Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “advection”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A Methodology for Estimating the Energy and Moisture Budget of the Convective Boundary Layer Using Continuous Ground-Based Infrared Spectrometer Observations

Abstract Land–atmosphere interactions play a critical role in both the atmospheric water and energy cycles. Changes in soil moisture and vegetation alter the partitioning of surface water and energy fluxes, influencing diurnal evolution of the planetary boundary layer (PBL). The mixing-diagram framework has proven useful in understanding the evolution of the heat and moisture budget within the convective boundary layer (CBL). We demonstrate that observations from the Department of Energy Atmospheric Radiation Measurement (ARM) Southern Great Plains site provide all of the needed inputs needed for the mixing-diagram framework, allowing us to quantify the impact from the surface fluxes, advection, radiative heating, encroachment, and entrainment on the evolution of the CBL. Profiles of temperature and humidity retrieved from the ground-based infrared spectrometer [Atmospheric Emitted Radiance Interferometer (AERI)] are a critical component in this analysis. Large-eddy simulation results demonstrate that mean mixed-layer values derived are shown to be critical to close the energy and moisture budgets. A novel approach demonstrated here is the use of network of AERIs and Doppler lidars to quantify the advective fluxes of heat and moisture. The framework enables the estimation of the entrainment fluxes as a residual, providing a way to observe the entrainment fluxes without using multiple lidar systems. The high temporal resolution of the AERI observations enables the morning, midday, and afternoon evolution of the CBL to be quantified. This work provides a new way to use observations in this framework to evaluate weather and climate models. Significance Statement The energy and moisture budget of the planetary boundary layer (PBL) is influenced by multiple sources, and accurately representing this evolution in numerical models is critical for weather forecasts and climate predictions. The mixing-diagram approach, driven by profiling observations as illustrated here, provides a powerful way to quantify the contributions from each of these sources. In particular, the energy and moisture mixed into the PBL from above the PBL can be determined accurately from ground-based remote sensors using this approach.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Characterizing Near-Surface Moisture Increase during the Clear-Sky Afternoon-to-Evening Transition Using a Single-Column Model

The afternoon-to-evening transition is the period when the atmospheric boundary layer transitions from convective to stable conditions. One noticeable feature during this transition period is the rapid increase in water vapor concentration near the surface. However, the mechanism behind the increase in water vapor remains poorly understood. This study investigated the processes contributing to the water vapor increase and the impacts of the land cover and horizontal advection on the water vapor increase using a single-column model for the clear-sky condition. Numerical experiments were conducted on three cases at the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site. Evapotranspiration was found to be the main moisture source to the water vapor increase, and that change of the near-surface vertical temperature gradient from negative to positive is the trigger for this increase during the afternoon-to-evening transition. This is because the near-surface turbulence divergence term decreases due to the change in the buoyancy profile caused by vertical temperature gradient change. The impact of horizontal advection on water vapor varies, and it can either lead to an increase or a decrease in water vapor, depending on the spatial horizontal water vapor gradient. This study also found that land cover can influence the timing of the water vapor increase since different land covers may have different Bowen ratios. Water vapor increases earlier under conditions with smaller Bowen ratios compared to those with larger values.

Atmosphere-land interaction↗
DOE OSTI2021

Evolution of Idealized Vortices in Monsoon-Like Shears: Application to Monsoon Depressions

Abstract This study examines processes fundamental to the development of South Asian monsoon depressions using an array of integrations of an idealized convection-permitting numerical model. In each integration, a wave of initially small amplitude is subjected to a different amount of vertical and meridional wind shear, with temperature and moisture fields constructed according to realistic constraints. Based on the evolution of this disturbance into monsoon depression–like vortices, two features of the background environment emerge as important: the low-level gradient of moist static energy (MSE) and the low-level meridional shear. As the low-level MSE gradient steepens, the disturbance becomes stronger and produces more rain. This strengthening results from the interaction of the vortex with latent heat release by convection that is in turn organized by positive MSE advection in the northerly flow west of the vortex. In this region of advection, moister air from the north ascends along upward-sloping isentropes, driving moist convection. The disturbance also becomes stronger with increasing meridional shear, which makes the environment more barotropically unstable. The absence of either of these two features of the background environment prevents substantial growth of the disturbance. Our results suggest that monsoon depression growth in South Asia is fostered by the coexistence of a strong low-level MSE gradient with strong meridional wind shear associated with the monsoon trough.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Large-Eddy Simulations of Marine Boundary Layer Clouds Associated with Cold-Air Outbreaks during the ACTIVATE Campaign. Part I: Case Setup and Sensitivities to Large-Scale Forcings

Large-eddy simulation (LES) is able to capture key boundary layer (BL) turbulence and cloud processes. Yet, large-scale forcing and surface turbulent fluxes of sensible and latent heat are often poorly prescribed for LESs. We derive these quantities from measurements and reanalysis obtained for two cold-air outbreak (CAO) events during Phase I of the Aerosol Cloud Meteorology Interactions over the Western Atlantic Experiment (ACTIVATE) in February–March 2020. We study the two contrasting CAO cases by performing LES and test the sensitivity of BL structure and clouds to large-scale forcings and turbulent heat fluxes. Profiles of atmospheric state and large-scale divergence and surface turbulent heat fluxes obtained from ERA5 data agree reasonably well with those derived from ACTIVATE field measurements for both cases at the sampling time and location. Therefore, we adopt the time-evolving heat fluxes, wind, and advective tendencies profiles from ERA5 data to drive the LES. We find that large-scale thermodynamic advective tendencies and wind relaxations are important for the LES to capture the evolving observed BL meteorological states characterized by the hourly ERA5 data and validated by the observations. We show that the divergence (or vertical velocity) is important in regulating the BL growth driven by surface heat fluxes in LESs. The evolution of liquid water path is largely affected by the evolution of surface heat fluxes. The liquid water path simulated in LES agrees reasonably well with the ACTIVATE measurements. This study paves the path to investigate aerosol–cloud–meteorology interactions using LES informed and evaluated by ACTIVATE field measurements.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

How Moist and Dry Intrusions Control the Local Hydrologic Cycle in Present and Future Climates

Models disagree on the magnitude of the intensification of hydrologic cycle extremes under climate change. Changes in these extremes are expected to scale with the Clausius-Clapeyron relation but may locally diverge due to the uncertain response of the atmospheric general circulation. Recent work has identified that the circulation contribution (the “dynamic” component) is the largest contributor to uncertainty in changes in hydrologic cycle extremes. In this work, we develop an exact budget for changes in wet and dry extremes based on changes in the associated moist and dry intrusions behind those extremes. We decompose changes into four contributors: thermodynamic, low-level convergence, anomalous meridional moisture advection, and zonal wave activity convergence. In analyzing these changes, we show that low-level convergence is the main dynamic contributor to the tropical and subtropical annual response, consistent with weakening of the Hadley circulation, and we show that anomalous meridional moisture advection is the primary dynamic contributor annually for the extratropics, consistent with storm track changes. We achieve a clean separation between dynamic and thermodynamic contributions through an empirical scaling between extremes and their associated wave activities, showing again that shifting storm tracks and expanding subtropics are critical to the dynamic response of the transient hydrologic cycle. We infer that changes in the large-scale circulation are predominantly responsible for the annual, dynamic response of hydrologic cycle extremes and therefore an important contributor to uncertainty in future projections.

Hydrological cycle, hydrological extremes, dynamic↗
DOE OSTI2021

ENSO Dynamics in the E3SM-1-0, CESM2, and GFDL-CM4 Climate Models

We report that this study examines historical simulations of ENSO in the E3SM-1-0, CESM2, and GFDL-CM4 climate models, provided by three leading U.S. modeling centers as part of the Coupled Model Intercomparison Project phase 6 (CMIP6). These new models have made substantial progress in simulating ENSO’s key features, including: amplitude; timescale; spatial patterns; phase-locking; spring persistence barrier; and recharge oscillator dynamics. However, some important features of ENSO are still a challenge to simulate. In the central and eastern equatorial Pacific, the models’ weaker-than-observed subsurface zonal current anomalies and zonal temperature gradient anomalies serve to weaken the nonlinear zonal advection of subsurface temperatures, leading to insufficient warm/cold asymmetry of ENSO’s sea surface temperature anomalies (SSTA). In the western equatorial Pacific, the models’ excessive simulated zonal SST gradients amplify their zonal temperature advection, causing their SSTA to extend farther west than observed. The models underestimate both ENSO’s positive dynamic feedbacks (due to insufficient zonal wind stress responses to SSTA) and its thermodynamic damping (due to insufficient convective cloud shading of eastern Pacific SSTA during warm events); compensation between these biases leads to realistic linear growth rates for ENSO, but for somewhat unrealistic reasons. The models also exhibit stronger-than-observed feedbacks onto eastern equatorial Pacific SSTAs from thermocline depth anomalies, which accelerates the transitions between events and shortens the simulated ENSO period relative to observations. Implications for diagnosing and simulating ENSO in climate models are discussed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A Vertically Resolved Analysis of Radiative Feedbacks on Moist Static Energy Variance in Tropical Cyclones

Abstract A vertically resolved moist static energy (MSE) variance budget framework is used to diagnose processes associated with the development of tropical cyclones (TCs) in a general circulation model (GCM) under realistic boundary conditions. Previous studies have shown that interactions between radiation and MSE promote TC development. Here, we examine the vertical contributions of radiation and its interactions with MSE by performing several mechanism-denial experiments in which synoptic-scale radiative interactions are suppressed either in the boundary layer or in the free troposphere. Partly suppressing radiative interactions results in a reduction in global TC frequency. However, the magnitude of reduction and structure of the feedback depend on the intensity and structure of the TCs in these mechanism-denial experiments, indicating that both the magnitude and the vertical location of radiative interactions can impact global TC frequency. Using instantaneous 6-hourly outputs, an explicit computation reveals distinct spatial patterns of the advection term: the vertical component is positive in the mid- to upper troposphere, which reflects an upward transport of MSE by deep convection, whereas the horizontal component is positive in the boundary layer. These results illustrate the impact of the vertical distribution of radiative interactions and vertically varied contribution of the advection term in the development of TCs.

Meteorology & Atmospheric Sciences↗
DOE OSTI2024

The Extraordinary March 2022 East Antarctica “Heat” Wave. Part I: Observations and Meteorological Drivers

Abstract Between 15 and 19 March 2022, East Antarctica experienced an exceptional heat wave with widespread 30°–40°C temperature anomalies across the ice sheet. This record-shattering event saw numerous monthly temperature records being broken including a new all-time temperature record of −9.4°C on 18 March at Concordia Station despite March typically being a transition month to the Antarctic coreless winter. The driver for these temperature extremes was an intense atmospheric river advecting subtropical/midlatitude heat and moisture deep into the Antarctic interior. The scope of the temperature records spurred a large, diverse collaborative effort to study the heat wave’s meteorological drivers, impacts, and historical climate context. Here we focus on describing those temperature records along with the intricate meteorological drivers that led to the most intense atmospheric river observed over East Antarctica. These efforts describe the Rossby wave activity forced from intense tropical convection over the Indian Ocean. This led to an atmospheric river and warm conveyor belt intensification near the coastline, which reinforced atmospheric blocking deep into East Antarctica. The resulting moisture flux and upper-level warm-air advection eroded the typical surface temperature inversions over the ice sheet. At the peak of the heat wave, an area of 3.3 million km 2 in East Antarctica exceeded previous March monthly temperature records. Despite a temperature anomaly return time of about 100 years, a closer recurrence of such an event is possible under future climate projections. In Part II we describe the various impacts this extreme event had on the East Antarctic cryosphere. Significance Statement In March 2022, a heat wave and atmospheric river caused some of the highest temperature anomalies ever observed globally and captured the attention of the Antarctic science community. Using our diverse collective expertise, we explored the causes of the event and have placed it within a historical climate context. One key takeaway is that Antarctic climate extremes are highly sensitive to perturbations in the midlatitudes and subtropics. This heat wave redefined our expectations of the Antarctic climate. Despite the rare chance of occurrence based on past climate, a future temperature extreme event of similar magnitude is possible, especially given anthropogenic climate change.

Wille, Jonathan D.↗
DOE OSTI2024

Moisture Recycling through Pumping by Mesoscale Convective Systems

Abstract Moisture recycling, the contribution of local evapotranspiration (ET) to precipitation, has been studied using bulk models assuming a well-mixed atmosphere. The latter is inconsistent with a climatologically stratified atmosphere that slants across latitudes. Reconciling the two views requires an understanding of overturning associated with different weather systems. In this study, we aim to better understand moisture recycling associated with mesoscale convective systems (MCSs). Using a convection-permitting WRF simulation equipped with water vapor tracers (WRF-WVT), we tag moisture from terrestrial ET in the U.S. Southern Great Plains during May 2015, when more than 20 MCS events occurred and produced significant precipitation and flooding. Water budget analysis reveals that approximately 76% of terrestrial ET is advected away from the region while the remaining 24% of terrestrial ET is “pumped” upward within the region, accounting for 12% of precipitation. Moisture recycling peaks during early night hours (1800–2400 LT) due to the mixing of the daytime accumulated ET by active convection. By focusing on five “diurnally driven” MCSs with less large-scale circulation influence than other MCSs during the same period, we find an upright pumping of terrestrial ET at the MCS initiation and development stages, which diverges into two branches during the MCS mature and decaying stages. One branch in the upper level advects the ET-sourced moisture downstream, while the other branch in the mid-to-upper level contributes to the trailing precipitation upstream. Overall, our analysis depicts a pumping mechanism associated with MCSs that mixes local ET vertically, highlighting its specific contributions to enhancing convective precipitation processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A Perturbative Solution for Nonlinear Stratified Upwelling over a Frictional Slope

Abstract A perturbative solution of simplified primitive equations for nonlinear weakly stratified upwelling over a frictional slope is found that resolves the vertical structure of velocity fields and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The solution uses assumptions consistent with the model proposed by Lentz and Chapman, including a steady-state, constant cross-shore density gradient, no alongshore gradients, laterally inviscid, and consideration of cross-shore advection of alongshore momentum. The solution resolves the vertical structure of velocity fields (including subsurface maxima of compensational flow, not resolved by Lentz and Chapman) and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The dynamics are similar to Lentz and Chapman; bottom stress balances alongshore wind stress in a homogeneous density ocean and is replaced by nonlinear cross-shore transport of alongshore momentum as the Burger number (S=αN/f, whereα,N, andfare the bottom slope, buoyancy frequency, Coriolis frequency, respectively) increases. When the solution uses the empirical relation between cross-shore and vertical density gradients proposed by Lentz and Chapman, vorticity conservation is not satisfied and the nonlinear momentum transport estimated by the solution linearly increases withS, asymptotically matching Lentz and Chapman forS< 1. When the solution conserves interior potential vorticity, the momentum transport is proportional toS 2 forS< 1 and is in better agreement with numerical simulations.

Oceanography↗
DOE OSTI2020

Improving Solution Accuracy and Convergence for Stochastic Physics Parameterizations with Colored Noise

Stochastic parameterizations are used in numerical weather prediction and climate modeling to help capture the uncertainty in the simulations and improve their statistical properties. Convergence issues can arise when time integration methods originally developed for deterministic differential equations are applied naively to stochastic problems. In previous studies, it has been demonstrated that a correction term, known in stochastic analysis as the Itô correction, can help improve solution accuracy for various deterministic numerical schemes and ensure convergence to the physically relevant solution without substantial computational overhead. The usual formulation of the Itô correction is valid only when the stochasticity is represented by white noise. In this study, a generalized formulation of the Itô correction is derived for noises of any color. The formulation is applied to a test problem described by an advection–diffusion equation forced with a spectrum of fast processes. We present numerical results for cases with both constant and spatially varying advection velocities to show that, for the same time step sizes, the introduction of the generalized Itô correction helps to substantially reduce time integration error and significantly improve the convergence rate of the numerical solutions when the forcing term in the governing equation is rough (fast varying); alternatively, for the same target accuracy, the generalized Itô correction allows for the use of significantly longer time steps and, hence, helps to reduce the computational cost of the numerical simulation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Tornadoes in Southeast South America: Mesoscale to Planetary-Scale Environments

Abstract A multiscale analysis of the environment supporting tornadoes in southeast South America (SESA) was conducted based on a self-constructed database of 74 reports. Composites of environmental and convective parameters from ERA5 were generated relative to tornado events. The distribution of the reported tornadoes maximizes over the Argentine plains, while events are rare close to the Andes and south of Sierras de Córdoba. Events are relatively common in all seasons except in winter. Proximity environment evolution shows enhanced instability, deep-layer vertical wind shear, storm-relative helicity, reduced convective inhibition, and a lowered lifting condensation level before or during the development of tornadic storms in SESA. No consistent signal in low-level wind shear is seen during tornado occurrence. However, a curved hodograph with counterclockwise rotation is present. The Significant Tornado Parameter (STP) is also maximized prior to tornadogenesis, most strongly associated with enhanced CAPE. Differences in the convective environment between tornadoes in SESA and the U.S. Great Plains are discussed. On the synoptic scale, tornado events are associated with a strong anomalous trough crossing the southern Andes that triggers lee cyclogenesis, subsequently enhancing the South American low-level jet (SALLJ) that increases moisture advection to support deep convection. This synoptic trough also enhances vertical shear that, along with enhanced instability, sustains organized convection capable of producing tornadic storms. At planetary scales, the tornadic environment is modulated by Rossby wave trains that appear to be forced by convection near northern Australia. Madden–Julian oscillation phase 3 preferentially occurs 1–2 weeks ahead of tornado occurrence. Significance Statement The main goal of this study is to describe what atmospheric conditions (from local to global scales) are present prior to and during tornadic storms impacting southeast South America (SESA). Increasing potential for deep convection, wind shear, and potential for rotating updrafts, as well as reducing convective inhibition and cloud-base height, are predominant a few hours before and during the events in connection to low-level northerly winds enhancing moisture transport to the region. Remote convective activity near northern Australia appears to influence large-scale atmospheric circulation that subsequently triggers convective storms supporting tornadogenesis 1–2 weeks later in SESA. Our findings highlight the importance of accounting for atmospheric processes occurring at different scales to understand and predict tornado occurrences.

Meteorology & Atmospheric Sciences↗
DOE OSTI2023

Intensification of Hurricane Sally (2020) over the Mississippi River Plume

Abstract Tropical Cyclone (TC) Sally formed on 11 September 2020, traveled through the Gulf of Mexico (GMX), and intensified rapidly before making landfall on the Alabama coast as a devastating category-2 TC with extensive coastal and inland flooding. In this study, using a combination of observations and idealized numerical model experiments, we demonstrate that the Mississippi River plume played a key role in the intensification of Sally near the northern Gulf Coast. As the storm intensified and its translation slowed before landfall, sea surface cooling was reduced along its track, coincident with a pronounced increase in SSS. Further analysis reveals that TC Sally encountered a warm Loop Current eddy in the northern GMX close to the Mississippi River plume. Besides deepening the thermocline, the eddy advected low-salinity Mississippi River plume water into the storm’s path. This resulted in the development of strong upper-ocean salinity stratification, with a shallow layer of freshwater lying above a deep, warm “barrier layer.” Consequently, TC-induced mixing and the associated sea surface cooling were reduced, aiding Sally’s intensification. These results suggest that the Mississippi River plume and freshwater advection by the Loop Current eddies can play an important role in TC intensification near the U.S. Gulf Coast.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Severe Convective Storms in Limited Instability Organized by Pattern and Distribution

Abstract Severe convection occurring in high-shear, low-CAPE (HSLC) environments is a common cool-season threat in the southeastern United States. Previous studies of HSLC convection document the increased operational challenges that these environments present compared to their high-CAPE counterparts, corresponding to higher false-alarm ratios and lower probability of detection for severe watches and warnings. These environments can exhibit rapid destabilization in the hours prior to convection, sometimes associated with the release of potential instability. Here, we use self-organizing maps (SOMs) to objectively identify environmental patterns accompanying HSLC cool-season severe events and associate them with variations in severe weather frequency and distribution. Large-scale patterns exhibit modest variation within the HSLC subclass, featuring strong surface cyclones accompanied by vigorous upper-tropospheric troughs and northward-extending regions of instability, consistent with prior studies. In most patterns, severe weather occurs immediately ahead of a cold front. Other convective ingredients, such as lower-tropospheric vertical wind shear, near-surface equivalent potential temperature (θ e ) advection, and the release of potential instability, varied more significantly across patterns. No single variable used to train SOMs consistently demonstrated differences in the distribution of severe weather occurrence across patterns. Comparison of SOMs based on upper and lower quartiles of severe occurrence demonstrated that the release of potential instability was most consistently associated with higher-impact events in comparison to other convective ingredients. Overall, we find that previously developed HSLC composite parameters reasonably identify high-impact HSLC events. Significance Statement Even when atmospheric instability is not optimal for severe convective storms, in some situations they can still occur, presenting increased challenges to forecasters. These marginal environments may occur at night or during the cool season, when people are less attuned to severe weather threats. Here, we use a sorting algorithm to classify different weather patterns accompanying such storms, and we distinguish which specific patterns and weather system features are most strongly associated with severe storms. Our goals are to increase situational awareness for forecasters and to improve understanding of the processes leading to severe convection in marginal environments.

Meteorology & Atmospheric Sciences↗
DOE OSTI2020

Discrete Fracture Network Modeling to Estimate Upscaled Parameters for the Topopah Spring, Lava Flow, and Tiva Canyon Aquifers at Pahute Mesa, Nevada National Security Site

This report describes the results of Discrete Fracture Network (DFN) simulations for the Topopah Spring Aquifer (TSA), Lava Flow Aquifer, and Tiva Canyon Aquifer (TCA), at Pahute Mesa on the Nevada National Security Site (NNSS), formerly the Nevada Test Site. The research focuses on calculating upscaled groundwater flow and contaminant transport parameters using DFNs generated according to fracture characteristics observed in the TSA, LFA and TCA at Pahute Mesa. The highly fractured and heterogeneous nature of these aquifers makes them candidates for stochastic DFN modeling of radionuclide transport on a small scale with subsequent upscaling. One hundred independent DFN realizations are generated for each aquifer, and the upscaled parameters for continuum simulations of subsurface flow and transport in fractured media at Pahute Mesa are calculated. Our goal is to implement a modeling approach that can translate parameters to larger-scale models that account for local-scale flow and transport processes, such as channelization of flow and transport along a few well connected, large fractures. Additionally, to simulate advective and advective-diffusive transport through the fracture networks, the Time Domain Random Walk (TDRW) approach is applied to account for matrix diffusion into a finite half-space. Moreover, a novel approach to calculate dynamic (active) fracture surface area to reflect flow channeling is implemented. This work will improve the representation of radionuclide transport processes in largescale, regulatory-focused models by providing estimates of hard-to-measure flow and contaminant transport parameters at large scales. In this report, we (1) show recent results of flow and transport simulations on multiple DFN realizations of the TSA, LFA, TCA; (2) discuss the resulting distributions of estimated upscaled parameters; (3) describe the estimation of upscaled parameters for an equivalent parallel-plate continuum model and (4) present a comparison between simulated transport from the equivalent continuum model and an actual DFN.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Nonlinear manifold-based reduced order model

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physicsinformed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LSROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers’ equations. A speedup of up to 2.6 for 1D Burgers’ and a speedup of 11.7 for 2D Burgers’ equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Finally, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport

We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus, we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation. Furthermore, we extend our analysis to the anisotropic diffusion-advection equation and prove well-posedness for fractional orders s ∊ [0.5, 1). We also present an application of the advection-diffusion equation to anomalous transport of solutes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Parallel-In-Time Integration for Hyperbolic Problems (Final Report)

The work for the subcontract was situated in the area of parallel-in-time integration for advection-dominated and hyperbolic partial differential equations (PDEs). Parallel-in-time integration is an active area of research due to its ability to enable faster numerical simulations for applications throughout many areas of science. Over the past two decades, much progress has been made in this area; however, this progress has largely been limited to non-hyperbolic, diffusion-dominated PDEs. Given the ubiquity of numerical simulations of advection-dominated hyperbolic PDEs throughout the sciences, there is a strong need to develop efficient parallel-in-time techniques for hyperbolic problems, which was the main topic of this subcontract.

97 MATHEMATICS AND COMPUTING↗