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At least 1,261 records · Page 70

Dynamic Inversion based Control of a Docking Mechanism

The problem of position and attitude control of the Stewart platform based docking mechanism is considered motivated by its future application in space missions requiring the autonomous docking capability. The control design is initiated based on the framework of the intelligent flight control architecture being developed at NASA Ames Research Center. In this paper, the baseline position and attitude control system is designed using dynamic inversion with proportional-integral augmentation. The inverse dynamics uses a Newton-Euler formulation that includes the platform dynamics, the dynamics of the individual legs along with viscous friction in the joints. Simulation results are presented using forward dynamics simulated by a commercial physics engine that builds the system as individual elements with appropriate joints and uses constrained numerical integration,

Kulkarni, Nilesh V.↗

Assimilation of Freeze - Thaw Observations into the NASA Catchment Land Surface Model

The land surface freeze-thaw (F-T) state plays a key role in the hydrological and carbon cycles and thus affects water and energy exchanges and vegetation productivity at the land surface. In this study, we developed an F-T assimilation algorithm for the NASA Goddard Earth Observing System, version 5 (GEOS-5) modeling and assimilation framework. The algorithm includes a newly developed observation operator that diagnoses the landscape F-T state in the GEOS-5 Catchment land surface model. The F-T analysis is a rule-based approach that adjusts Catchment model state variables in response to binary F-T observations, while also considering forecast and observation errors. A regional observing system simulation experiment was conducted using synthetically generated F-T observations. The assimilation of perfect (error-free) F-T observations reduced the root-mean-square errors (RMSE) of surface temperature and soil temperature by 0.206 C and 0.061 C, respectively, when compared to model estimates (equivalent to a relative RMSE reduction of 6.7 percent and 3.1 percent, respectively). For a maximum classification error (CEmax) of 10 percent in the synthetic F-T observations, the F-T assimilation reduced the RMSE of surface temperature and soil temperature by 0.178 C and 0.036 C, respectively. For CEmax=20 percent, the F-T assimilation still reduces the RMSE of model surface temperature estimates by 0.149 C but yields no improvement over the model soil temperature estimates. The F-T assimilation scheme is being developed to exploit planned operational F-T products from the NASA Soil Moisture Active Passive (SMAP) mission.

GEOS5↗

First-excursion probability in non-stationary random vibration.

The first-excursion probability of a non-stationary Gaussian process with zero mean has been studied. Within the framework of the point process approach, a variety of analytical approximations applicable to stationary random processes is extended herein to non-stationary random processes. The extension is possible owing to a recent definition of non-stationary envelope processes proposed by the author. With the aid of numerical examples, merits of each approximation are examined by comparing with the results of simulation. It is found that under non-stationary excitations with short duration, the Markov approximation is the best among all the approximations discussed in this paper.

Yang, J.-N.↗

Demonstration of Prognostics-Enabled Decision Making Algorithms on a Hardware Mobile Robot Test Platform

Prognostics-enabled Decision Making (PDM) is an emerging research area that aims to integrate prognostic health information and knowledge about the future operating conditions into the process of selecting subsequent actions for the system. Previous work developing and testing PDM algorithms has been done in simulation; this paper describes the effort leading to a successful demonstration of PDM algorithms on a hardware mobile robot platform. The hardware platform, based on the K11 planetary rover prototype, was modified to allow injection of selected fault modes related to the rover’s electrical power subsystem. The PDM algorithms were adapted to the hardware platform, including development of a software module framework, a new route planner, and modifications to increase the algorithms’ robustness to sensor noise and system timing issues. A set of test scenarios was chosen to demonstrate the algorithms’ capabilities. The modifications to run with a hardware platform, the test scenarios, and the test results are described in detail. The results show a successful use of PDM algorithms on a hardware test platform to optimize mission planning in the presence of electrical system faults.

Prognosis↗

Splashdown Visualization of Spent Stages

The state of the art for many Earth-to-orbit trajectory analysis toolsets used at NASA is somewhat dated in terms of the languages they are written in and their user interfaces. Many of these programs are written in languages like Fortran or C that are no longer considered modern in the technology industry, and are command-line based without any means of interpreting the data outputs. This presentation is meant to demonstrate a specific use case for a newly developed web app that visualizes the output data for one of these tools. Specifically, one key usage is to investigate and validate launches for notional multi-stage vehicle concepts to various non-standard high-inclination orbits. Some NASA requirements dictate that trajectories be designed such that no surviving debris lands closer than 200 nautical miles (nm) from foreign landmasses or 27 nm from the continental United States, therefore validating re-entry locations of spent stages is an integral part of the launch planning process. In addition, at programmatic levels it can prove insightful and clarifying for the decision-making process to enhance the technical results of numerical simulations with visualizations. The intent with this tool is to provide the mission analyst and program level management with an intuitive and clear grasp of key information on possible mission scenarios either departing from or arriving at Earth, and in the future, the moon or Mars as well. The software tool was developed with an agile development approach and utilizes the latest frameworks and technologies. The front end uses the React JavaScript library for making a state of the art frontend and a backend based on the Django Python framework for handling data using Python’s powerful and free scientific libraries. In addition, the CesiumJS open-source library is key for visualizing these end-to-end trajectories on a high-resolution Earth model. The presentation will demonstrate the current capability and tested use cases.

Jack Agolli↗

Regimes of Cloud Vertical Structure From Active Observations

We introduce a new type of cloud class, which we call “active cloud regime” (ACR), owing to its provenance from active (lidar and cloud radar) spaceborne cloud observations. ACRs intend to provide a climatological description based on cloud vertical structure (CVS) of the most prevalent monthly CVS mixtures encountered at large spatial scales of ~400 km. ACRs are thus a way to create a gridded dataset of a vertically-resolved cloud mask that can facilitate joint analysis with other gridded datasets. The detailed 2D cloud mask comes from the 2B-CLDCLASS-LIDAR CloudSat dataset fusing CALIPSO (lidar) and CloudSat (cloud radar) cloud detections. We show that the global classification of cloudiness under the ACR framework provides valuable insights on how the world’s dominant cloud systems regulate the two major components of atmospheric energetics, precipitation and radiative cooling. NASA’s GEOS model allows us to demonstrate the feasibility of applying the ACR concept in Earth System Models that have the capability to produce subgrid cloudiness obeying pre-specified vertical overlap rules. Comparison of observed and simulated ACRs provides thus another means to assess the realism of modeled clouds.

cloud vertical structure↗

Macromolecular recognition: Structural aspects of the origin of the genetic system

Theoretical simulation of prebiotic chemical processes is an invaluable tool for probing the phenomenon of the evolution of life. Using computational and modeling techniques and guided by analogies from present day systems, we seek to understand the emergence of the genetic apparatus, enzymatic catalysis and protein synthesis under prebiotic conditions. Modeling of the ancestral aminoacyl-tRNA-synthetases (aRS) may provide important clues to the emergence of the genetic code and the protein synthetic machinery. The minimal structural requirements for the catalysis of tRNA aminoacylation are being explored. A formation of an aminoacyl adenylate was studied in the framework of ab initio molecular orbital theory. The role of individual residues in the vicinity of the TyrRS active site was examined, and the effect of all possible amino acids substitutions near the active site was examined. A formation of aminoacyl tRNA was studied by the molecular modeling system SYBYL with the high resolution crystallographic structures of the present day tRNA, aRS's complexes. The ultimate goal is to propose a simple RNA segment that is small enough to be build in the primordial chemical environment but maintains the specificity and catalytic activity of the contemporary RNA enzyme. To understand the mechanism of ribozyme catalyzed reactions, ab initio and semi-empirical (ZINDO) programs were used to investigate the reaction path of transphosphorylation. A special emphasis was placed on the possible catalytic and structural roles played by the coordinated magnesium cation. Both the inline and adjacent mechanisms of transphosphorylation were studied. The structural characteristics of the target helices, particularly a possible role for the G-T pair, is also studied by a molecular dynamics (MD) simulation technique.

Rein, Robert↗

Agricultural Productivity Forecasts for Improved Drought Monitoring

Water stresses on agricultural crops during critical phases of crop phenology (such as grain filling) has higher impact on the eventual yield than at other times of crop growth. Therefore farmers are more concerned about water stresses in the context of crop phenology than the meteorological droughts. However the drought estimates currently produced do not account for the crop phenology. US Department of Agriculture (USDA) and National Oceanic and Atmospheric Administration (NOAA) have developed a drought monitoring decision support tool: The U.S. Drought Monitor, which currently uses meteorological droughts to delineate and categorize drought severity. Output from the Drought Monitor is used by the States to make disaster declarations. More importantly, USDA uses the Drought Monitor to make estimates of crop yield to help the commodities market. Accurate estimation of corn yield is especially critical given the recent trend towards diversion of corn to produce ethanol. Ethanol is fast becoming a standard 10% ethanol additive to petroleum products, the largest traded commodity. Thus the impact of large-scale drought will have dramatic impact on the petroleum prices as well as on food prices. USDA's World Agricultural Outlook Board (WAOB) serves as a focal point for economic intelligence and the commodity outlook for U.S. WAOB depends on Drought Monitor and has emphatically stated that accurate and timely data are needed in operational agrometeorological services to generate reliable projections for agricultural decision makers. Thus, improvements in the prediction of drought will reflect in early and accurate assessment of crop yields, which in turn will improve commodity projections. We have developed a drought assessment tool, which accounts for the water stress in the context of crop phenology. The crop modeling component is done using various crop modules within Decision Support System for Agrotechnology Transfer (DSSAT). DSSAT is an agricultural crop simulation system, which integrates the effects of soil, crop phenotype, weather, and management options. It has been in use for more than 15 years by researchers, growers and has become a de-facto standard in crop modeling communities spanning over 100 countries. The meteorological forcings to DSSAT are provided by NASA s National Land Data Assimilation System (NLDAS) datasets. NLDAS is a framework that incorporates atmospheric forcing and land parameter values along with land surface models to diagnose and predict the state of the land surface.

Limaye, Ashutosh↗

Loci-STREAM Version 0.9

Loci-STREAM is an evolving computational fluid dynamics (CFD) software tool for simulating possibly chemically reacting, possibly unsteady flows in diverse settings, including rocket engines, turbomachines, oil refineries, etc. Loci-STREAM implements a pressure- based flow-solving algorithm that utilizes unstructured grids. (The benefit of low memory usage by pressure-based algorithms is well recognized by experts in the field.) The algorithm is robust for flows at all speeds from zero to hypersonic. The flexibility of arbitrary polyhedral grids enables accurate, efficient simulation of flows in complex geometries, including those of plume-impingement problems. The present version - Loci-STREAM version 0.9 - includes an interface with the Portable, Extensible Toolkit for Scientific Computation (PETSc) library for access to enhanced linear-equation-solving programs therein that accelerate convergence toward a solution. The name "Loci" reflects the creation of this software within the Loci computational framework, which was developed at Mississippi State University for the primary purpose of simplifying the writing of complex multidisciplinary application programs to run in distributed-memory computing environments including clusters of personal computers. Loci has been designed to relieve application programmers of the details of programming for distributed-memory computers.

Wright, Jeffrey↗

Performance of the Goddard Multiscale Modeling Framework with Goddard Ice Microphysical Schemes

The multiscale modeling framework (MMF), which replaces traditional cloud parameterizations with cloud-resolving models (CRMs) within a host atmospheric general circulation model (GCM), has become a new approach for climate modeling. The embedded CRMs make it possible to apply CRM-based cloud microphysics directly within a GCM. However, most such schemes have never been tested in a global environment for long-term climate simulation. The benefits of using an MMF to evaluate rigorously and improve microphysics schemes are here demonstrated. Four one-moment microphysical schemes are implemented into the Goddard MMF and their results validated against three CloudSat/CALIPSO cloud ice products and other satellite data. The new four-class (cloud ice, snow, graupel, and frozen drops/hail) ice scheme produces a better overall spatial distribution of cloud ice amount, total cloud fractions, net radiation, and total cloud radiative forcing than earlier three-class ice schemes, with biases within the observational uncertainties. Sensitivity experiments are conducted to examine the impact of recently upgraded microphysical processes on global hydrometeor distributions. Five processes dominate the global distributions of cloud ice and snow amount in long-term simulations: (1) allowing for ice supersaturation in the saturation adjustment, (2) three additional correction terms in the depositional growth of cloud ice to snow, (3) accounting for cloud ice fall speeds, (4) limiting cloud ice particle size, and (5) new size-mapping schemes for snow and graupel. Despite the cloud microphysics improvements, systematic errors associated with subgrid processes, cyclic lateral boundaries in the embedded CRMs, and momentum transport remain and will require future improvement.

snow↗

An investigation of fighter aircraft agility

This report attempts to unify in a single document the results of a series of studies on fighter aircraft agility funded by the NASA Ames Research Center, Dryden Flight Research Facility and conducted at the University of Kansas Flight Research Laboratory during the period January 1989 through December 1993. New metrics proposed by pilots and the research community to assess fighter aircraft agility are collected and analyzed. The report develops a framework for understanding the context into which the various proposed fighter agility metrics fit in terms of application and testing. Since new metrics continue to be proposed, this report does not claim to contain every proposed fighter agility metric. Flight test procedures, test constraints, and related criteria are developed. Instrumentation required to quantify agility via flight test is considered, as is the sensitivity of the candidate metrics to deviations from nominal pilot command inputs, which is studied in detail. Instead of supplying specific, detailed conclusions about the relevance or utility of one candidate metric versus another, the authors have attempted to provide sufficient data and analyses for readers to formulate their own conclusions. Readers are therefore ultimately responsible for judging exactly which metrics are 'best' for their particular needs. Additionally, it is not the intent of the authors to suggest combat tactics or other actual operational uses of the results and data in this report. This has been left up to the user community. Twenty of the candidate agility metrics were selected for evaluation with high fidelity, nonlinear, non real-time flight simulation computer programs of the F-5A Freedom Fighter, F-16A Fighting Falcon, F-18A Hornet, and X-29A. The information and data presented on the 20 candidate metrics which were evaluated will assist interested readers in conducting their own extensive investigations. The report provides a definition and analysis of each metric; details of how to test and measure the metric, including any special data reduction requirements; typical values for the metric obtained using one or more aircraft types; and a sensitivity analysis if applicable. The report is organized as follows. The first chapter in the report presents a historical review of air combat trends which demonstrate the need for agility metrics in assessing the combat performance of fighter aircraft in a modern, all-aspect missile environment. The second chapter presents a framework for classifying each candidate metric according to time scale (transient, functional, instantaneous), further subdivided by axis (pitch, lateral, axial). The report is then broadly divided into two parts, with the transient agility metrics (pitch lateral, axial) covered in chapters three, four, and five, and the functional agility metrics covered in chapter six. Conclusions, recommendations, and an extensive reference list and biography are also included. Five appendices contain a comprehensive list of the definitions of all the candidate metrics; a description of the aircraft models and flight simulation programs used for testing the metrics; several relations and concepts which are fundamental to the study of lateral agility; an in-depth analysis of the axial agility metrics; and a derivation of the relations for the instantaneous agility and their approximations.

Valasek, John↗

Some More Sensitive Measures of Sensitivity and Response Bias

In this article, the author proposes a new pair of sensitivity and response bias indices and compares them to other measures currently available, including d' and Beta of signal detection theory. Unlike d' and Beta, these new performance measures do not depend on specific distributional assumptions or assumptions about the transformation from stimulus information to a discrimination judgment with simulated and empirical data, the new sensitivity index is shown to be more accurate than d' and 16 other indices when these measures are used to compare the sensitivity levels of 2 experimental conditions. Results from a perceptual discrimination experiment demonstrate the feasibility of the new distribution-free bias index and suggest that biases of the type defined within the signal detection theory framework (i.e., the placement of a decision criterion) do not exist, even under an asymmetric payoff manipulation.

Balakrishnan, J. D.↗

A Test of Sensitivity to Convective Transport in a Global Atmospheric CO2 Simulation

Two approximations to convective transport have been implemented in an offline chemistry transport model (CTM) to explore the impact on calculated atmospheric CO2 distributions. GlobalCO2 in the year 2000 is simulated using theCTM driven by assimilated meteorological fields from the NASA s Goddard Earth Observation System Data Assimilation System, Version 4 (GEOS-4). The model simulates atmospheric CO2 by adopting the same CO2 emission inventory and dynamical modules as described in Kawa et al. (convective transport scheme denoted as Conv1). Conv1 approximates the convective transport by using the bulk convective mass fluxes to redistribute trace gases. The alternate approximation, Conv2, partitions fluxes into updraft and downdraft, as well as into entrainment and detrainment, and has potential to yield a more realistic simulation of vertical redistribution through deep convection. Replacing Conv1 by Conv2 results in an overestimate of CO2 over biospheric sink regions. The largest discrepancies result in a CO2 difference of about 7.8 ppm in the July NH boreal forest, which is about 30% of the CO2 seasonality for that area. These differences are compared to those produced by emission scenario variations constrained by the framework of Intergovernmental Panel on Climate Change (IPCC) to account for possible land use change and residual terrestrial CO2 sink. It is shown that the overestimated CO2 driven by Conv2 can be offset by introducing these supplemental emissions.

Bian, H.↗

Lunabotics Mining Competition: Inspiration Through Accomplishment

NASA's Lunabotics Mining Competition is designed to promote the development of interest in space activities and STEM (Science, Technology, Engineering, and Mathematics) fields. The competition uses excavation, a necessary first step towards extracting resources from the regolith and building bases on the moon. The unique physical properties of lunar regolith and the reduced 1/6th gravity, vacuum environment make excavation a difficult technical challenge. Advances in lunar regolith mining have the potential to significantly contribute to our nation's space vision and NASA space exploration operations. The competition is conducted annually by NASA at the Kennedy Space Center Visitor Complex. The teams that can use telerobotic or autonomous operation to excavate a lunar regolith geotechnical simulant, herein after referred to as Black Point-1 (or BP-1) and score the most points (calculated as an average of two separate 10-minute timed competition attempts) will eam points towards the Joe Kosmo Award for Excellence and the scores will reflect ranking in the on-site mining category of the competition. The minimum excavation requirement is 10.0 kg during each competition attempt and the robotic excavator, referred to as the "Lunabot", must meet all specifications. This paper will review the achievements of the Lunabotics Mining Competition in 2010 and 2011, and present the new rules for 2012. By providing a framework for robotic design and fabrication, which culminates in a live competition event, university students have been able to produce sophisticated lunabots which are tele-operated. Multi-disciplinary teams are encouraged and the extreme sense of accomplishment provides a unique source of inspiration to the participating students, which has been shown to translate into increased interest in STEM careers. Our industrial sponsors (Caterpillar, Newmont Mining, Harris, Honeybee Robotics) have all stated that there is a strong need for skills in the workforce related to robotics and automated machines. In 2010, 22 United States (US) universities competed, and in May 2011 the competition was opened to international participation, with 46 Universities attending. There were 12 international teams and 34 US teams. This combined total directly inspired an estimated 544 university students. More students and the public were engaged via internet broadcasting and social networking media. This is expected to be of value for actual future space missions, as knowledge is gained from testing many innovative prototypes in simulated lunar regolith. More information is available at www.nasa.gov/lunabotics/.

Mueller, Robert P.↗

A theory of neutral gas emissions from a plasma contactor and its effect on electrodynamic tether performance

An existing anisotropic anodic plasma contactor model is extended to include neutral gas emissions. Within the framework of the contactor model, the inclusion of external ionization leads to an integrodifferential equation. By choosing the ratio of the contactor radius to the neutral gas-electron ionization mean free path at the contactor exit as a suitable expansion parameter, an analytical expression for the current-voltage characteristic can be found. The performance of this contactor model is examined via a dynamic simulation model developed for electrodynamic tethers. Detailed models of the geomagnetic field and the ionosphere are used to create a realistic environment. The highly nonlinear contactor voltagle-current characteristic is incorporated into a circuit equation, which includes radiation impedance, and is solved along the tether's orbit. Results show that it is more effective to fully ionize the contactor gas internally, than to partially ionize it externally, and that based on the specific power for the tether system, the optimum gas to use is argon. In addition, the effect of the radiation impedance on tether system performance is examined.

Roy, R. I. S.↗

A Virtual Laboratory for Aviation and Airspace Prognostics Research

Integration of Unmanned Aerial Vehicles (UAVs), autonomy, spacecraft, and other aviation technologies, in the airspace is becoming more and more complicated, and will continue to do so in the future. Inclusion of new technology and complexity into the airspace increases the importance and difficulty of safety assurance. Additionally, testing new technologies on complex aviation systems and systems of systems can be challenging, expensive, and at times unsafe when implementing real life scenarios. The application of prognostics to aviation and airspace management may produce new tools and insight into these problems. Prognostic methodology provides an estimate of the health and risks of a component, vehicle, or airspace and knowledge of how that will change over time. That measure is especially useful in safety determination, mission planning, and maintenance scheduling. In our research, we develop a live, distributed, hardware- in-the-loop Prognostics Virtual Laboratory testbed for aviation and airspace prognostics. The developed testbed will be used to validate prediction algorithms for the real-time safety monitoring of the National Airspace System (NAS) and the prediction of unsafe events. In our earlier work1 we discussed the initial Prognostics Virtual Laboratory testbed development work and related results for milestones 1 & 2. This paper describes the design, development, and testing of the integrated tested which are part of milestone 3, along with our next steps for validation of this work. Through a framework consisting of software/hardware modules and associated interface clients, the distributed testbed enables safe, accurate, and inexpensive experimentation and research into airspace and vehicle prognosis that would not have been possible otherwise. The testbed modules can be used cohesively to construct complex and relevant airspace scenarios for research. Four modules are key to this research: the virtual aircraft module which uses the X-Plane simulator and X-PlaneConnect toolbox, the live aircraft module which connects fielded aircraft using onboard cellular communications devices, the hardware in the loop (HITL) module which connects laboratory based bench-top hardware testbeds and the research module which contains diagnostics and prognostics tools for analysis of live air traffic situations and vehicle health conditions. The testbed also features other modules for data recording and playback, information visualization, and air traffic generation. Software reliability, safety, and latency are some of the critical design considerations in development of the testbed.

LVC-DE↗

Understanding the Impacts of Land Surface and PBL Observations on the Terrestrial and Atmospheric Legs of Land-Atmosphere Coupling

Accurately representing land-atmosphere (L-A) interactions and coupling in NWP systems remains a challenge. New observations, incorporated into models via assimilation or calibration, hold the promise of improved forecast skill, but erroneous model coupling can hinder the benefits of such activities. To better understand model representation of coupled interactions and feedbacks, this study demonstrates a novel framework for coupled calibration of the Single Column Model (SCM) capability of the NASA Unified Weather Research and Forecasting (NU-WRF) system coupled to NASA’s Land Information System (LIS). The local land-atmosphere coupling (LoCo) process chain paradigm is used to assess the processes and connections revealed by calibration experiments. Two summer case studies in the U. S. Southern Great Plains are simulated in which LSM parameters are calibrated to diurnal observations of LoCo process chain components including 2-meter temperature, 2-meter humidity, surface fluxes (Bowen ratio), and PBL height. Results show a wide range of soil moisture and hydraulic parameter solutions depending on which L-A variable (i.e. observation) is used for calibration, highlighting that improvement in either SHP or ISM when not in tandem with the other can provide undesirable results. Overall, this work demonstrates that a process chain calibration approach can be used to assess L-A connections, feedbacks, strengths, and deficiencies in coupled models, as well as quantify the potential impact of new sources of observations of land-PBL variables on coupled prediction.

Patricia Lawston-Parker↗

Wall-Modeled LES of a Swept Wing with Leading-Edge Ice Using LAVA Curvilinear, Unstructured, and Cartesian Solvers

Wall-modeled large-eddy simulation (LES) of a swept wing with leading-edge ice build up is performed using three mesh paradigms and associated flow solvers and compared to experimental results. The study focuses on an 8.9% scale model of the CRM65 swept wing featuring both high-fidelity and smooth leading-edge ice shapes. The assessment is conducted using the Launch, Ascent, and Vehicle Aerodynamics (LAVA) framework using the three actively supported meshing paradigms in LAVA: structured curvilinear overset, unstructured, andCartesian. For the iced configurations, these paradigms use hybrid body-fitted/source-term immersed-boundary, body-fitted, and ghost-cell immersed-boundary strategies, respectively.The unstructured and Cartesian mesh paradigms are particularly attractive for complex ice shapes as they avoid the manual mesh generation effort associated with the curvilinear approach. For the high-fidelity ice shape, good agreement with the experiment can be obtained with all three strategies; however, the curvilinear method is particularly sensitive to the source-term immersed-boundary timescale and span wise mesh resolution, and the Cartesian implementation is sensitive to the choice of numerical flux. For the smooth ice, larger discrepancies are observed across all methods. However, a mesh refinement study guided by flow visualizations leads to an improved comparison with the experiment that is particularly pronounced for the unstructured mesh paradigm.

TTT↗