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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

SIERRA Low Mach Module: Fuego Verification Manual - Version 5.30

The SIERRA Low Mach Module: Fuego, henceforth referred to as Fuego, is the key element of the ASC fire environment simulation project. The fire environment simulation project is directed at characterizing both open large-scale pool fires and building enclosure fires. Fuego represents the turbulent, buoyantly-driven incompressible flow, heat transfer, mass transfer, combustion, soot, and absorption coefficient model portion of the simulation software. Sierra/PMR handles the participating-media thermal radiation mechanics. This project is an integral part of the SIERRA multi-mechanics software development project. Fuego depends heavily upon the core architecture developments provided by SIERRA for massively parallel computing, solution adaptivity, and mechanics coupling on unstructured grids.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Temperatures of Anvil Clouds and Radiative Tropopause in a Wide Array of Cloud-Resolving Simulations

Here, we present 123 cloud-resolving simulations to study how temperatures of anvil clouds and radiative tropopause (RT) change with surface warming. Our simulation results show that the RT warms at approximately the same rate as anvil clouds. This relationship persists across a variety of modeling choices, including surface temperature, greenhouse gas concentration, and the representation of radiative transfer. We further show that the shifting ozone profile associated with climate warming may give rise to a fixed RT temperature as well as a fixed anvil temperature. This result points to the importance of faithful treatment of ozone in simulating clouds and climate change; the robust anvil–RT relationship may also provide alternative ways to understand what controls anvil temperature.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Challenging Common Assumptions of Thick-Wall Chamber Dynamics in Inertial Fusion Systems Using MOOSE-based Multiphysics Simulations

As an increasing number of companies look toward commercial Inertial Fusion Energy (IFE) designs, there is a pressing need to understand the physics of thick-wall chamber gas dynamics. The thick liquid wall approach implements a renewable wall to mitigate the fusion target emissions, thereby reducing the radiation damage rate and significantly extending the lifetime of chamber structures, leading to increased plant availability and reduced waste streams in comparison to dry wall chamber designs. It is necessary, however, to assess the critical performance and safety aspects of these systems. For example, it is crucial to predict (1) where the mass ablated from the liquid walls will vent, which determines the placement of condensing surfaces; (2) debris propagation up the beam lines, which provides essential information for design and protection requirements; (3) peak pressures and impulse on chamber walls, which affect chamber structural design; and (4) momentum transfer to the liquid jets, which constrains the shape and positioning of the jets. In turn, the chamber design and its liquid walls affect shielding requirements, material activation, and tritium fuel cycle. Currently available simulation tools, however, are unable to accurately capture key thick-wall chamber dynamics. Significant assumptions are often made to simplify the system and reduce computational cost and modeling capability needs, but the impact of these assumptions on simulation predictions has not been evaluated. For example, no three-dimensional simulations can be found in the open literature to evaluate gas venting and momentum transfer to the jets with simulations using two-dimensional domains to represent complex three-dimensional geometries. Moreover, limited studies have been dedicated to jet breakup due to both turbulence and neutron heating, and no studies have been found that evaluate how jet breakup can impact shock-jet interaction. Furthermore, effects of radiative heat transfer have rarely been included for the hydrodynamic phase of shock propagation, and integration of proper equations of state in shock dynamics codes has been mostly exploratory. In this study, we use the flexible, high-fidelity Multiphysics Object-Oriented Simulation Environment (MOOSE) to model these complex phenomena and inform design and safety studies. Capabilities to model thick-wall chamber gas dynamics are being developed, and the impact of the assumptions listed above (i.e., two-dimensional vs three-dimensional, absence of jet breakout, no radiative heat transfer, and ideal gas behavior) are being quantified.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

3D simulations of inertial confinement fusion implosions part 2: systematic flow anomalies and impact of low modes on performances in OMEGA experiments

We present the first 3D radiation-hydrodynamic simulations of directly driven inertial confinement fusion implosions with an inline package for polarized crossed-beam energy transfer, which were used to assess the impact of the current distributed polarization rotators (DPRs) on OMEGA as well as other known sources of asymmetry. Applied to OMEGA implosions, the simulations predict bang times with no need for ad hoc multipliers, as well as yields—if you separately account for the impacts of imprint and fuel age. The magnitude of the flow is well reproduced when the low mode sources are large, whereas the modeling of the stalk is thought to be required to match the flow magnitude in the remaining cases. For the cases explored in more detail, polarized cross-beam energy transfer (CBET)—the only known systematic drive asymmetry, brought the results closest to the measured flow vectors. The remaining discrepancies are shown to be stemming from the limited knowledge of the laser pointing modes. For typical current levels of beam mispointing, power imbalance, target offset, and asymmetry caused by polarized CBET, low modes degrade the yield by more than 40%. The current strategy of attempting to compensate the mode-1 asymmetry with a preimposed target offset recovers only about one-third of the losses caused by the low modes due to the dynamic nature of the multiple asymmetries and the presence of low modes other than l = 1. Furthermore, addressing the root causes of the drive asymmetries is apt to be more beneficial. To that end, one possible solution to the specific issue of polarized CBET (10 µm DPRs) is shown to work well.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Radiation Hydrodynamics in the Lagrangian Application Project’s LUMOS code

Starting in 2019, the Lagrangian Applications Project (LAP) and the Transport Project set out to develop a new ALE/Lagrangian radiation-hydrodynamics (RH) capability in a new code product named LUMOS. This work was done under the guidance of the Advanced Simulation and Computing (ASC) program with the goal of producing software capable of leveraging the high-order thermal radiative transfer (TRT) solvers provided by the Jayenne and Capsaicin software projects. This capability supplements the existing gray diffusion solver that is currently available in LAP’s FLAG code [1, 2, 3] for RH. The remainder of this memo describes the coupling of the radiation and hydrodynamics solvers within LAP’s LUMOS code. Initially delivered in 2020 as part of an L2 milestone [4], this capability continues to mature in FY21 with more efficient and robust algorithms, new support for ALE, and support for mixed materials per cell. Today, LUMOS is provided as a standard end-user product in the suite of LAP tools provided in each release cycle. Code access can be requested at https://asc.lanl.gov.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Explicitly determined sea ice emissivity and emission temperature over the Arctic for surface–sensitive microwave channels

Data assimilation of satellite microwave measurements is one of the important keys to improving weather forecasting over the Arctic region. However, the use of surface-sensitive microwave-sounding channel measurements for data assimilation or retrieval has been limited, especially during winter, due to the poorly constrained sea ice emissivity. In this study, aiming at more use of those channel measurements in the data assimilation, we propose an explicit method for specifying the surface radiative boundary conditions (namely emissivity and emitting layer temperature of snow and ice). These were explicitly determined with a radiative transfer model for snow and ice and with snow/ice physical parameters (i.e., snow/ice depths and vertical distributions of temperature, density, salinity, and grain size) simulated from the thermodynamically-driven snow/ice growth model. Here we conducted 1-D Var experiments in order to examine whether this approach can help to use the surface-sensitive microwave temperature channel measurements over the Arctic sea ice region for data assimilation. Results show that (1) the surface-sensitive microwave channels can be used in the 1-D Var retrieval, and (2) the specification of the radiative boundary condition at the surface using the snow/sea ice emission model can significantly improve the atmospheric temperature retrieval, especially in the lower troposphere (500 hPa to surface). The successful retrieval suggests that useful information can be extracted from surface-sensitive microwave-sounding channel radiances over sea ice surfaces through the explicit determination of snow/ice emissivity and emitting layer temperature.

1-D Var retrieval↗
DOE OSTI2023

Implementation of Chemistry in the Athena++ Code

Chemistry plays a key role in many aspects of astrophysical fluids. Atoms and molecules are agents for heating and cooling, determine the ionization fraction, serve as observational tracers, and build the molecular foundation of life. We present the implementation of a chemistry module in the publicly available magnetohydrodynamic code Athena++ . We implement several chemical networks and heating and cooling processes suitable for simulating the interstellar medium (ISM). A general chemical network framework in the KIDA format is also included, allowing users to easily implement their own chemistry. Radiation transfer and cosmic-ray ionization are coupled with chemistry and solved with the simple six-ray approximation. The chemical and thermal processes are evolved as a system of coupled ordinary differential equations with an implicit solver from the CVODE library. We perform and present a series of tests to ensure the numerical accuracy and convergence of the code. Many tests combine chemistry with gas dynamics, including comparisons with analytic solutions, 1D problems of the photodissociation regions and shocks, and realistic 3D simulations of the turbulent ISM. We release the code with the new public version of Athena++ , aiming to provide a robust and flexible code for the astrochemical simulation community.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

How numerical simulations helped to achieve breakeven on the NIF

The inertial confinement fusion program relies upon detailed simulations with inertial confinement fusion (ICF) codes to design targets and to interpret the experimental results. These simulations treat as much physics from essential principles as is practical, including laser deposition, cross beam energy transfer, x-ray production and transport, nonlocal thermal equilibrium kinetics, thermal transport, hydrodynamic instabilities, thermonuclear burn, and transport of reaction products. Improvements in radiation hydrodynamic code capabilities and vast increases in computing power have enabled more realistic, accurate 3D simulations that treat all known asymmetry sources. We describe how numerical simulations helped to guide the program, assess the impediments to breakeven, and optimize every aspect of target design. A preshot simulation of the first National Ignition Facility experiment that surpassed breakeven predicted an increased yield that matches the experimental result, within the preshot predicted uncertainty, with a target gain of 1.5. We will cover the key developments in Lawrence Livermore National Laboratory ICF codes that enabled these simulations and give specific examples of how they helped to guide the program.

Marinak, M. M. (ORCID:0009000331127696)↗
DOE OSTI2020

High-Temperature Particle Heat Exchanger for sCO2 Power Cycles [Award 30342]

This report describes the design, development, and testing of a prototype 100 kWt particle-to-supercritical CO 2 (sCO2) heat exchanger. An analytic hierarchy process was implemented to compare and evaluate alternative heat-exchanger designs (fluidized bed, shell-and-plate moving packed bed, and shell-and-tube moving packed bed) that could meet the high pressure (≥ 20 MPa) and high temperature (≥ 700 °C) operational requirements associated with sCO2 power cycles. Cost, heat-transfer coefficient, structural reliability, manufacturability, parasitics and heat losses, scalability, compatibility, erosion and corrosion, transient operation, and inspection ease were considered in the evaluation. A 100 kWt shell-and-plate design was selected for construction and integration with Sandia’s falling particle receiver system that heats the particles using concentrated sunlight. Sandia worked with industry to design and construct the moving packed-bed shell-and-plate heat exchanger. Tests were performed to evaluate its performance using both electrical heating and concentrated sunlight to heat the particles. Overall heat transfer coefficients at off-design conditions (reduced operating temperatures and only three stainless steel banks in the counter-crossflow heat exchanger) were measured to be approximately ~25 - 70 W/m 2 -K, significantly lower than simulated values of >100 W/m 2 -K. Tests using the falling particle receiver to heat the particles with concentrated sunlight yielded overall heat transfer coefficients of ~35 – 80 W/m 2 -K with four banks (including a nickel-alloy bank above the three stainless steel banks). The overall heat transfer coefficient was observed to decrease with increasing particle inlet temperatures, which contrasted the results of simulations that showed an increase in heat transfer coefficient with temperature due to increased effective particle-bed thermal conductivity from radiation. The likely cause of the discrepancy was particle-flow maldistributions and funnel flow within the heat exchanger caused by internal ledges and cross-bracing, which could have been exacerbated by increased particle-wall friction at higher temperatures. Additional heat loss at higher temperatures may also contribute to a lower overall heat-transfer coefficient. Design challenges including pressure drop, particle and sCO2 flow maldistribution, and reduced heat transfer coefficient are discussed with approaches for mitigation in future designs. Lessons learned regarding instrumentation, performance characterization, and operation of particle components and sCO2 flow loops are also discussed. Finally, a 200 MWt commercial-scale shell-and-plate heat-exchanger design based on the concepts investigated in this report is proposed.

14 SOLAR ENERGY↗
DOE OSTI2023

Assessment of ITER radiation environment during the remote-handling operation of In-Vessel components with D1SUNED

During ITER operational life, a remote-handled cask will be used to transfer In-Vessel components to the Hot Cell for maintenance, storage and decommissioning purposes. Due to the distribution of penetrations for system allocation in the facility, the radiation field of each transfer operation presents a high spatial variability; all operations must be studied independently for workers and electronics protection. In this paper, we present a fully representative approach to describe the radiation environment during the complete remote-handling scenario of In-Vessel components in the ITER facility. The impact of all relevant radiation sources during different stages of the operation is addressed. As-built structures and 2020 baseline designs are considered to produce the most detailed neutronics model of the Tokamak Complex, the 400,000-tonne civil structure hosting the tokamak, up to date. Novel capabilities of the D1SUNED code have allowed to compute the integral dose, the dose rate and the photon-induced neutron flux of both moving and static radiation sources. Time bins are included in the simulations to compute the dose rate caused by In-Vessel components at all positions along the transfer. The time evolution of the dose rate is built in video format with a 1-m resolution, especially valuable for hot-spots identification.

42 ENGINEERING↗
DOE OSTI2021

General relativistic MHD simulations of non-thermal flaring in Sagittarius A*

Sgr A* exhibits regular variability in its multiwavelength emission, including daily X-ray flares and roughly continuous near-infrared (NIR) flickering. The origin of this variability is still ambiguous since both inverse Compton and synchrotron emission are possible radiative mechanisms. The underlying particle distributions are also not well constrained, particularly the non-thermal contribution. In this work, we employ the GPU-accelerated general relativistic magnetohydrodynamics code H-AMR to perform a study of flare flux distributions, including the effect of particle acceleration for the first time in high-resolution 3D simulations of Sgr A*. For the particle acceleration, we use the general relativistic ray-tracing code bhoss to perform the radiative transfer, assuming a hybrid thermal+non-thermal electron energy distribution. We extract ~60 h light curves in the sub-millimetre, NIR and X-ray wavebands, and compare the power spectra and the cumulative flux distributions of the light curves to statistical descriptions for Sgr A* flares. Our results indicate that non-thermal populations of electrons arising from turbulence-driven reconnection in weakly magnetized accretion flows lead to moderate NIR and X-ray flares and reasonably describe the X-ray flux distribution while fulfilling multiwavelength flux constraints. These models exhibit high rms per cent amplitudes, $\gtrsim 150{{\ \rm per\ cent}}$ both in the NIR and the X-rays, with changes in the accretion rate driving the 230 GHz flux variability, in agreement with Sgr A* observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

2D end-to-end modelling of kilonovae from binary neutron star merger remnants

We investigate the kilonova emission resulting from outflows produced in a 3D general-relativistic magnetohydrodynamic (GRMHD) simulation of a hypermassive neutron star (HMNS) remnant. We map the outflows into the flash hydrodynamics code to model their expansion in axisymmetry, and study the effects of employing different r-process heating rates. Except for the highest heating rate prescription, we find no significant differences with respect to overall ejecta dynamics and morphology compared to the simulation without heating. Once homologous expansion is attained, typically after ~2s for these ejecta, we map the outflows to the sedona radiative transfer code and compute the spectral evolution of the kilonova and broad-band light curves in various Legacy Survey of Space and Time (LSST) bands. The kilonova properties depend on the remnant lifetime, with peak luminosities and peak time-scales increasing for longer lived remnants that produce more massive ejecta. For all models, there is a strong dependence of both the bolometric and broad-band light curves on the viewing angle. While the short-lived (12 ms) remnant produces higher luminosities when viewed from angles closer to the pole, longer lived remnants (240 ms and 2.5 s) are more luminous when viewed from angles closer to the equator. Our results highlight the importance of self-consistent, long-term modelling of merger ejecta, and taking viewing-angle dependence into account when interpreting observed kilonova light curves. We find that magnetized outflows from an HMNS – if it survives long enough – could explain blue kilonovae, such as the blue emission seen in AT2017gfo.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Validation Assessment of Turbulent Reacting Flow Model Using The Area-Validation Metric on Medium-Scale Methanol Pool Fire Results

Accident analysis and ensuring power plant safety are pivotal in the nuclear energy sector. Significant strides have been achieved over the past few decades regarding fire protection and safety, primarily centered on design and regulatory compliance. Yet, after the Fukushima accident a decade ago, the imperative to enhance measures against fire, internal flooding, and power loss has intensified. Hence, a comprehensive, multilayered protection strategy against severe accidents is needed. Consequently, gaining a deeper insight into pool fires and their behavior through extensive validated data can greatly aid in improving these measures using advanced validation techniques. A model validation study was performed at Sandia National Laboratories in which a 30-cm diameter methanol pool fire was modeled using the SIERRA/Fuego turbulent reacting flow code. This validation study used a standard validation experiment to compare model results against, and conclusions have been published. The fire was modeled with a Large Eddy Simulation (LES) turbulence model with subgrid turbulent kinetic energy closure. Combustion was modeled using a strained laminar flamelet library approach. Radiative heat transfer was accounted for with a model utilizing the gray-gas approximation. In the present study, additional validation analysis is performed using the area validation metric (AVM). These activities are done on multiple datasets involving different variables and temporal/spatial ranges and intervals. In conclusion, the results provide insight into the use of the area validation metric on such temporally varying datasets and the importance of physics-aware use of the metric for proper analysis.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2024

High Fidelity Simulations of Air-Cooled Reactor Cavity Cooling System

Nuclear energy is increasingly acknowledged as pivotal in the global shift towards cleaner energy solutions. Advanced nuclear technologies, including High Temperature Gas-cooled Reactors (HTGRs), stand out as appealing options among Generation IV reactors due to their high temperature heat output and potential for cogeneration. HTGR designs incorporate passive safety systems, such as the Reactor Cavity Cooling System (RCCS), which utilize natural principles to manage heat dissipation from the reactor pressure vessel (RPV) during accidents or routine shutdowns. Regulatory bodies require thorough validation of safety systems like the RCCS to ensure they meet specified standards. Consequently, there is a pressing need within the industry for advanced simulation tools capable of assessing these systems’ performance accurately. There is a knowladge gap in the literature concerning high-fidelity data for the RCCS, which motivates the focus of this study. This research focuses on a specific RCCS designed for the Modular High-Temperature Gas Reactor developed by General Atomics (GA- MHTGR). Experimental studies on a scaled version of the air-cooled RCCS of GA-MHTGR were conducted by the University of Wisconsin-Madison. This work contributes to a broader initiative aimed at establishing a numerical benchmark based on the UW-Madison experiments. As first step we performed high fidelity simulations of the experimental facility setup, to analyze flow physics in such systems and validate NekRS and the MOOSE heat transfer and radiation modules.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Beyond the visible: Accounting for ultraviolet and far‐red radiation in vegetation productivity and surface energy budgets

Photosynthetically active radiation (PAR) is typically defined as light with a wavelength within 400–700 nm. However, ultra-violet (UV) radiation within 280–400 nm and far-red (FR) radiation within 700–750 nm can also excite photosystems, though not as efficiently as PAR. Vegetation and land surface models (LSMs) typically do not explicitly account for UV's contribution to energy budgets or photosynthesis, nor FR's contribution to photosynthesis. However, whether neglecting UV and FR has significant impacts remains unknown. Here, we explored how canopy radiative transfer (RT) and photosynthesis are impacted when explicitly implementing UV in the canopy RT model and accounting for UV and FR in the photosynthesis models within a next-generation LSM that can simulate hyperspectral canopy RT. We validated our improvements using photosynthesis measurements from plants under different light sources and intensities and surface reflection from an eddy-covariance tower. Our model simulations suggested that at the whole plant level, after accounting for UV and FR explicitly, chlorophyll content, leaf area index (LAI), clumping index, and solar radiation all impact the modeling of gross primary productivity (GPP). At the global scale, mean annual GPP within a grid would increase by up to 7.3% and the increase is proportional to LAI; globally integrated GPP increases by 4.6 PgC year −1 (3.8% of the GPP without accounting for UV + FR). Further, using PAR to proxy UV could overestimate surface albedo by more than 0.1, particularly in the boreal forests. Our results highlight the importance of improving UV and FR in canopy RT and photosynthesis modeling and the necessity to implement hyperspectral or multispectral canopy RT schemes in future vegetation and LSMs.

energy budget↗
DOE OSTI2022

Impacts of Sub‐Grid Topographic Representations on Surface Energy Balance and Boundary Conditions in the E3SM Land Model: A Case Study in Sierra Nevada

Abstract Sub‐grid topographic heterogeneity has large impacts on surface energy balance and land‐atmosphere interactions. However, the impacts of representing sub‐grid topographic effects in land surface models (LSMs) on surface energy balance and boundary conditions remain unclear. This study analyzed and evaluated the impacts of sub‐grid topographic representations on surface energy balance, turbulent heat flux, and scalar (co‐)variances in the Energy Exascale Earth System Model (E3SM) land model (ELM). Three sub‐grid topographic representations in ELM were compared: (a) the default sub‐grid structure (D), (b) the recently developed sub‐grid topographic structure (T), and (c) high spatial resolution (1KM). Additionally, two different solar radiation schemes in ELM were compared: (a) the default plane‐parallel radiative transfer scheme (PP) and (b) the parameterization scheme (TOP) that accounts for sub‐grid topographic effects on solar radiation. A series of offline simulations with the three grid discretization structures (D, T, and 1KM) and two schemes of solar radiation (TOP and PP) were carried out using the Sierra Nevada, California. 1KM simulations with TOP well capture the spatial heterogeneity of surface fluxes compared to Moderate Resolution Imaging Spectroradiometer remote sensing data. There are significant differences between TOP and PP in the 1‐km simulated surface energy balance, but the differences in mean values and standard deviations become small when aggregated to the grid scale (i.e., 0.5°). The T configuration better mimics the 1KM simulations with TOP than the D configuration and better captures the sub‐grid topographic effects on surface energy balance and boundary conditions. These results underline the importance of representing sub‐grid topographic heterogeneities in LSMs and motivate future research to understand the sub‐grid topographic effects on land‐atmosphere interactions over mountainous areas.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Progress on the National Solar Radiation Data Base (NSRDB): A new DNI computation

This study introduces a new technique to compute direct normal irradiance (DNI) for improving the National Solar Radiation Data Base (NSRDB). A finite-surface integration algorithm is developed to compute solar radiation in differential solid angles and efficiently infer its contribution to a surface perpendicular to the solar direction. A lookup table of cloud bi-directional transmittance distribution function (BTDF) is developed by use of the discrete ordinates radiative transfer (DISORT) model for possible solar and observing directions and various cloud optical and microphysical properties. In each solar incident direction, DNI is given by the cloud BTDFs from approximately 200 differential solid angles. The simulated DNI is calibrated and evaluated using surface observations at the National Renewable Energy Laboratory's (NREL's) Solar Energy Research Laboratory (SRRL) and the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) facility.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

SIERRA Low Mach Module: Fuego User Manual - Version 4.56

The SIERRA Low Mach Module: Fuego, henceforth referred to as Fuego, is the key element of the ASC fire environment simulation project. The fire environment simulation project is directed at characterizing both open large-scale pool fires and building enclosure fires. Fuego represents the turbulent, buoyantly-driven incompressible flow, heat transfer, mass transfer, combustion, soot, and absorption coefficient model portion of the simulation software. Using MPMD coupling, Scefire and Nalu handle the participating-media thermal radiation mechanics. This project is an integral part of the SIERRA multi-mechanics software development project. Fuego depends heavily upon the core architecture developments provided by SIERRA for massively parallel computing, solution adaptivity, and mechanics coupling on unstructured grids.

97 MATHEMATICS AND COMPUTING↗