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

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Drop size distribution broadening mechanisms in a bin microphysics Eulerian model

In this study, processes that broaden drop size distributions (DSDs) in Eulerian models with two-moment bin microphysics are analyzed. Numerous tests are performed to isolate the effects of different physical mechanisms that broaden DSDs in two- and three-dimensional Weather Research and Forecasting model simulations of an idealized ice-free cumulus cloud. Additionally, sensitivity of these effects to modifying horizontal and vertical model grid spacings is also examined. As expected, collision-coalescence is a key process broadening the modeled DSDs. In-cloud droplet activation also contributes substantially to DSD broadening, whereas evaporation has only a minor effect and sedimentation has little effect. Cloud dilution (mixing of cloud-free and cloudy air) also broadens the DSDs considerably, whether or not it is accompanied by evaporation. This mechanism involves the reduction of droplet concentration from dilution along the cloud’s lateral edges, leading to locally high supersaturation and enhanced drop growth when this air is subsequently lifted in the updraft. DSD broadening ensues when the DSDs are mixed with those from the cloud core. Decreasing the horizontal and vertical model grid spacings from 100 m to 30 m has limited impact on the DSDs. However, when these physical broadening mechanisms (in-cloud activation, collision-coalescence, dilution, etc.) are turned off, there is a reduction of DSD width by up to ~20-50% when the vertical grid spacing is decreased from 100 m to 30 m, consistent with effects of artificial broadening from vertical numerical diffusion. Nonetheless, this artificial numerical broadening appears to be relatively unimportant overall for DSD broadening when physically based broadening mechanisms in the model are included for this cumulus case.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Effects of Horizontal Resolution, Domain Size, Boundary Conditions, and Surface Heterogeneity on Coarse LES of a Convective Boundary Layer

Atmospheric properties in a convective boundary layer vary over a wide range of spatial scales and are commonly studied using large-eddy simulations (LES) in various configurations. We examine how the boundary layer depth and distribution of variability across scales are affected by LES grid spacing, domain size, inhomogeneity of surface properties, and external forcing. Two different setups of the Weather Research and Forecasting (WRF) model are analyzed. A semi-idealized configuration uses a periodic domain, flat surface, prescribed homogeneous surface heat fluxes, and horizontally uniform profiles of large-scale advective tendencies. A nested LES setup employs a larger domain and realistic initial and boundary conditions, including an interactive land surface model with representative topography and vegetation and soil types. Subdomains of identical size are analyzed for all simulations. Characteristic structure sizes are quantified using the variability scales L 50 and L 95 , defined such that features smaller than that contain 50% and 95% of the total variance, respectively. Progressive increase in L 50 from vertical velocity to temperature and moisture structures is systematically reproduced in all simulation configurations. This dependence of L 50 on the considered variable complicates the development of scale-aware parameterizations for models with grid spacing in the “terra incognita”. In simulations using a larger domain with heterogeneous surface properties, the development of internal mesoscale patterns significantly affects variance distributions inside analyzed subdomains. Sizes of boundary layer structures also strongly depend on the LES grid spacing and, in case of heterogeneous surface and topography, on location of the subdomain inside a larger computational domain.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Characteristics of Precipitation and Mesoscale Convective Systems Over the Peruvian Central Andes in Multi 5‐Year Convection‐Permitting Simulations

Abstract Using the Weather Research and Forecasting model with two planetary boundary layer schemes, ACM2 and MYNN, convection‐permitting model (CPM) regional climate simulations were conducted for a 6‐year period, including a one‐year spin‐up period, at a 15‐km grid spacing covering entire South America and a nested convection‐permitting 3‐km grid spacing covering the Peruvian central Andes region. These two CPM simulations along with a 4‐km simulation covering South America produced by National Center for Atmospheric Research (NCAR), three gridded precipitation products, and rain gauge data in Peru and Brazil, are used to document the characteristics of precipitation and mesoscale convective systems (MCSs) in the Peruvian central Andes region. Results show that all km‐scale simulations generally capture the spatiotemporal patterns of precipitation and MCSs at both seasonal and diurnal scales, although biases exist in aspects such as precipitation intensity and MCS frequency, size, propagation speed, and associated precipitation intensity. The 3‐km simulation using MYNN scheme generally outperforms the other simulations in capturing seasonal and diurnal precipitation over the mountain, while both it and the 4‐km simulation demonstrate superior performance in the western Amazon Basin, based on the comparison to the gridded precipitation products and gauge data. Dynamic factors, primarily low‐level jet and terrain‐induced uplift, are the key drivers for precipitation and MCS genesis along the east slope of the Andes, while thermodynamic factors control the precipitation and MCS activity in the western Amazon Basin and over elevated mountainous regions. The study suggests model improvements and better model configurations for future regional climate projections.

Meteorology & Atmospheric Sciences↗
DOE OSTI2024

Editorial: Resolving atmospheric flow in complex environments: recent experiments in terrain and forest canopies

The characterization of atmospheric flows in complex environments, which may include steep terrain slopes and heterogeneous vegetation and/or forest cover, is a long-standing challenge in boundary-layer meteorology. Atmospheric observations are complicated by the presence of transient, terrain-induced flow features, forest-canopy-atmosphere interactions, and atmospheric stability effects, not to mention the logistical hurdles involved with instrument deployment, data analysis, and quality control. Furthermore, challenges in atmospheric modeling arise due to numerical errors associated with complex terrain flows, as well as reliance on simplified parameterizations for unresolved processes such as turbulent mixing and land-surface or forest-canopy-atmosphere interactions. These modeling challenges are exacerbated in the so-called “gray zone,” wherein features of interest have length scales that are similar to the model grid spacing, or when the principal flow layer is smaller than the grid spacing (e.g., slope flows).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Multiscale Simulation of Precipitation Over East Asia by Variable Resolution CAM-MPAS

This study evaluates the precipitation over East Asia simulated by the variable resolution CAM-MPAS featuring the Model for Prediction Across Scales (MPAS) atmospheric dynamical core coupled with the physics parameterizations of the Community Atmosphere Model (CAM) version 5.4. Two CAM-MPAS experiments, one with a global quasi-uniform resolution mesh of 120 km (MPAS-UR) and the other with a variable resolution mesh of 30 to 120 km refined over East Asia (MPAS-VR), are conducted from 1989 to 2005 following the Atmospheric Model Intercomparison Project protocol. Two regional climate model simulations at ~25 km resolution from the Coordinated Regional Downscaling Experiment East Asia second plan are also analyzed for comparison. Results show that CAM-MPAS performs better than the selected regional models in simulating the precipitation climatology over East Asia. Compared with MPAS-UR, MPAS-VR with refinement over East Asia better simulates the precipitation over and around the Tibetan Plateau (TP), the frequency distribution of light, moderate, and heavy precipitation in various regions of China, and the interannual precipitation pattern associated with the East Asian summer monsoon. The improvements in MPAS-VR relative to MPAS-UR largely come from the decreased grid spacing rather than the use of finer-scale terrain information. Particularly, decreased grid spacing is more essential for simulating the precipitation magnitude over TP and the location of peak precipitation south of TP, likely due to the better resolved physical and dynamical processes associated with orographic precipitation. The 30-120 km CAM-MPAS model is shown to be a promising tool for precipitation simulation over East Asia.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

On the Dependence of Simulated Convection on Domain Size in CRMs

Abstract We present a heuristic model to explain the suppression of deep convection in convection‐resolving models (CRMs) with a small number of grid columns, such as those used in super‐parameterized or multi‐scale modeling framework (MMF) general circulation models (GCM) of the atmosphere. Domains with few grid columns require greater instability to sustain convection because they force a large convective fraction, driving strong compensating subsidence warming. Updraft dilution, which is stronger for reduced horizontal grid spacing, enhances this effect. Thus, suppression of deep convection in CRMs with few grid columns can be reduced by increasing grid spacing. Radiative‐convective equilibrium simulations using standalone CRM simulations with the System for Atmospheric Modeling (SAM) and using GCM‐coupled CRM simulations with the Energy Exascale Earth System Model (E3SM)‐MMF confirm the heuristic model results.

CRM↗
DOE OSTI2022

Effect of the Grell-Freitas Deep Convection Scheme in Quasi-Uniform and Variable-Resolution Aquaplanet CAM Simulations

The Grell-Freitas deep convection scheme (GF) has been implemented in the Community Atmosphere Model (CAM) with the nonhydrostatic Model for Prediction Across Scales (MPAS) dynamical core. Aquaplanet simulations have been performed with a global quasi-uniform resolution mesh with ~120 km grid spacing and a variable resolution mesh employing a circular refined region with ~30 km grid spacing centering at the equator and ~120 km elsewhere. GF produces overall patterns of the general circulations comparable to those of other aquaplanet experiments, including those produced using the default Zhang-McFarlane convection scheme (ZM) in CAM Version 5.4. GF alleviates the overestimated occurrence of weak intensity precipitation characteristic of ZM due to GF’s different closure methods and deep-convection trigger conditions. Compared to ZM, the GF characteristics of the equatorial Kelvin waves are closer to observations. GF also better simulates precipitation at variable resolution, with no unrealistic wave distortion by the refinement. Overall, GF shows less sensitivity of convective precipitation and heating/moistening tendencies to changes in horizontal resolution compared to ZM. However, vertically-overlapped total cloud fraction simulated with GF in the tropics is more sensitive to the resolution than ZM due to the larger resolution-sensitivity of high-level cloud fraction in the tropics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Representations of Precipitation Diurnal Cycle in the Amazon as Simulated by Observationally Constrained Cloud‐System Resolving and Global Climate Models

Abstract The ability of an observationally‐constrained cloud‐system resolving model (Weather Research and Forecasting; WRF, 4‐km grid spacing) and a global climate model (Energy Exascale Earth System Model; E3SM, 1‐degree grid spacing) to represent the precipitation diurnal cycle over the Amazon basin during the 2014 wet season is assessed. The WRF model coupled with a 3‐D variational data assimilation scheme reproduces the spatial variability of the precipitation diurnal cycle over the basin and the lifecycle of westward propagating MCSs initiated by the coastal sea‐breeze front. In contrast, a single morning peak in rainfall is produced by E3SM for simulations despite the nudging of large‐scale winds toward global reanalysis, indicating precipitation in E3SM is largely controlled by local convection associated with diurnal heating. The role of propagating MCS on the environment are discussed by using a multivariate perturbation analysis. We also find that the advection of moisture perturbations from ocean to inland regions have a higher correlation with the occurrence of MCSs in the Amazon than the intensity of colder air intrusion associated with sea breezes along the coast. Moreover, the presence of large cold pools over the central Amazon basin are responsible for the maintenance of propagating deep convection.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Realistic large eddy and dispersion simulation experiments during project sagebrush phase 1

Typical dispersion simulations use mesoscale models at grid spacing greater than 1 km to simulate pollutant transport. Advances in computing power have allowed Large Eddy Simulations (LES), (grid spacing less than 100 m) to be run with boundary conditions in the grayscale regime (grid size of 1 km–100 m). We used the WRF mesoscale/LES model and the HYSPLIT particle dispersion model to simulate SF 6 transport from Project Sagebrush Phase 1, using a grayscale-aware scheme with 4 nests of 3 km, 1 km, 200 m, 67 m. The WRF/LES simulation was in satisfactory agreement with meteorological observations but the HYSPLIT SF6 simulations indicated insufficient sub-grid turbulence kinetic energy, especially in the lowest 100 m. This resulted in over predictions of the surface SF6 concentration and insufficient vertical transport. Best agreement with the Sagebrush observations was obtained with the WRF/LES large-scale and sub-grid turbulence, enhanced with a HYSPLIT parameterized turbulence profile.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Reducing Long‐Standing Surface Ozone Overestimation in Earth System Modeling by High‐Resolution Simulation and Dry Deposition Improvement

The overestimation of surface ozone concentration in low‐resolution global atmospheric chemistry and climate models has been a long‐standing issue. We first update the ozone dry deposition scheme in both high‐ (0.25°) and low‐resolution (1°) Community Earth System Model (CESM) version 1.3 runs, by adding the effects of leaf area index and correcting the sunlit and shaded fractions of stomatal resistances. With this update, 5‐year‐long summer simulations (2015–2019) using the low‐resolution CESM still exhibit substantial ozone overestimation (by 6.0–16.2 ppbv) over the U.S., Europe, eastern China, and ozone pollution hotspots. The ozone dry deposition scheme is further improved by adjusting the leaf cuticle conductance, reducing the mean ozone bias by 19%, and increasing the model resolution further reduces the ozone overestimation by 43%. We elucidate the mechanism by which model grid spacing influences simulated ozone, revealing distinctive pathways in urban versus rural areas. In rural areas, grid spacing mainly affects daytime ozone levels, where additional NO x emissions from nearby urban areas result in an ozone boost and overestimation in low‐resolution simulations. In contrast, over urban areas, daytime ozone overestimation follows a similar mechanism due to the influence of volatile organic compounds from surrounding rural areas. However, nighttime ozone overestimation is closely linked to weakened NO titration owing to the redistribution of urban NO x to rural areas. Additionally, stratosphere‐troposphere exchange may also contribute to reducing ozone bias in high‐resolution simulations, warranting further investigation. This optimized high‐resolution CESM may enhance understanding of ozone formation mechanisms, sources, and changes in a warming climate.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Comparison of Lagrangian Superdroplet and Eulerian Double-Moment Spectral Microphysics Schemes in Large-Eddy Simulations of an Isolated Cumulus Congestus Cloud

Abstract Advanced microphysics schemes (such as Eulerian bin and Lagrangian superdroplet) are becoming standard tools for cloud physics research and parameterization development. This study compares a double-moment bin scheme and a Lagrangian superdroplet scheme via large-eddy simulations of nonprecipitating and precipitating cumulus congestus clouds. Cloud water mixing ratio in the bin simulations is reduced compared to the Lagrangian simulations in the upper part of the cloud, likely from numerical diffusion, which is absent in the Lagrangian approach. Greater diffusion in the bin simulations is compensated by more secondary droplet activation (activation above cloud base), leading to similar or somewhat higher droplet number concentrations and smaller mean droplet radius than the Lagrangian simulations for the nonprecipitating case. The bin scheme also produces a significantly larger standard deviation of droplet radius than the superdroplet method, likely due to diffusion associated with the vertical advection of bin variables. However, the spectral width in the bin simulations is insensitive to the grid spacing between 50 and 100 m, suggesting other mechanisms may be compensating for diffusion as the grid spacing is modified. For the precipitating case, larger spectral width in the bin simulations initiates rain earlier and enhances rain development in a positive feedback loop. However, with time, rain formation in the superdroplet simulations catches up to the bin simulations. Offline calculations using the same drop size distributions in both schemes show that the different numerical methods for treating collision–coalescence also contribute to differences in rain formation. The stochastic collision–coalescence in the superdroplet method introduces more variability in drop growth for a given rain mixing ratio.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Supersaturation Variability from Scalar Mixing: Evaluation of a New Subgrid-Scale Model Using Direct Numerical Simulations of Turbulent Rayleigh–Bénard Convection

We report that supersaturation fluctuations in the atmosphere are critical for cloud processes. A nonlinear dependence on two scalars - water vapor and temperature - leads to different behavior than single scalars in turbulent convection. For modeling such multiscalar processes at subgrid scales (SGS) in large-eddy simulations (LES) or convection-permitting models, a new SGS scheme is implemented in CM1 that solves equations for SGS water vapor and temperature fluctuations and their covariance. The SGS model is evaluated using benchmark direct-numerical simulations (DNS) of turbulent Rayleigh–Bénard convection with water vapor as in the Michigan Tech Pi Cloud Chamber. This idealized setup allows thorough evaluation of the SGS model without complications from other atmospheric processes. DNS results compare favorably with measurements from the chamber. Results from LES using the new SGS model compare well with DNS, including profiles of water vapor and temperature variances, their covariance, and supersaturation variance. SGS supersaturation fluctuations scale appropriately with changes to the LES grid spacing, with the magnitude of SGS fluctuations decreasing relative to those at the resolved scale as the grid spacing is decreased. Sensitivities of covariance and supersaturation statistics to changes in water vapor flux relative to thermal flux are also investigated by modifying the sidewall conditions. Relative changes in water vapor flux substantially decrease the covariance and increase supersaturation fluctuations even away from boundaries.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Impact of Advection Schemes on Tracer Interrelationships in Large-Eddy Simulations of Deep Convection

This study investigates the preservation of tracer interrelationships during advection in large-eddy simulations of an idealized deep convective cloud, which is particularly relevant to chemistry, aerosol, and cloud microphysics models. Employing the Cloud Model 1, advection is represented using third-, fifth-, and seventh-order weighted essentially non-oscillatory schemes. As a simplified analogy for cloud hydrometeors and aerosols, several inert passive tracers following linear and nonlinear relationships are initialized after the cloud reaches ~6-km depth. Numerical mixing in the simulated turbulent convective clouds leads to significant deviations from the initial nonlinear relationships between tracers. In these simulations, a considerable fraction of the grid points where the tracers’ nonlinear relationships are altered from advection are classified as unrealistic (e.g., ~13% for the environmental tracers on average), including errors from range-preserving unmixing and overshooting. Errors in the sum of three tracers are also relatively large, ranging between ~1% and 16% for 5% of the grid points in and near the cloud. The magnitude of unrealistic mixing and errors in the sum of three tracers generally increase with the order of accuracy of the advection scheme. These results are consistent across model grid spacings ranging from 50 to 200 m, and across three different flow realizations for each combination of grid spacing and advection scheme tested. Tests employing a previously proposed scalar normalization procedure show substantially reduced errors in the sum of three tracers with a relatively small negative impact on other tracer relationships. This analysis, therefore, suggests efficacy of the normalization procedure when applied to turbulent three-dimensional cloud simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Framework for idealized climate simulations with spatiotemporal stochastic clouds and planetary-scale circulations

In climate predictions, clouds are the leading source of uncertainty. This is partly because, to simulate the fluid dynamics of climate over the entire globe, a large grid spacing must be used, so clouds are a subgrid-scale parametrization rather than a resolved feature. Here, a framework is investigated with finer grid spacing of O(1) or O(10)km so that some clouds are not subgrid-scale; instead, clouds evolve on the numerical grid. This cloud evolution is achieved using stochastic modeling. Hence, the framework is idealized in the sense that the full fluid dynamics of cloud circulations is still not resolved, and simplified vertical structures are used. Nevertheless, the fluid dynamics model includes evolving clouds that interactively adjust in size, shape, lifetime, and regional coverage. In addition, different cloud types are included with different roles in the climate system, including deep convective clouds and also boundary-layer clouds such as shallow cumulus and stratocumulus clouds. Other basic aspects of the idealized climate system are planetary-scale circulations (e.g., Walker circulation) and radiation. With these ingredients (evolving clouds, planetary-scale circulations, and radiation), the framework has the potential for idealized investigations of climate change with interactive cloud–radiative feedback of individual clouds. Here, the formulation of the model equations is presented, and numerical simulations are shown to illustrate the model dynamics and climate change.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Design of proton deflectometry with in situ x-ray fiducial for magnetized high-energy-density systems

We report a design and implementation of proton deflectometry with an in situ reference x-ray image of a mesh to precisely measure non-uniform magnetic fields in expanding plasmas at the OMEGA and OMEGA EP laser facilities. The technique has been developed with proton and x-ray sources generated from both directly driven capsule implosions and short pulse laser–solid interactions. The accuracy of the measurement depends on the contrast of both the proton and x-ray images. Here we present numerical and analytic studies to optimize the image contrast using a variety of mesh materials and grid spacings. Our results show clear enhancement of the image contrast by factors of four to six using a high Z mesh with large grid spacing. This leads to further improvement in the accuracy of the magnetic field measurement using this technique in comparison with its first demonstration at the OMEGA laser facility [Rev. Sci. Instrum. 93, 023502 (2022) [CrossRef]].

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

A new method to construct a horizontal resolution-dependent wind speed adjustment factor for tropical cyclones in global climate model simulations

A new method to construct a horizontal resolution-dependent wind speed adjustment factor for evaluating tropical cyclones (TCs) in global climate models (GCMs) is presented here. In contrast to the previous studies that used idealized axisymmetric wind fields, this study analyzes 48 hours of 10-second surface wind fields from 1-km TC simulations. The adjustment factor is derived from filtering the simulated TC wind fields onto various horizontal grid spacings typical of those used in GCMs. The new adjustment factor leads to TCs with greater intensity than the existing adjustment factors for horizontal grid spacings smaller than 30 km. This difference is attributed to more realistic wind fields in the TC simulations that contain highly asymmetric, localized patches of higher wind speeds instead of axisymmetric wind fields. Applying the new adjustment factor to select GCM simulations suggests the common interpretation of low-intensity bias in GCM-simulated TCs might be slightly exaggerated.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Impact of Tropical Cyclone Wind Forcing on the Global Climate in a Fully Coupled Climate Model

Tropical cyclones (TCs) alter upper-ocean temperature and influence ocean heat content via enhanced turbulent mixing. A better understanding of the role of TCs within the climate system requires a fully coupled modeling framework, where TC-induced ocean responses feed back to the atmosphere and subsequently to the climate mean state and variability. Here, we investigate the impacts of TC wind forcing on the global ocean and the associated feedbacks within the climate system using the fully coupled Community Earth System Model version 1.3 (CESM1.3). Using the low-resolution version of CESM1.3 (1° atmosphere and ocean grid spacing) with no intrinsic TCs, we conduct a suite of sensitivity experiments by inserting TC winds extracted from a high-resolution (0.25° atmosphere grid spacing) TC-permitting simulation into the low-resolution model. Results from the low-resolution TC experiment are compared to a low-resolution control simulation to diagnose TCs’ impact. We found that the added TC winds can increase ocean heat content by affecting ocean vertical mixing, air–sea enthalpy fluxes, and cloud amount. Here, the added TCs can influence mean SST, precipitation, ocean subsurface temperature, and ocean mixed layer depth. We found a strengthening of the wind-driven subtropical cells and a weakening of the Atlantic meridional overturning circulation due to the changes of surface buoyancy fluxes. TCs in the model cause anomalous equatorward ocean heat convergence in the deep tropics and an increase of poleward ocean heat transport out of the subtropics. Our modeling results provide new insights into the multiscale interactions between TCs and the coupled climate system.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe–Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn–Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗