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

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Anisotropic fluid dynamical simulations of heavy-ion collisions

We present VAH, a (3+1)–dimensional simulation that evolves the far-from-equilibrium quark-gluon plasma produced in ultrarelativistic heavy-ion collisions with anisotropic fluid dynamics. We solve the hydrodynamic equations on an Eulerian grid using the Kurganov–Tadmor algorithm in combination with a new adaptive Runge–Kutta method. Our numerical scheme allows us to start the simulation soon after the nuclear collision, largely avoiding the need to integrate it with a separate pre-equilibrium dynamics module. We test the code's performance by simulating on the Eulerian grid conformal and non-conformal Bjorken flow as well as conformal Gubser flow, whose (0+1)–dimensional solutions are precisely known. Finally, we compare non-conformal anisotropic hydrodynamics to second-order viscous hydrodynamics in central Pb+Pb collisions and find that the former's longitudinal flow profile responds more consistently to the fluid's gradients along the spacetime rapidity direction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Thermodynamic analysis of a two-stage binary-fluid ejector heat pump water heater

Ejector heat pump water heaters (EHPWHs) could significantly increase the thermal efficiency of domestic water heating and reduce greenhouse gas emissions. This study addresses two major technical barriers to using EHPWHs in domestic water heating—low heating cycle coefficient of performance (COP) and low condensation temperatures—using binary fluid pairs as a working fluid in a two-stage ejector system. A comprehensive, geometry-free model of binary-fluid ejectors was built and validated to predict the entrainment ratios of binary-fluid ejectors. A thermodynamic model of a two-stage binary-fluid ejector EHPWH was built to predict the heating cycle COP of EHPWHs. The performance of the EHPWH was theoretically evaluated using HFE7000 and Novec649 as primary fluids and R600 and R1234ze(Z) as secondary fluids. HFE7000/R600 gave the highest heating cycle COP (i.e., 1.356) in producing domestic hot water at 60.0 °C. An optimum evaporation temperature of the primary fluid was identified for the maximum effective entrainment ratio and effective pressure lift ratio of two-stage ejectors. Here, the effective entrainment ratio of the two-stage ejector dominated the heating cycle COP of the EHPWH. Primary fluids with lower latent heats of evaporation and/or secondary fluids with higher latent heats of evaporation yielded higher heating cycle COPs of EHPWHs.

42 ENGINEERING↗
DOE OSTI2020

Specimen for evaluating pressure pulse cavitation in rock formations

An apparatus 300 for simulating a pulsed pressure induced cavitation technique (PPCT) from a pressurized working fluid (F) provides laboratory research and development for enhanced geothermal systems (EGS), oil, and gas wells. A pump 304 is configured to deliver a pressurized working fluid (F) to a control valve 306, which produces a pulsed pressure wave in a test chamber 308. The pulsed pressure wave parameters are defined by the pump 304 pressure and control valve 306 cycle rate. When a working fluid (F) and a rock specimen 312 are included in the apparatus, the pulsed pressure wave causes cavitation to occur at the surface of the specimen 312, thus initiating an extensive network of fracturing surfaces and micro fissures, which are examined by researchers.

03 NATURAL GAS↗
DOE OSTI2021

Analysis of Completion Design Impact on Cluster Efficiency and Pressure-Based Well Communication in HFTS-2 Delaware Basin

The Hydraulic Fracturing Test Site 2 (HFTS-2) is a joint industry project in the Delaware basin to advance hydraulic fracturing understanding and improve productivity in shale reservoirs. The project integrates multi-disciplinary approaches to evaluate different completion designs, well spacing, inter-well communication, and stimulated rock volume, among other factors. This paper focused on two major areas related to hydraulic fracture performance. First, an analysis of different completion designs on cluster efficiency based on near well Distributed Acoustic Sensing (DAS). Second, an evaluation of well and completion designs on inter-well fracture driven interactions (FDIs) based on downhole pressure monitoring. Fluid/sand distribution and cluster efficiency analyses were based on near wellbore DAS data collected from two adjacent horizontal wells completed in two different landing zones in the Wolfcamp formation. These wells had different completion designs aiming to evaluate the effect of normal vs. extended stage lengths, perforation hole tapering and limited entry. Standard deviation from ideal fluid/sand distribution and waterfall plots were used to evaluate cluster efficiency for each design and stage. Inter-well FDIs analysis was conducted among the horizontal wells and a vertical monitor well. One horizontal well served as the monitor well while the other horizontal well was being treated. The vertical well was instrumented with downhole pressure and temperature gauges to aid monitoring fracture height growth. The pressure response during and after fracturing was characterized based on maximum pressure increase value and slope. Pressure response vs. FDIs trigger factors such distance, cluster efficiency and stage fluid volume were also analyzed. Based on the different completion and perforation designs tested, DAS analysis suggests that limited entry design worked best. Extreme limited entry showed the potential of high perforation erosion and reduced cluster efficiency. Here, the limited entry and tapered perforation design demonstrated potential to improve the cluster efficiency for extended stage lengths. Pressure monitoring across formation units proved to be critical to understand fracture interactions and fracture vertical growth. Pressure communication across different formation units during hydraulic fracturing operation indicate fractures grew upwards during Wolfcamp wells fracturing. However, this pressure communication dissipated over time. High intensity FDIs were recorded when the frac stages Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/21URTC/1-21URTC/D011S018R001/2477607/urtec-2021-5289-ms.pdf/1 by Carol Worster on 28 February 2022 URTeC 5289 were closer to the pressure gauge location in the monitor wells. Some of these stages that produced high intensity FDIs also had high fluid volume per cluster and low cluster efficiency. The multi-disciplinary and high-quality data collected from HFTS-2 helped to further understand why completion approaches such as limited entry and tapered perforation design are successful in improving cluster efficiency. The DAS data combined with downhole high-resolution pressure measurements also helped to quantify the effect of lower cluster efficiency data on the incidence and intensity of FDIs.

58 GEOSCIENCES↗
DOE OSTI2022

Latent Space Simulation for Carbon Capture Design Optimization

The CO2 capture efficiency in solvent-based carbon capture systems (CCSs) critically depends on the gas-solvent interfacial area (IA), making maximization of IA a foundational challenge in CCS design. While the IA associated with a particular CCS design can be estimated via a computational fluid dynamics (CFD) simulation, using CFD to derive the IAs associated with numerous CCS designs is prohibitively costly. However, previous works such as Deep Fluids (Kim et al., 2019) show that large simulation speed-ups and low error are achievable by replacing CFD simulators with neural-network (NN) surrogates that mimic the CFD simulation process. This raises the possibility for a fast, accurate replacement for a CFD simulator, and thus computationally feasible IA-based CCS-design optimization. As such, here, we explore whether an existing NN-surrogate approach (and variants we develop) can successfully be applied to our complex carbon-capture CFD simulations, with the ultimate goal of obtaining a fast and accurate simulator for our CCS-design application. Our experiments build on the Deep Fluids approach and find that resulting surrogates can produce large speed ups (4000x) while maintaining IA relative errors as low as 4% on unseen CCS configurations (interpolating between configurations seen during training). Thus, despite less faithfulness to the underlying physics of the problem, NN surrogates may be a promising tool for our CCS design optimization problem. Notably, though, the Deep Fluids approach has limitations for our application (such as model non-transferability to CCS-packing changes), which we discuss. We conclude with potential directions for future work that may, like innovations we introduced here (e.g., transformer-based dynamics prediction), improve performance on our complicated dataset of CCS CFD simulations.

AI Surrogate Simulation, Carbon Capture, design op↗
DOE OSTI2024

Primordial black holes from bubble collisions during a first-order phase transition

We study the possibility of production of primordial black holes (PBHs) from bubble collisions during a first-order phase transition. While typical colliding bubbles are small and irrelevant for PBH production, we find that those that can produce PBHs must have a macroscopically thick fluid shell and have been born much before the typical nucleation time. Particularly large uncertainties arise from an exponential sensitivity of the nucleation rate on the required duration of bubble growth which depends on the details of the collisions and the evolution of the spacetime metric toward the end of the phase transition. We introduce a few parameters to be obtained from future numerical simulation to represent those unknowns, and estimate the PBH abundance in an Abelian Higgs benchmark model and show that it can be significant. We predict an approximately monochromatic PBH mass spectrum, and find regions in the parameter space where the PBHs can constitute entire dark matter or even overclose the Universe. Our result thus shows that models with a first-order phase transition can be constrained by overabundant PBHs or null results of other PBH searches. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Reduced diffusion and enhanced retention of multiple radionuclides from pore structure characterization of barrier materials for enhanced repository performance

Fluid flow and chemical transport in porous media are the macroscopic consequences of pore structure, which integrates geometry (e.g., pore size and surface area, pore-size distribution) and topology (e.g., pore connectivity). Low-permeability geological media whose pores are poorly interconnected will exhibit the characteristics of anomalous diffusion and sample size-dependent effective porosity, which will strongly impact long-term net diffusion and retention of radionuclides in geological repository settings involving different host rocks and barrier materials. A suite of innovative and complementary experimental approaches is utilized to study the microscopic pore structure and macroscopic fluid flow & chemical transport for a range of host rocks and barrier materials, in addition to standard clay minerals and reference rocks. With a particular focus on quantifying the presence and magnitude of “isolated” pores for a reduced effective porosity in low-permeability geomedia, the integrated methodologies for basic properties and pore structure characterization of these geomedia include X-ray diffraction, thin section petrography, grain size distribution, water immersion porosimetry after vacuum-pulling for full saturation, mercury intrusion porosimetry, nitrogen physisorption, scanning electron microscopy, X-ray computed tomography, and (ultra-)small angle neutron (X-ray) scattering. In addition, custom-designed gas diffusion, tracer recipe involving a range of anionic and cationic chemicals with subsequent analyses by laser ablation and inductively coupled plasma-mass spectrometry, along with batch sorption, column transport, and imbibition tests were conducted for coupled effects of pore structure and chemical retention/transport. From the perspectives of pore structure in conjunction with multiple and complementary approaches to examining a range of sample sizes under different observational scales, we find that the poor pore connectivity is prevalent in low-permeability media (mudstone and crystalline rock) that is related to geological processes (e.g., compaction, diagenesis and thermal maturation). For example, the deep and organic matter-rich mudstones have a much smaller effective porosity than the total porosity (as a result of poor pore connectivity) and associated diffusion coefficient, and the effective porosity & diffusion coefficients are also dependent upon the sample sizes used in the measurement. Similarly, most of the pore space in the shallow mudstone is also controlled by pore-throat diameters in the 5-50 nm range of intergranular pore types from its fine-grained nature, but with an overall good pore connectivity. However, the nm-sized pore space (physically pore-network architecture) and strong sorption capacities (chemical retention from clay minerals) of both shallow and deep mudstones lead to the synergistic retention of cationic radionuclides and their utilities as effective host rocks and barrier materials. Our unique approaches of studying how the micro-scale pore structure affect macro-scale fluid flow, diffusion & retention, and chemical transport produce improved mechanistic understanding, and realistic quantification, of diffusion and retention of typical radionuclides in a range of generic host rocks and barrier materials (clay/shale, salt, crystalline rock, and tuff), with the overall results leading to scientifically-based understanding of enhanced isolation (from both diffusion and retention) of radionuclides and improved confidence on the long-term performance of geological repository to store high-level radioactive wastes. In addition to the training of 25 undergraduates, graduates, and postdocs of UTA, the scientists (organizations) involved in performing this work (e.g., discussion, sample sharing, and operation of SANS and SAXS instruments) include Ed Matteo, Yifeng Wang, and Kristopher Kuhlman (Sandia National Laboratories), Jens Birkholzer, Liange Zheng, Tim Kneafsey, and Sharon Borglin (Lawrence Berkeley National Laboratory), Mavrik Zavarin (Lawrence Livermore National Laboratory), Yukio Tachi and Yuta Fukatsu (Japan Atomic Energy Agency), Mieke de Craen (Euridice, Belgium), Markus Bleuel (NIST), Wei-Ren Chen, Gergely Nagy, Changwoo Do, William Heller, Larry Anovitz, and Kenneth Littrell (ORNL), as well as Jan Illvsky, Ivan Kuzmenko, Ju-Sang Park and Jon Almers (ANL). Key deliverables include a total of 13 peer-reviewed journal articles (nine published and three under review), 23 presentations at scientific conferences (AAPG, AAPG Southwest Section, AGU, Asian Clay Conference, GSA, GSA South-Central Section, IHLRWM, InterPore, International Conference on Chemistry and Migration Behavior of Actinides and Fission Products in the Geosphere, International Conference on Coupled Processes in Fractured Geological Media: Observation, Modeling and Application), and academic institutions (UTA, New Mexico State University; University of Poitiers, France; University of Helsinki, Finland; Uppsala University, Sweden; Istanbul Technical University, Turkey) and other organizations (Andra, France; Posiva Oy, Finland).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Mesophase pitch-based high performance carbon fiber production using coal extracts from mild direct coal liquefaction

Mild direct coal liquefaction (autogenous pressure, no catalyst, no H2 gas) of Springfield coal in fluid catalytic cracking decant oil is shown to effectively produce coal extract precursors to spinnable mesophase pitch. Here this work demonstrates that the coal extract can be thermally treated to obtain mesophase pitch in a facile one-step process, bypassing the production of an intermediate isotropic pitch. Furthermore, the presence of 25 wt.% coal in the initial slurry can increase the yield to mesophase pitch nearly twofold and yield to carbon fiber by approximately 70%. The coal extract-derived mesophase pitch was melt-spun and heat treated to produce carbon fiber with graphitic texture, high modulus (>400 GPa) and tensile strength up to 943 MPa. Overall, this work demonstrates that coal can be effectively utilized to markedly amplify the mesophase pitch and carbon fiber yield from fluid catalytic cracking decant oil by relatively simple processing, while conserving utility as a precursor to high performance carbon fiber and potentially other high value graphitic products.

36 MATERIALS SCIENCE↗
DOE OSTI2023

HTGR Validation: NEUP Survey and Database Database Development for HTGR Thermal-Fluid Experiments

This set of slides is aimed to improve access to the High-Temperature Gas-cooled Reactor (HTGR) validation data and optimize the return on the significant investment made by DOE. Supported by the Advanced Reactor Technologies (ART) Gas-Cooled Reactor (GCR) program. Slides include information from FY2009 to FY2023, there are in total 35 DOE NEUP projects focusing on the thermal-fluid experiments related with High-Temperature Gas-cooled Reactor (HTGR), producing a large amount of high-quality validation data. NEUP Survey and Database Development for HTGR Thermal-Fluid Experiments is distributed at universities and has not been disseminated to the HTGR community. More collaborating with university PIs and refining the HTGR phenomena summary chart continuously is expected in the future.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

How slowly can the early Universe expand?

When the expansion of the Universe is dominated by a perfect fluid with equation of state parameter w and a sound speed c s satisfying w = $c^{2}_{s}$ ≤ 1 , the Hubble parameter H and time t satisfy the bound Ht ≥ 1/3 . There has been recent interest in “ultraslow” expansion laws with Ht <1/3 (sometimes described as “fast expanding” models). Here, we examine various models that can produce ultraslow expansion: scalar fields with negative potentials, barotropic fluids, braneworld models, or a loitering phase in the early Universe. Scalar field models and barotropic models for ultraslow expansion are unstable to evolution toward w = 1 or w → ∞ in the former case and w → ∞ in the latter case. Braneworld models can yield ultraslow expansion but require an expansion law beyond the standard Friedman equation. Loitering early universe models can produce a quasistatic expansion phase in the early Universe but require an exotic negative-density component. These results suggest that appeals to an ultraslow expansion phase in the early Universe should be approached with some caution, although the loitering early universe may be worthy of further investigation. These results do not apply to ultraslow contracting models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

A geospatial model for the analysis of time-dependent land subsidence induced by reservoir depletion

Land subsidence due to fluid depletion is an outcome of physical processes operating across a wide range of time and length scales. Although geomechanical models are crucial to simulate reservoir compaction and predict its long-term fate, their use across large regions often bears prohibitive computational costs. To overcome this obstacle, this paper proposes a simplified modelling framework consisting of (i) a near-field numerical solver simulating the coupling between fluid flow and rock deformation with reference to a simplified one-dimensional geometry and (ii) a far-field geospatial algorithm mapping ground settlements across a region through the superposition of poroelastic computations at multiple wells. The model computes the delay between depletion history and reservoir compaction in proximity of a producing well by assuming basal depletion of a fluid-saturated deformable disk, while the Geertsma solution of nucleus of strain is used to extrapolate the impact of such time-varying reservoir compaction around the well. This approach has been used to back-analyze the spatio-temporal progression of subsidence at the Groningen gas field. The results are compared against measurements collected over 50 year of production at 25 benchmark locations scattered over an area of 900 km 2 . It is shown that coupled simulations based on average values of rock compressibility and permeability lead to nonlinear trends of subsidence evolution in good agreement with field measurements, while uncoupled analyses overpredict settlements by more than 70%. Lastly, synthetic forecasts based on different rates of depletion were provided. The results suggest that slower depletion rates lead to lower subsidence at a given time, and that residual subsidence may continue to develop for several decades after interruption of production activities.

58 GEOSCIENCES↗
DOE OSTI2020

Electrodeposition of Zinc in Aqueous Electrolytes Containing High Molecular Weight Polymers

Strong polarization of the ion distribution in liquid electrolytes subjected to potential differences exceeding the thermal voltage, V T = kT/e, produces a hydrodynamic instability termed electroconvection at ion-selective interfaces. Electroconvection is desirable in some situations (e.g., electrodialysis) because it promotes mixing in a stagnant electrolyte layer, enhancing the ion flux at a fixed potential difference. It is undesirable in others (e.g., electrodeposition of metals) where early experiments show that convective fluid rolls associated with hydrodynamic instability in bounded electrolytes produce preferential metal deposition at localized regions on an electrode. Such localized deposition drives the family of morphological instabilities loosely termed dendritic electrodeposition. We experimentally investigate the effect of ultrahigh molecular weight polymer additives on the onset conditions and physical characteristics of both instabilities. Direct observations of electrodeposit morphology and tracer particle motions used in tandem with indirect electrokinetic measurements reveal that even at moderate concentrations, the polymer additives have a large beneficial effect in extending the range of electric potentials where stable electrodeposition is observed. Additionally, we report that at polymer concentrations above the entanglement threshold, high molecular weight polymers impart elasticity to liquid electrolytes which dampen electroconvective flow at a cation-selective interface but have at most a minimal effect on the bulk ionic conductivity of the liquid.

25 ENERGY STORAGE↗
DOE OSTI2020

One piece ceramic heat exchanger for concentrating solar power electric plants

Using additive manufacturing techniques, a ceramic heat exchanger was optimized for a concentrating solar power (CSP) electric power plant with a corrosive molten salt at atmospheric pressure as the solar field heat transfer fluid and supercritical carbon dioxide at 200 bar as the power block fluid. Temperatures ranged from 750 °C to 540 °C. The plant heat exchanger was optimized for heat transfer and stress using 1 m³ modules arranged in parallel. Heat transfer was optimized using COMSOL Multiphysics software resulting in a unique semi-elliptical cross section for the fluid flow channels in a counter-flow configuration. Counter-flow was made possible through additive manufacturing of the fluid headers as part of each modular heat exchanger thus producing the entire module as a single piece and minimizing cost. Using reasonable parametric values, a heat exchanger module was optimized to 0.5 MW/m³, and a section of it was manufactured including the fluid headers. Here, parametric studies showed the potential for a module to reach 3.5 MW/m³.

14 SOLAR ENERGY↗
DOE OSTI2021

Multi-fidelity modeling to predict the rheological properties of fiber suspensions

Unveiling the rheological properties of fiber suspensions is of paramount interest to many industrial applications like biofuel production. The 3D numerical simulations of the suspension of fibers are often computationally expensive and time-consuming. Machine learning methods such as neural networks can simplify the prediction of rheological behavior; however, they require a relatively large training data set. Multi -fidelity models, which combine high-fidelity data from numerical simulations and less expensive lower fidelity data from resources such as simplified physical equations, can lead to optimized predictions. Here, we focus on a neural network with two levels of fidelity, i.e., high and low fidelity networks. To produce high-fidelity data, we perform direct numerical simulations to model the fibers as one-dimensional inextensible slender bodies that obey the Euler- Bernoulli beam equation. The Navier-Stokes equations govern the suspended fluid, and an immersed boundary method is used to couple the fluid and solid motion. The low-fidelity data is produced by using constitutive equations. Noticeable improvements have been observed in the accuracy of predicting the rheological behavior when a multi-fidelity network is used compared to the single-fidelity network.

Boodaghidizaji, Miad↗
DOE OSTI2020

A general metriplectic framework with application to dissipative extended magnetohydrodynamics

General equations for conservative yet dissipative (entropy producing) extended magnetohydrodynamics are derived from two-fluid theory. Keeping all terms generates unusual cross-effects, such as thermophoresis and a current viscosity that mixes with the usual velocity viscosity. While the Poisson bracket of the ideal version of this model has already been discovered, we determine its metriplectic counterpart that describes the dissipation. This is done using a new and general thermodynamic point of view to derive dissipative brackets, a means of derivation that is natural for understanding and creating dissipative dynamics without appealing to underlying kinetic theory orderings. Finally, the formalism is used to study dissipation in the Lagrangian variable picture where, in the context of extended magnetohydrodynamics, non-local dissipative brackets naturally emerge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Enhanced Recovery of Critical Minerals and Geological Hydrogen in The Mine of the Future

invited perspective article: The rapid demand for critical minerals (CMs) and hydrogen (H2) necessitates innovative solutions beyond conventional mining. This study explores enhanced mineral recovery (EMR) and geological hydrogen production (GeoH2) by leveraging the Earth’s subsurface as a reactive platform. Using ultramafic rocks and engineered fluids, the approach simultaneously mobilizes critical resources and produces H2 through natural processes like serpentinization. This paradigm offers a transformative pathway to secure essential materials and diversify energy resources, setting a foundation for the Terrestrial Mine of the Future

Yan, Keju↗
DOE OSTI2025

An evaporite sequence from ancient brine recorded in Bennu samples

Evaporation or freezing of water-rich fluids with dilute concentrations of dissolved salts can produce brines, as observed in closed basins on Earth and detected by remote sensing on icy bodies in the outer Solar System. The mineralogical evolution of these brines is well understood in regard to terrestrial environments, but poorly constrained for extraterrestrial systems owing to a lack of direct sampling. Here we report the occurrence of salt minerals in samples of the asteroid (101955) Bennu returned by the OSIRIS-REx mission. These include sodium-bearing phosphates and sodium-rich carbonates, sulfates, chlorides and fluorides formed during evaporation of a late-stage brine that existed early in the history of Bennu’s parent body. Discovery of diverse salts would not be possible without mission sample return and careful curation and storage, because these decompose with prolonged exposure to Earth’s atmosphere. Similar brines probably still occur in the interior of icy bodies Ceres and Enceladus, as indicated by spectra or measurement of sodium carbonate on the surface or in plumes.

58 GEOSCIENCES↗
DOE OSTI2024

Comparison of Full-Field and Integrated CFD Convergence Based on Richardson Extrapolation

This work investigated the usefulness of Richardson extrapolation--based discretization error estimates across all points in a solution field to produce a spatial convergence field for a computational fluid dynamics (CFD) simulation. The presented work used previously developed methods for Richardson extrapolation to compute the convergence orders of a CFD simulation at all points of the base (coarsest) mesh solution. Three test cases of increasing complexity were considered: Poiseuille flow, incompressible flow around a sharp corner, and transonic flow over an RAE 2822 airfoil. These test cases highlighted the potential of the proposed method to identify error sources and their relation to the model system-response-quantity convergence orders. However, these test cases also revealed the immaturity of the proposed method stemming from the unreliability of computing observed convergence orders at single points. Nonetheless, the test cases highlighted that the observed convergence orders allow for a more accurate diagnosis of constructive and destructive error transport than mesh pair error estimates. In the long run, the proposed method can be a tool for developing efficient and advanced error management strategies like adaptive mesh refinement.

Weinmeister, Justin↗