Combined Eulerian and Lagrangian approaches in peridynamic material modeling.
Abstract not provided.
Silling, Stewart A.↗
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Results for “Lagrangian modeling”
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Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model
In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.
97 MATHEMATICS AND COMPUTING↗
Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models
We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.
Melott, A. L.↗
Forecasting for ESCAPE: A Multi-Institution Hybrid Forecasting and Nowcasting Operation for Sea-Breeze Convection Supporting a Ground-Based and Airborne Field Campaign
The Experiment of Sea-Breeze Convection, Aerosols, Precipitation and Environment (ESCAPE) field project deployed two aircraft and ground-based assets in the vicinity of Houston, Texas, between 27 May and 2 July 2022, examining how meteorological conditions, dynamics, and aerosols control the initiation, early growth stage, and evolution of coastal convective clouds. To ensure that airborne- and ground-based assets were deployed appropriately, a forecasting and nowcasting team was formed. Daily forecasts guided real-time decision-making by assessing synoptic weather conditions, environmental aerosol, and a variety of atmospheric modeling data to assign a probability for meeting specific ESCAPE campaign objectives. During the research flights, a small team of forecasters provided “nowcasting” support by analyzing radar, satellite, and new model data in real time. The nowcasting team proved invaluable to the campaign operation, as sometimes changing environmental conditions affected, for example, the timing of convective initiation. In addition to the success of the forecasting and nowcasting teams, the ESCAPE campaign offered a unique “testbed” opportunity where in-person and virtual support both contributed to campaign objectives. The forecasting and nowcasting teams were each composed of new and experienced forecasters alike, where new forecasters were given invaluable experience that would otherwise be difficult to attain. Both teams received training on forecast models, map analysis, Hybrid Single-Particle Lagrangian Integrated Trajectory model (HYSPLIT), and thermodynamic sounding analysis before the beginning of the campaign. In this article, the ESCAPE forecasting and nowcasting teams reflect on these experiences, providing potentially useful advice for future field campaigns requiring forecasting and nowcasting support in a hybrid virtual/in-person framework.
54 ENVIRONMENTAL SCIENCES↗
Dynamic Subgrid Turbulence Modeling for Shallow Cumulus Convection Simulations beyond LES Resolutions
A scale-dependent dynamic Smagorinsky model is implemented in the Met Office/NERC Cloud (MONC) model using two averaging flavors, along Lagrangian pathlines and local moving averages. The dynamic approaches were compared against the conventional Smagorinsky–Lilly scheme in simulating the diurnal cycle of shallow cumulus convection. The simulations spanned from the LES to the near-gray-zone and gray-zone resolutions and revealed the adaptability of the dynamic model across the scales and different stability regimes. The dynamic model can produce a scale- and stability-dependent profile of the subfilter turbulence length scale across the chosen resolution range. At gray-zone resolutions the adaptive length scales can better represent the early precloud boundary layer leading to temperature and moisture profiles closer to the LES compared to the standard Smagorinsky. As a result, the initialization and general representation of the cloud field in the dynamic model is in good agreement with the LES. In contrast, the standard Smagorinsky produces a less well-mixed boundary layer, which fails to ventilate moisture from the boundary layer, resulting in the delayed spinup of the cloud layer. Moreover, strong downgradient diffusion controls the turbulent transport of scalars in the cloud layer. However, the dynamic approaches rely on the resolved field to account for nonlocal transports, leading to overenergetic structures when the boundary layer is fully developed and the Lagrangian model is used. Introducing the local averaging version of the model or adopting a new Lagrangian time scale provides stronger dissipation without significantly affecting model behavior.
54 ENVIRONMENTAL SCIENCES↗
Locally adaptive artificial viscosity strategies for Lagrangian hydrodynamics
To accurately model inviscid flow with shock waves using staggered-grid Lagrangian hydrodynamics, artificial viscosity is introduced to convert kinetic energy into internal energy, thereby providing a mechanism to generate the required entropy increase across shocks. In this paper, we propose a new method for constructing an adaptive, artificial viscosity in the context of one-dimensional, staggered-grid Lagrangian hydrodynamics. Our adaptive, artificial viscosity is defined in terms of two parameters that depend on density locally in a neighborhood around a shock, and hence, vary cell-by-cell. Our methodology is based on building a reference set of pre-computed optimal, globally constant artificial viscosity coefficients for a family of isolated shock test problems. For arbitrary flows, the evaluation of the unknown coefficients is automated by first estimating shock intensity locally, and second computing the corresponding adaptive parameter value via interpolation over the data from the pre-computed reference set of optimal, globally constant coefficient values. To illustrate the performance of our new approach, we compare our results against two existing methods. The first method is a limiter-based approach, which relies on estimating velocity gradients of the flow, and the second method is utilized in several commercial codes. Finally, we demonstrate that our new adaptive methodology produces more accurate results for a variety of tests with propagating shock waves, as well as for the aforementioned family of isolated shock problems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Evaluating the Lagrangian Evolution of Subtropical Low Clouds in GCMs Using Observations: Mean Evolution, Time Scales, and Responses to Predictors
In this work, a Lagrangian framework is developed to show the daily-scale time evolution of low clouds over the eastern subtropical oceans. An identical framework is applied to two general circulation models (GCMs): the CAM5 and UKMET and a set of satellite observations. This approach follows thousands of parcels as they advect downwind in the subtropical trade winds, comparing cloud evolution in time and space. This study tracks cloud cover, in-cloud liquid water path (CLWP), droplet concentration $N_d$, planetary boundary layer (PBL) depth, and rain rate as clouds transition from regions with predominately stratiform clouds to regions containing mostly trade cumulus. The two models generate fewer clouds with greater $N_d$ relative to observations. Models show stronger Lagrangian cloud cover decline and greater PBL deepening when compared with observations. In comparing frequency distributions of cloud variables over time, it is seen that models generate increasing frequencies of nearly clear conditions at the expense of overcast conditions, whereas observations show transitions from overcast to cloud amounts between 50% and 90%. Lagrangian decorrelation time scales ($\mathcal{e}$-folding time $\tau$) of cloud cover and CLWP are between 11 and 19 h for models and observations, although they are a bit shorter for models. A Lagrangian framework applied here resolves and compares the time evolution of cloud systems as they adjust to environmental perturbations in models and observations. Increasing subsidence in the overlying troposphere leads to declining cloud cover, CLWP, PBL depth, and rain rates in models and observations. Modeled cloud responses to other meteorological variables are less consistent with observations, suggesting a need for continuing mechanical improvements in GCMs.
58 GEOSCIENCES↗
In Situ Observations and Sampling of Volcanic Emissions with Unmanned Aircraft: A NASA/UCR Case Study at Turrialba Volcano, Costa Rica
Burgeoning new technology in the design and development of robotic aircraft-unmanned aerial vehicles (UAVs)-presents unprecedented opportunities for the volcanology community to observe, measure, and sample eruption plumes and drifting volcanic clouds in situ. While manned aircraft can sample dilute parts of such emissions, demonstrated hazards to air breathing, and most particularly turbine, engines preclude penetration of the zones of highest ash concentrations. Such areas within plumes are often of highest interest with respect to boundary conditions of applicable mass-loading retrieval models, as well as Lagrangian, Eulerian, and hybrid transport models used by hazard responders to predict plume trajectories, particularly in the context of airborne hazards. Before the 2010 Ejyafyallajokull eruption in Iceland, ICAO zero-ash-tolerance rules were typically followed, particularly for relatively uncrowded Pacific Rim airspace, and over North and South America, where often diversion of aircraft around ash plumes and clouds was practical. The 2010 eruption in Iceland radically changed the paradigm, in that critical airspace over continental Europe and the United Kingdom were summarily shut by local civil aviation authorities and EURO CONTROL. A strong desire emerged for better real-time knowledge of ash cloud characteristics, particularly ash concentrations, and especially for validation of orbital multispectral imaging. UAV platforms appear to provide a viable adjunct, if not a primary source, of such in situ data for volcanic plumes and drifting volcanic clouds from explosive eruptions, with prompt and comprehensive application to aviation safety and to the basic science of volcanology. Current work is underway in Costa Rica at Turrialba volcano by the authors, with the goal of developing and testing new small, economical UAV platforms, with miniaturized instrument payloads, within a volcanic plume. We are underway with bi-monthly deployments of tethered SO2-sondes and are in the planning stages for the deployment of the SIERRA UAV to our site in March 2013. We will be conducting in situ observations simultaneously with ASTER orbital multispectral TIR data acquisitions, in order to compare in situ measurements with estimates of SO2 mass loading and dispersion derived from ASTER data. Though small UAVs are now being considered for use in active volcanic areas for in situ sampling of emissions (e.g., efforts by our group, and by our colleagues at the INGV in Italy and the Applied Science University in Dusseldorf, Germany, and others in the United Kingdom and Iceland), and also for remote sensing, much more needs to be done in the way of instrument development, and in developing small UAVs for both low altitude (tropospheric) and high altitude (stratospheric) applications. In particular, the development of all weather and day/night operational flight capabilities in close proximity to hazardous topography is crucial to a truly responsive volcano in situ measurement system. Finally, it is imperative that national civil aviation authorities recognize the unique benefits of such platforms. It is important that authorities understand that severely restricting or not deploying such tools in airspace over restless volcanoes or within eruption plumes, ostensibly because of the perceived (small) risk that such unmanned aircraft pose to manned air operations, itself poses a bigger transcendental risk to proximal populations and particularly to the aviation community, itself.
Volcanic Ash Advisory Centers (VAACs)↗
Modeling Soft X‐Ray Emissions at the Dayside Magnetopause
In this study, we simulate the Solar Wind Charge Exchange (SWCX) soft X-ray emissions at dayside magnetosheath and cusps by using magnetohydrodynamic (MHD) and LAtmos TEst Particle (LaTeP) models. MHD models are unable to resolve the particle kinetic effects, such as the different behaviors of ions with different q/m, or distinguish the magnetospheric plasma from the solar wind plasma. We investigate these effects with the LaTeP model. As the LaTeP model does not self-compute magnetic and electric field, the magnetic and electric field data obtained from Open Geospace General Circulation Model (OpenGGCM) and Lagrangian version of the piecewise parabolic method (PPMLR) MHD model are used as the input to LaTeP model. The soft X-ray emissivity maps simulated from pure OpenGGCM and PPMLR MHD approaches and from LaTeP-OpenGGCM and LaTeP-PPMLR approaches are presented and compared. The results indicate that the LaTeP model can well resolve the kinetic effects and can be used to investigate the individual spectral characteristics. Therefore, the LaTeP model is a complementary approach for simulating the X-ray emissions near the dayside magnetopause. We also calculate the ratio of integrated OVII/OVIII line intensities, produced by charge exchange of O7+ ions and O8+ ions, respectively. We find a relatively higher ratio at the bow shock compared to the surrounding areas, suggesting that this ratio can be an effective parameter to identify the bow shock location.
Qiuyu Xu↗
A Regional CO2 Observing System Simulation Experiment Using ASCENDS Observations and WRF-STILT Footprints
Knowledge of the spatiotemporal variations in emissions and uptake of CO2 is hampered by sparse measurements. The recent advent of satellite measurements of CO2 concentrations is increasing the density of measurements, and the future mission ASCENDS (Active Sensing of CO2 Emissions over Nights, Days and Seasons) will provide even greater coverage and precision. Lagrangian atmospheric transport models run backward in time can quantify surface influences ("footprints") of diverse measurement platforms and are particularly well suited for inverse estimation of regional surface CO2 fluxes at high resolution based on satellite observations. We utilize the STILT Lagrangian particle dispersion model, driven by WRF meteorological fields at 40-km resolution, in a Bayesian synthesis inversion approach to quantify the ability of ASCENDS column CO2 observations to constrain fluxes at high resolution. This study focuses on land-based biospheric fluxes, whose uncertainties are especially large, in a domain encompassing North America. We present results based on realistic input fields for 2007. Pseudo-observation random errors are estimated from backscatter and optical depth measured by the CALIPSO satellite. We estimate a priori flux uncertainties based on output from the CASA-GFED (v.3) biosphere model and make simple assumptions about spatial and temporal error correlations. WRF-STILT footprints are convolved with candidate vertical weighting functions for ASCENDS. We find that at a horizontal flux resolution of 1 degree x 1 degree, ASCENDS observations are potentially able to reduce average weekly flux uncertainties by 0-8% in July, and 0-0.5% in January (assuming an error of 0.5 ppm at the Railroad Valley reference site). Aggregated to coarser resolutions, e.g. 5 degrees x 5 degrees, the uncertainty reductions are larger and more similar to those estimated in previous satellite data observing system simulation experiments.
Wang, James S.↗
Numerical modeling of pollutant transport using a Lagrangian marker particle technique
A derivation and code were developed for the three-dimensional mass transport equation, using a particle-in-cell solution technique, to solve coastal zone waste discharge problems where particles are a major component of the waste. Improvements in the particle movement techniques are suggested and typical examples illustrated. Preliminary model comparisons with analytic solutions for an instantaneous point release in a uniform flow show good results in resolving the waste motion. The findings to date indicate that this computational model will provide a useful technique to study the motion of sediment, dredged spoils, and other particulate waste commonly deposited in coastal waters.
Spaulding, M.↗
Population balance modeling of polyurethane foam formation with pressure‐dependent growth kernel
Abstract Polyurethane foams are widely used materials often chosen for their useful characteristics such as low thermal conductivity, ease of application, and high strength‐to‐weight ratios. Computational models are needed to predict the dynamics of the flow and expansion, and the resulting material properties, to improve manufacturing processes. In this paper, a model for PMDI, a water‐blown polyurethane foam, is presented. By extending a kinetics‐based approach by adding bubble‐scale information via a population balance equation (PBE) using the quadrature method of moments, we can track bubble size distributions during foaming. We present results from a three‐dimensional computational fluid dynamics model using arbitrary Lagrangian–Eulerian interface tracking implemented in finite element software. The model compares favorably with experimental data, including dynamics, bubble distributions measured by both camera and diffusion wave spectroscopy, and post‐test bubble size from scanning electron microscopy and density measurements from x‐ray computed tomography.
Ortiz, Weston↗
Estimated impacts of forest restoration scenarios on smoke exposures among outdoor agricultural workers in California
Abstract As wildfires continue to worsen across western United States, forest managers are increasingly employing prescribed burns as a way to reduce excess fuels and future wildfire risk. While the ecological benefits of these fuel treatments are clear, little is known about the smoke exposure tradeoffs of using prescribed burns to mitigate wildfires, particularly among at-risk populations. Outdoor agricultural workers are a population at increased risk of smoke exposure because of their time spent outside and the physical demands of their work. Here, we assess the smoke exposure impacts among outdoor agricultural workers resulting from the implementation of six forest management scenarios proposed for a landscape in the Central Sierra, California. We leverage emissions estimates from LANDIS-II to model daily PM 2.5 concentrations with the Hybrid Single Particle Lagrangian Integrated Trajectory Model (HYSPLIT) and link those to agricultural employment data from the Bureau of Labor Statistics. We find a u-shaped result, in that moderate amounts of prescribed burning result in the greatest reduction in total smoke exposure among outdoor agricultural workers, particularly during months of peak agricultural activity due to wildfire-specific smoke reductions. The reduction in total smoke exposure, relative to scenarios with the least amount of management, decreases as more prescribed burning is applied to the landscape due to the contributions of the fuel treatments themselves to overall smoke burden. The results of this analysis may contribute to preparedness efforts aimed at reducing smoke exposures among outdoor agricultural workers, while also informing forest management planning for this specific landscape.
Environmental Sciences & Ecology↗
A Vertically Lagrangian Finite-Volume Dynamical Core for Global Models
A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water dynamical system. The 2D horizontal-to-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split- explicit, with large-time-step for scalar transport, and small fractional time step for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for mapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with physical parameterizations and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave growth tests and long-term integrations using the Held-Suarez forcing are presented. Impact of the monotonicity constraint is discussed.
Lin, Shian-Jiann↗
A quasi-Lagrangian diagnostic case study of the effect of satellite sounding data assimilation on model cyclone prediction
A quasi-Lagrangian diagnostic study was performed to compare weather forecast accuracy with and without use of satellite data. Attention was focused on the mass and angular momentum budgets of the cyclone. The diagnostic study isolated the effects of physical processes within a cyclone and the effects of transport processes moving with the cyclone. Satellite data furnished different initialization values for horizontal mass and eddy angular momentum. Colder temperatures and weaker stabilities in the NW quadrant lower layers in the budget volume and increased stability in the middle and lower layers of another quadrant were obtained when the satellite data were considered. The addition of satellite data was concluded to have enhanced the accuracy of the forecast.
Vergin, J. M.↗
A Nonlinear Multigrid Solver for an Atmospheric General Circulation Model Based on Semi-Implicit Semi-Lagrangian Advection of Potential Vorticity
This work represents a part of a project to develop an atmospheric general circulation model based on the semi-Lagrangian advection of potential vorticity (PC) with divergence as the companion prognostic variable.
McCormick, S.↗
Semi-Lagrangian integration of a grid-point shallow water model on the sphere
This paper describes a semi-Lagrangian technique for integrating the equations of motion on the global domain. The technique uses an auxiliary spherical coordinate system at each near-polar gridpoint of the latitude-longitude grid; the auxiliary system is obtained by a rotation such that the new equator passes through the gridpoint in question and the new coordinate directions coincide with those of the original system at that point. The technique was applied to the shallow water equations, incorporating a semiimplicit treatment of the adjustment terms on a C-grid, with two-time levels. A five day integration was successfully carried out for a situation involving strong cross-polar flow. No filtering or diffusion was required to maintain stability over a five day period.
Mcdonald, A.↗
Coupled Stochastic Time-Inverted Lagrangian Transport/Weather Forecast and Research/Vegetation Photosynthesis and Respiration Model: Simulations of Tower-Based and Airborne CO2 Measurements - Part II
This paper evaluates simulations of atmospheric CO2 measured in 2004 at continental surface and airborne receptors, intended to test the capability to use data with high temporal and spatial resolution for analyses of carbon sources and sinks at regional and continental scales. The simulations were performed using the Stochastic Time-Inverted Lagrangian Transport (STILT) model driven by the Weather Forecast and Research (WRF) model, and linked to surface fluxes from the satellite-driven Vegetation Photosynthesis and Respiration Model (VPRM). The simulations provide detailed representations of hourly CO2 tower data and reproduce the shapes of airborne vertical profiles with high fidelity. WRF meteorology gives superior model performance compared with standard meteorological products, and the impact of including WRF convective mass fluxes in the STILT trajectory calculations is significant in individual cases. Important biases in the simulation are associated with the nighttime CO2 build-up and subsequent morning transition to convective conditions, and with errors in the advected lateral boundary condition. Comparison of STILT simulations driven by the WRF model against those driven by the Brazilian variant of the Regional Atmospheric Modeling System (BRAMS) shows that model-to-model differences are smaller than between an individual transport model and observations, pointing to systematic errors in the simulated transport. Future developments in the WRF model s data assimilation capabilities, basic research into the fundamental aspects of trajectory calculations, and intercomparison studies involving other transport models, are possible venues for reducing these errors. Overall, the STILT/WRF/VPRM offers a powerful tool for continental and regional scale carbon flux estimates.
Eluszkiewicz, Janusz↗