produced by recently developed conversion reaction synthesis (CRS) methods. Microstructure analysis of as-synthesized samples via whole pattern fitting showed that the NPMs exhibit domain sizes that increase as Co < Fe < Cu, with both Fe and Co having crystallite sizes below 3.0 nm. The as-synthesized metal/salt NCs had similar metal sizes, and additionally, the salt in the composite had unusually large lattice microstrain whose origin is attributed to chemical substitution of metal ions into the salt (e.g., Li $1–3x$ Fe $x$ Cl for Fe 3+ ). When thermal annealing is used to modify crystallite size, pore collapse often occurs in NPMs but NCs can be effectively tuned without this problem. While the NC coarsening occurs slowly at low temperatures, it was found that there is a drastic acceleration of the reaction rate at a specific onset temperature that results in the crystallite size increasing by an order of magnitude in about a minute. Curiously, there was no evidence in the diffraction data for salt melting at this onset temperature. However, there was a sharp reduction in the salt chemical lattice strain at the onset temperature, indicating that rapid metal coarsening is facilitated by the salt. Importantly, this behavior indicates an unexpectedly coupled reaction mechanism by which the metal ions needed for grain growth are supplied by the salt in a rate-limiting fashion.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Indicators of Global Climate Change 2023: annual update of key indicators of the state of the climate system and human influence

Intergovernmental Panel on Climate Change (IPCC) assessments are the trusted source of scientific evidence for climate negotiations taking place under the United Nations Framework Convention on Climate Change (UNFCCC). Evidence-based decision-making needs to be informed by up-to-date and timely information on key indicators of the state of the climate system and of the human influence on the global climate system. However, successive IPCC reports are published at intervals of 5–10 years, creating potential for an information gap between report cycles. We follow methods as close as possible to those used in the IPCC Sixth Assessment Report (AR6) Working Group One (WGI) report. We compile monitoring datasets to produce estimates for key climate indicators related to forcing of the climate system: emissions of greenhouse gases and short-lived climate forcers, greenhouse gas concentrations, radiative forcing, the Earth's energy imbalance, surface temperature changes, warming attributed to human activities, the remaining carbon budget, and estimates of global temperature extremes. The purpose of this effort, grounded in an open-data, open-science approach, is to make annually updated reliable global climate indicators available in the public domain. As they are traceable to IPCC report methods, they can be trusted by all parties involved in UNFCCC negotiations and help convey wider understanding of the latest knowledge of the climate system and its direction of travel. The indicators show that, for the 2014–2023 decade average, observed warming was 1.19 [1.06 to 1.30] °C, of which 1.19 [1.0 to 1.4] °C was human-induced. For the single-year average, human-induced warming reached 1.31 [1.1 to 1.7] °C in 2023 relative to 1850–1900. The best estimate is below the 2023-observed warming record of 1.43 [1.32 to 1.53] °C, indicating a substantial contribution of internal variability in the 2023 record. Human-induced warming has been increasing at a rate that is unprecedented in the instrumental record, reaching 0.26 [0.2–0.4] °C per decade over 2014–2023. This high rate of warming is caused by a combination of net greenhouse gas emissions being at a persistent high of 53±5.4 Gt CO 2 e yr -1 over the last decade, as well as reductions in the strength of aerosol cooling. Despite this, there is evidence that the rate of increase in CO 2 emissions over the last decade has slowed compared to the 2000s, and depending on societal choices, a continued series of these annual updates over the critical 2020s decade could track a change of direction for some of the indicators presented here.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

NRC Multiphysics Analysis Capability Deployment FY2020: Part 3

This report details progress and activities of Idaho National Laboratory (INL) on the Nuclear Regulatory Commission (NRC) project “Development and Modeling Sup- port for Advanced Non-Light Water Reactors.” The tasks completed for this report are: Task2c: Explicit modeling of pebble transient temperature response. In this simulation, the 400 MWth Pebble-Bed Modular Reactor (PBMR) design, PBMR- 400, experiences a 20-second power ramp from 100% to 150% power. This is followed by a similar reduction in the power back to 100%. Several multiscale pebble coupling approaches are tested with one pebble per mesh element in the active core region. The results show good conservation behavior and the stability of the coupling.; Extended scope part 1: An assessment of the computational efficiency of the Discontinuous Finite Element Method (DFEM) heat transfer solver shows good scalability. The DFEM solver is a factor of 4 more expensive in solution time than the Finite Element Method (FEM) solver for heat transfer problems due to the increased number of degrees of freedom. Nonetheless, the DFEM approach provides the user with the flexibility to model gap heat transfer problems.; Extended scope part 2: The GapHeatTransferInterfaceMaterial was improved to give the user increased flexibility with the modeling of heat transfer through gaps with the DFEM solver. A number of gap parameters can now be coupled both through functions and variables.; Extended scope part 3: Demonstration of how the gap width between hexagonal fuel cells can be calculated during a heat-up transient and used in the GapHeatTransferInterface model. A full-domain DFEM model with gap expansion is coupled to a SubApp that models the thermal expansion of the base plate. The results show the expected physical behavior, although have not been fully bench-marked at this point in time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Implicit fast sweeping method for hyperbolic systems of conservation laws

Implicit time-accurate methods are often used to integrate stiff problems where explicit schemes impose severe time step restrictions. This paper presents an efficient numerical framework based on the Fast Sweeping Method (FSM) for solving linear and nonlinear hyperbolic systems of conservation laws. The solution at each discrete location is computed by sweeping the numerical domain in several predetermined directions that follow the causality of the characteristic families. The use of a fractional step strategy eliminates the need for a solution selection criterion while one-sided stencils limit the number of sweeps to at most 2 d for d space dimensions. This work focuses on the first-order implicit upwind method since it constitutes the building block for high-order conservative schemes. For problems where the degree of stiffness evolves over time, implicit-explicit hybridization can be accomplished with the same algorithm by simply switching the stencil at each time level. As opposed to traditional implicit solvers, the sweeping method does not require a local time linearization of the fluxes thereby preserving the nonlinear stability properties of the original implicit scheme. It also avoids the large computational and memory requirements associated with solving large block-diagonal systems of equations. Here, a series of one- and two-dimensional test cases are presented for the inviscid Burgers' equation and the reactive Euler equations. The results indicate that the implicit FSM can allow a major reduction in the number of time steps even in the presence of discontinuous solution profiles.

74 ATOMIC AND MOLECULAR PHYSICS↗