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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A data-driven global soil heterotrophic respiration dataset and the drivers of its inter-annual variability

Soil heterotrophic respiration (SHR), one of the primary carbon fluxes from terrestrial ecosystems to the atmosphere, is important for carbon-climate feedbacks because of its sensitivity to available litter and soil carbon, climatic conditions, and nutrient availability. However, until recently limited SHR data were available, and most published global SHR estimates have either a short time span, coarse spatial resolution, or reply on overly-simple model formulations. To better understand and quantify the global distribution of SHR and its sensitivity to climate variability, we produced a new global SHR dataset using Random Forest algorithms, up-scaling 455 point data from the Global Soil Respiration Database (SRDB 4.0) with gridded fields of climatic, edaphic and productivity as explanatory variables. We estimated a global total SHR of 46.8 Pg C yr-1 over 1985-2013 (95% confidence interval: 38.6-56.3 Pg C yr-1), with a significant increasing trend of 0.03 Pg C yr-2 during this period. We found that the choice of soil moisture datasets contributes more to the difference among these data-driven SHR members rather than that of productivity, temperature and precipitation data sources. We also analyzed the influence of climatic variables on the inter-annual variability (IAV) of our SHR product. Water availability was the dominant driver of IAV at global scales, although the inferred sensitivity depends on the choice of the soil moisture gridded dataset. At the ecosystem scale, temperature strongly controls the IAV of SHR in tropical forests, while water availability dominates in extra-tropical forest and semi-arid regions. Our machine-learning gridded SHR dataset and outputs from process-based land surface models (TRENDYv6) show agreement for a strong association between water variability and SHR IAV at the global scale, but the two approaches lead to different temporal trend globally and different controlling variables for IAV at the ecosystem scale. Our study provides evidence for the pervasive and important role of water availability in driving SHR, indicating both a direct effect limiting decomposition rates and an indirect effect through the amount of fresh organic matter made available to SHR from productivity. In consideration of potential limitations and uncertainties remaining in our data-driven SHR datasets, we call for a more scientifically designed observation network for SHR, more observation data compilation, and increased use of deep learning methods making maximum use of observation data in hand. This will benefit process-based models, and improve our understanding of SHR response to future anomalous environmental conditions.

Yao, Yitong↗
NASA NTRS2021

Improved Representation of the Global Dust Cycle Using Observational Constraints on Dust Properties and Abundance

Even though desert dust is the most abundant aerosol by mass in Earth’s atmosphere, atmospheric models 25 struggle to accurately represent its spatial and temporal distribution. These model errors are partially caused byfundamental difficulties in simulating dust emission in coarse-resolution models and in accurately representing dust microphysical properties. Here we mitigate these problems by developing a new methodology that yields an improved representation of the global dust cycle. We present an analytical framework that uses inverse modeling to integrate an ensemble of global model simulations with observational constraints on the dust size distribution, 30 extinction efficiency, and regional dust aerosol optical depth. We then compare the inverse model results against independent measurements of dust surface concentration and deposition flux and find that errors are reduced by approximately a factor of two relative to current model simulations of the Northern Hemisphere dust cycle. The inverse model results show smaller improvements in the less dusty Southern Hemisphere, most likely because both the model simulations and the observational constraints used in the inverse model are less accurate. On a global 35 basis, we find that the emission flux of dust with geometric diameter up to 20 μm (PM20) is approximately 5,000 Tg/year, which is greater than most models account for. This larger PM20 dust flux is needed to match observational constraints showing a large atmospheric loading of coarse dust. We obtain gridded data sets of dust emission, vertically integrated loading, dust aerosol optical depth, (surface) concentration, and wet and dry deposition fluxes that are resolved by season and particle size. As our results indicate that this data set is more accurate than current 40 model simulations and the MERRA-2 dust reanalysis product, it can be used to improve quantifications of dust impacts on the Earth system.

aerosols, dust↗
NASA NTRS2021

Improved representation of the global dust cycle using observational constraints on dust properties and abundance

Even though desert dust is the most abundant aerosol by mass in Earth's atmosphere, atmospheric models struggle to accurately represent its spatial and temporal distribution. These model errors are partially caused by fundamental difficulties in simulating dust emission in coarse-resolution models and in accurately representing dust microphysical properties. Here we mitigate these problems by developing a new methodology that yields an improved representation of the global dust cycle. We present an analytical framework that uses inverse modeling to integrate an ensemble of global model simulations with observational constraints on the dust size distribution, extinction efficiency, and regional dust aerosol optical depth. We then compare the inverse model results against independent measurements of dust surface concentration and deposition flux and find that errors are reduced by approximately a factor of 2 relative to current model simulations of the Northern Hemisphere dust cycle. The inverse model results show smaller improvements in the less dusty Southern Hemisphere, most likely because both the model simulations and the observational constraints used in the inverse model are less accurate. On a global basis, we find that the emission flux of dust with a geometric diameter up to 20 µm (PM20) is approximately 5000 Tg yr−1, which is greater than most models account for. This larger PM20 dust flux is needed to match observational constraints showing a large atmospheric loading of coarse dust. We obtain gridded datasets of dust emission, vertically integrated loading, dust aerosol optical depth, (surface) concentration, and wet and dry deposition fluxes that are resolved by season and particle size. As our results indicate that this dataset is more accurate than current model simulations and the MERRA-2 dust reanalysis product, it can be used to improve quantifications of dust impacts on the Earth system.

Dust cycle↗
NASA NTRS2005

Short-term, seasonal and interannual variability of the vertical distribution of water vapor observed by AIRS

The Atmospheric Infrared Sounder (AIRS) consists of a suite of instruments on board the Aqua spacecraft which retrieve atmospheric parameters over the globe at radiosonde quality on a daily basis in non-precipitating fields of view with less than 80% cloud cover. Although quantitative global measurements of water vapor have been available since the 1980's, the vertical resolution of these measurements was very coarse. AIRS provides global coverage amounting to 324,000 precipitable water vapor profiles with spatial resolution at nadir of 45 km and a vertical resolution in the troposphere of 2 km.

remote sounding↗
NASA NTRS1998

PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes

Dynamic mesh adaption on unstructured grids is a powerful tool for computing large-scale problems that require grid modifications to efficiently resolve solution features. Unfortunately, an efficient parallel implementation is difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive large-scale numerical computations in a message-passing environment. First, we present an efficient parallel implementation of a tetrahedral mesh adaption scheme. Extremely promising parallel performance is achieved for various refinement and coarsening strategies on a realistic-sized domain. Next we describe PLUM, a novel method for dynamically balancing the processor workloads in adaptive grid computations. This research includes interfacing the parallel mesh adaption procedure based on actual flow solutions to a data remapping module, and incorporating an efficient parallel mesh repartitioner. A significant runtime improvement is achieved by observing that data movement for a refinement step should be performed after the edge-marking phase but before the actual subdivision. We also present optimal and heuristic remapping cost metrics that can accurately predict the total overhead for data redistribution. Several experiments are performed to verify the effectiveness of PLUM on sequences of dynamically adapted unstructured grids. Portability is demonstrated by presenting results on the two vastly different architectures of the SP2 and the Origin2OOO. Additionally, we evaluate the performance of five state-of-the-art partitioning algorithms that can be used within PLUM. It is shown that for certain classes of unsteady adaption, globally repartitioning the computational mesh produces higher quality results than diffusive repartitioning schemes. We also demonstrate that a coarse starting mesh produces high quality load balancing, at a fraction of the cost required a fine initial mesh. Results indicate that our parallel load balancing strategy will remain viable on large numbers of processors.

Oliker, Leonid↗
DOE OSTI2022

Asynchronous Truncated Multigrid-Reduction-in-Time

In this paper, we present the new “asynchronous truncated multigrid-reduction-in-time” (AT-MGRIT) algorithm for introducing time parallelism to the solution of discretized time-dependent problems. The new algorithm is based on the multigrid-reduction-in-time (MGRIT) approach, which, in certain settings, is equivalent to another common multilevel parallel-in-time method, Parareal. In contrast to Parareal and MGRIT that both consider a global temporal grid over the entire time interval on the coarsest level, the AT-MGRIT algorithm uses truncated local time grids on the coarsest level, each grid covering certain temporal subintervals. Further, these local grids can be solved completely in an independent way from each other, which reduces the sequential part of the algorithm and, thus, increases parallelism in the method. Here, we study the effect of using truncated local coarse grids on the convergence of the algorithm, both theoretically and numerically, and show, using challenging nonlinear problems, that the new algorithm consistently outperforms classical Parareal/MGRIT in terms of time to solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Optimality of Gradient-MUSIC for Spectral Estimation

We introduce the Gradient-MUSIC algorithm for estimating the unknown frequencies and amplitudes of a nonharmonic signal from noisy time samples. While the classical MUSIC algorithm performs a computationally expensive search over a fine grid, Gradient-MUSIC is significantly more efficient and eliminates the need for discretization over a fine grid by using optimization techniques. It coarsely scans the 1D landscape to find initialization simultaneously for all frequencies followed by parallelizable local refinement via gradient descent. We also analyze its performance when the noise level is sufficiently small and the signal frequencies are separated by at least 8π/m, where π/m is the standard resolution of this problem. Even though the 1D landscape is nonconvex, we prove a global convergence result for Gradient-MUSIC: coarse scanning provably finds suitable initialization and gradient descent converges at a linear rate. In addition to convergence results, we also upper bound the error between the true signal frequencies and amplitudes with those found by Gradient-MUSIC. For example, if the noise has $\ell^\infty$ norm at most ϵ, then the frequencies and amplitudes are recovered up to error at most Cϵ/m and Cϵ respectively, which are minimax optimal in m and ϵ. Our theory can also handle stochastic noise with performance guarantees under nonstationary independent Gaussian noise. Our main approach is a comprehensive geometric analysis of the landscape, a perspective that has not been explored before.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Impact of the numerical solution approach of a plant hydrodynamic model (v0.1) on vegetation dynamics

Abstract. Numerous plant hydrodynamic models have started to be implemented in vegetation dynamics models, reflecting the central role of plant hydraulic traits in driving water, energy, and carbon cycles, as well as plant adaptation to climate change. Different numerical approximations of the governing equations of the hydrodynamic models have been documented, but the numerical accuracy of these models and its subsequent effects on the simulated vegetation function and dynamics have rarely been evaluated. Using different numerical solution methods (including implicit and explicit approaches) and vertical discrete grid resolutions, we evaluated the numerical performance of a plant hydrodynamic module in the Functionally Assembled Terrestrial Ecosystem Simulator (FATES-HYDRO version 0.1) based on single-point and global simulations. Our simulation results showed that when near-surface vertical grid spacing is coarsened (grid size >10 cm), the model significantly overestimates aboveground biomass (AGB) in most of the temperate forest locations and underestimates AGB in the boreal forest locations, as compared to a simulation with finer vertical grid spacing. Grid coarsening has a small effect on AGB in the tropical zones of Asia and South America. In particular, coarse surface grid resolution should not be used when there are large and prolonged water content differences among soil layers at depths due to long dry-season duration and/or well-drained soil or when soil evaporation is a dominant fraction of evapotranspiration. Similarly, coarse surface grid resolution should not be used when there is lithologic discontinuity along the soil depth. This information is useful for uncertainty quantification, sensitivity analysis, or the training of surrogate models to design the simulations when computational cost limits the use of ensemble simulations.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2012

Spatial Variability in Column CO2 Inferred from High Resolution GEOS-5 Global Model Simulations: Implications for Remote Sensing and Inversions

Column CO2 observations from current and future remote sensing missions represent a major advancement in our understanding of the carbon cycle and are expected to help constrain source and sink distributions. However, data assimilation and inversion methods are challenged by the difference in scale of models and observations. OCO-2 footprints represent an area of several square kilometers while NASA s future ASCENDS lidar mission is likely to have an even smaller footprint. In contrast, the resolution of models used in global inversions are typically hundreds of kilometers wide and often cover areas that include combinations of land, ocean and coastal areas and areas of significant topographic, land cover, and population density variations. To improve understanding of scales of atmospheric CO2 variability and representativeness of satellite observations, we will present results from a global, 10-km simulation of meteorology and atmospheric CO2 distributions performed using NASA s GEOS-5 general circulation model. This resolution, typical of mesoscale atmospheric models, represents an order of magnitude increase in resolution over typical global simulations of atmospheric composition allowing new insight into small scale CO2 variations across a wide range of surface flux and meteorological conditions. The simulation includes high resolution flux datasets provided by NASA s Carbon Monitoring System Flux Pilot Project at half degree resolution that have been down-scaled to 10-km using remote sensing datasets. Probability distribution functions are calculated over larger areas more typical of global models (100-400 km) to characterize subgrid-scale variability in these models. Particular emphasis is placed on coastal regions and regions containing megacities and fires to evaluate the ability of coarse resolution models to represent these small scale features. Additionally, model output are sampled using averaging kernels characteristic of OCO-2 and ASCENDS measurement concepts to create realistic pseudo-datasets. Pseudo-data are averaged over coarse model grid cell areas to better understand the ability of measurements to characterize CO2 distributions and spatial gradients on both short (daily to weekly) and long (monthly to seasonal) time scales

Ott, L.↗
NASA NTRS1976

Spectral and spatial energetics of the GISS model atmosphere

A calculation of the spectral and spatial energetics of the Goddard Institute for Space Studies (GISS) 9-level model of the global atmosphere is given. Results are presented from a model simulation of January 1973 and compared with previous model studies and an observational analysis for the Northern Hemisphere. The spectral analysis permits detailed study of those physical processes of scale larger than the grid spacing and allows indirect conclusions concerning unresolved subgrid-scale processes. Major conclusions for larger-than-grid-scale processes are that (1) the GISS model with a relatively coarse resolution of 4 deg latitude by 5 deg longitude produces significant nonlinear energy transfers; and (2) baroclinic conversion is large near planetary wave-number 6, but both the GISS model and another orographic model show a less peaked structure than nonorographic models and observations. A linear fit to the kinetic energy spectrum yields a power law of -2.6 in the wavenumber region 8 to 15. For subgrid-scale processes, the turbulence theory result of very small energy flux cascade is obtained.

Tenenbaum, J.↗
NASA NTRS1983

Efficient three-dimensional global models for climate studies - Models I and II

Climate modeling based on numerical solution of the fundamental equations for atmospheric structure and motion permits the explicit modeling of physical processes in the climate system and the natural treatment of interactions and feedbacks among parts of the system. The main difficulty concerning this approach is related to the computational requirements. The present investigation is concerned with the development of a grid-point model which is programmed so that both horizontal and vertical resolutions can easily be changed. Attention is given to a description of Model I, the performance of sensitivity experiments by varying parameters, the definition of an improved Model II, and a study of the dependence of climate simulation on resolution with Model II. It is shown that the major features of global climate can be simulated reasonably well with a horizontal resolution as coarse as 1000 km. Such a resolution allows the possibility of long-range climate studies with moderate computer resources.

Russel, G.↗
DOE OSTI2020

A Baseline for Global Weather and Climate Simulations at 1 km Resolution

In an attempt to advance the understanding of the Earth's weather and climate by representing deep convection explicitly, we present a global, four-month simulation (November 2018 to February 2019) with ECMWF's hydrostatic Integrated Forecasting System (IFS) at an average grid spacing of 1.4 km. The impact of explicitly simulating deep convection on the atmospheric circulation and its variability is assessed by comparing the 1.4 km simulation to the equivalent well-tested and calibrated global simulations at 9 km grid spacing with and without parametrized deep convection. The explicit simulation of deep convection at 1.4 km results in a realistic large-scale circulation, better representation of convective storm activity, and stronger convective gravity wave activity when compared to the 9 km simulation with parametrized deep convection. Comparison of the 1.4 km simulation to the 9 km simulation without parametrized deep convection shows that switching off deep convection parametrization at a too coarse resolution (i.e., 9 km) generates too strong convective gravity waves. Based on the limited statistics available, improvements to the Madden-Julian Oscillation or tropical precipitation are not observed at 1.4 km, suggesting that other Earth system model components and/or their interaction are important for an accurate representation of these processes and may well need adjusting at deep convection resolving resolutions. Overall, the good agreement of the 1.4 km simulation with the 9 km simulation with parametrized deep convection is remarkable, despite one of the most fundamental parametrizations being turned off at 1.4 km resolution and despite no adjustments being made to the remaining parametrizations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Evaluating fine-resolution, regional outputs of a variable resolution global climate model

Climate models have been used to study water resources and regional hydrologic responses to climate change, but climate model outputs must be downscaled to provide relevant regional data. However, the accuracy of this regional data is limited by uncertainties across and within downscaling methods, uncertainty across global outputs, and discontinuities at downscaled boundaries. A new alternative to traditional downscaling is a variable resolution model that incorporates fine-resolution regions directly into a coarse-resolution, global climate simulation in order to capture contiguous dynamics across resolution boundaries. In this study, we used the Variable-Resolution Community Earth System Model (VR-CESM) to generate one-eighth degree (14 km) fine-resolution outputs for the western U.S. and eastern China from 1970-2006. We focus our evaluation on precipitaiton, temperature, snow pack, solar radiation, and wind. We compare the model outputs with remote-sensing-based precipitation data, and both reanalysis and gridded weather station data for precipitation and temperature. VR-CESM generally has a cold bias in winter and a warm bias in summer in the western U.S., which compensate each other to reduce the annual bias. In eastern China, however, the sign of temperature biases are more consistent throughout the year with cold biases in the higher mountains and warm biases throughout most of the rest of the region. Precipitation biases are dependent upon reference data, and show slight overestimation in high mountain regions in both the U.S. and China with respect to gridded weather station data. Simulated snow cover in the western U.S. is reasonable compared to remote sensing data, but snow cover and snow water equivalent have larger biases when compared to reanalysis data. In eastern China there are widespread snow cover biases compared to remote sensing data. VR-CESM underestimates downward shortwave radiation to a greater degree in summer than in winter, and underestimates surface layer windspeed over mountains to a greater degree than in other areas. Comparison between VR-CESM and a coarser simulation (1-degree Beijing Climate Center model) shows reduced precipitation biases in the mountainous regions with finer resolution, indicating the value of variable-resolution modeling for reigonal studies.

Di Vittorio, Alan↗
DOE OSTI2021

Stochastic simulations of temporally and spatially variable Fe cycling within a floodplain aquifer

This data package contains model input and output files for local and global sensitivity analysis (SA) of a reactive transport model simulating redox cycling within a floodplain aquifer. The reaction network is implemented in CrunchFlow and focuses on spatially and temporally heterogeneous Fe cycling, though it contains several other species and redox pathways (37 aqueous species and 7 minerals in total). The package contains data from 600 Monte Carlo simulations (for global SA) and 104 one-at-a-time simulations (for local SA). It includes all input files required to run the CrunchFlow model, as well as limited model output – .csv files containing time series of primary species concentrations at 21 grid cells within the domain. These time series files contain the following species: H+, CO32-, SO42-, Cl-, Ca2+, Mg2+, Na+, K+, Fe(II), Fe(III), HS-, CH3COO-, O2(aq), S(aq), and Br-.These data were used to demonstrate the application of a novel form of global SA, distance-based generalized sensitivity analysis (DGSA) to a reactive transport model. The 2D model simulates the export of reduced species from pockets of fine-grained, organic-rich sediments embedded in a coarse sand aquifer. Stochastic simulations jointly varied 17 key model input parameters across several orders of magnitude, including the spatial variability of each parameter. DGSA on the model results reveal that the amplitude and variability of exported Fe(II) are most sensitive to the interaction between sand permeability and individual reaction rates. By contrast, the propagation of reducing conditions downgradient from the fine-grained lenses depends most heavily on the rate of dissolved organic carbon and sulfate release from the fines.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Adaptive Grid Redistribution for a 1D Model of Turbulence and Clouds

In global atmospheric models, resolving stratocumulus (Sc) in the vertical is computationally expensive. However, Sc appear only under special meteorological conditions. Therefore, there is motivation to refine the vertical grid levels adaptively. In order to facilitate the possibility of parallelization on graphical processing units, our grid adaptation method prescribes the number of vertical levels a priori. Then grid levels are relocated toward altitude ranges in need of refinement. Because the method relocates existing grid levels, rather than adding extra levels, there is a risk of creating regions with overly coarse grid spacing, that is, voids in the grid mesh. To prevent such voids from forming, a simple method is developed to impose a maximum grid spacing. To decide where to place enhanced resolution, the authors develop an empirical mesh refinement criterion. It refines grid spacing near the ground, near strong temperature gradients, and within clouds. Our grid adaptation method is implemented in a single-column model and evaluated on four test cases: decaying stratocumulus, developing shallow cumulus, a quasi-stationary stratocumulus deck, and the diurnal cycle of a dry boundary layer. In the stratocumulus cases, mesh refinement leads to improvements in both the time evolution of fields and their time averages. The other two cases show smaller differences.

Carstensen, Steffen [Univ. of Wisconsin, Milwaukee↗
NASA NTRS2007

Global Aerosol Optical Models and Lookup Tables for the New MODIS Aerosol Retrieval over Land

Since 2000, MODIS has been deriving aerosol properties over land from MODIS observed spectral reflectance, by matching the observed reflectance with that simulated for selected aerosol optical models, aerosol loadings, wavelengths and geometrical conditions (that are contained in a lookup table or 'LUT'). Validation exercises have showed that MODIS tends to under-predict aerosol optical depth (tau) in cases of large tau (tau greater than 1.0), signaling errors in the assumed aerosol optical properties. Using the climatology of almucantur retrievals from the hundreds of global AERONET sunphotometer sites, we found that three spherical-derived models (describing fine-sized dominated aerosol), and one spheroid-derived model (describing coarse-sized dominated aerosol, presumably dust) generally described the range of observed global aerosol properties. The fine dominated models were separated mainly by their single scattering albedo (omega(sub 0)), ranging from non-absorbing aerosol (omega(sub 0) approx. 0.95) in developed urban/industrial regions, to neutrally absorbing aerosol (omega(sub 0) approx.90) in forest fire burning and developing industrial regions, to absorbing aerosol (omega(sub 0) approx. 0.85) in regions of savanna/grassland burning. We determined the dominant model type in each region and season, to create a 1 deg. x 1 deg. grid of assumed aerosol type. We used vector radiative transfer code to create a new LUT, simulating the four aerosol models, in four MODIS channels. Independent AERONET observations of spectral tau agree with the new models, indicating that the new models are suitable for use by the MODIS aerosol retrieval.

Levy, Robert C.↗
DOE OSTI2023

A Consistent Representation of Cloud Overlap and Cloud Subgrid Vertical Heterogeneity

Many global climate models underestimate the cloud cover and overestimate the cloud albedo, especially for low-level clouds. We determine how a correct representation of the vertical structure of clouds can fix part of this bias. We use the 1D McICA framework and focus on low-level clouds. Using Large Eddy Simulations results as reference, we propose a method based on exponential-random overlap that represents the cloud overlap between layers and the subgrid cloud properties over several vertical scales, with a single value of the overlap parameter. Starting from a coarse vertical grid, representative of atmospheric models, this algorithm is used to generate the vertical profile of the cloud fraction with a finer vertical resolution, or to generate it on the coarse grid but with subgrid heterogeneity and cloud overlap that ensures a correct cloud cover. Doing so we find decorrelation lengths are dependent on the vertical resolution, except if the vertical subgrid heterogeneity and interlayer overlap are taken into account coherently. We confirm that the frequently used maximum-random overlap leads to a significant error by underestimating the low-level cloud cover with a relative error of about 50%, that can lead to an error of SW cloud albedo as big as 70%. Not taking into account the subgrid vertical heterogeneity of clouds can cause a relative error of 20% in brightness, assuming the cloud cover is correct.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1991

Three dimensional unstructured multigrid for the Euler equations

The three-dimensional Euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy. The driving algorithm consists of an explicit vertex-based finite-element scheme, which employs an edge-based data-structure to assemble the residuals. The multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady-state of the fine grid solution. Variables, residuals and corrections are passed back and forth between the various grids of the sequence using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm. The preprocessing operation is shown to require a negligible fraction of the CPU time required by the overall solution procedure, while gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350,000 vertices. Solutions using globally regenerated fine meshes as well as adaptively refined meshes are given.

Mavriplis, D. J.↗