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342 records · Page 19

Modeling Self-Pressurization and Spray Bar Pressure Control of a Cryogenic Storage Tank in Normal Gravity

This paper presents Computational Fluid Dynamics (CFD) models for simulating self-pressurization and spray bar cooling processes in a large-scale liquid hydrogen storage tank under normal gravity. The self-pressurization model utilizes the kinetics-based Schrage equation with the Volume-Of-Fluid (VOF) model to account for the evaporative and condensing interfacial mass fluxes. It uses a laminar approach to model natural convection and compares the pressures and temperatures predicted by the CFD model with experimental data from the Multipurpose Hydrogen Test Bed (MHTB) self-pressurization experiment. Additionally, the predicted interfacial mass flux is presented. A CFD model for simulating pressure control using a spray bar is also presented. An Eulerian-Lagrangian approach models the interactions between the discrete droplets and the continuous ullage phase. The spray model is coupled with the VOF model by tracking particles in the ullage, removing particles from the ullage when they reach the interface, and then adding their contributions to the liquid. The T-sat model is used to calculate the droplet-ullage heat and mass transfer. In this model, droplets warm up to the saturation temperature corresponding to the ullage vapor pressure thereafter evaporating while remaining at the saturation temperature. The tank pressure, vapor, and liquid temperature evolutions are validated against data from the MHTB spray bar mixing experiment.

Self-Pressurization↗

Modeling and Trade Space for Fuel Cell Powered Aircraft

Hydrogen has gained significant traction in research as a potential carbon-neutral fuel for future aircraft propulsion. The focus of this paper is on the hydrogen-electric aircraft (HEA) propulsion system which is a highly integrated network of high-power electrical, mechanical, fluidic, cryogenic, and thermal management components. These systems require careful analysis to determine the most efficient and light-weight design that ultimately reduces carbon emissions and operating cost. Fuel cell and energy storage sizing and optimization will be major factors that contribute to the aircraft feasibility independent of hydrogen storage. This paper describes the framework and modeling approach for the analysis of hydrogen-electric aircraft (HEA) propulsion systems for a under the National Aeronautics and Space Administration (NASA) Commercially-viable Hydrogen Aircraft for Reduction of Greenhouse Emissions (CH 2 ARGE) Project. For the first time, the Electrical Power System – Sizing and Analysis Tool (EPS-SAT) is used to conduct the sizing and trade studies on the hydrogen-electric aircraft propulsion system.

Hydrogen Electric Aircraft↗

Functional Task Tests in Partial Gravity During Parabolic Flight

BACKGROUND Understanding how critical mission tasks are performed in partial gravity such as on the moon or Mars is necessary to define effective and comprehensive countermeasure strategies for preserving crew performance during exploration missions. We studied the performance of tasks such as standing, balancing, walking, and jumping during the partial gravity phases of parabolic flight. We hypothesized that the acute effects of partial gravity on vestibular, proprioceptive, and sensorimotor functions would negatively impact performance. METHODS Twelve subjects (6F, 6M; 40.2 ± 8.5 years) were tested over three flights of 30 parabolas each, including 10 parabolas at 0.25g, 10 parabolas at 0.5g, and 10 parabolas at 0.75g. Subjects also performed tests in 1g between parabolas. During the seat egress and walk task, subjects rose from a seated position and walked as quickly as possible straight ahead towards a cone (4 m distance), stepped over a 30 cm high obstacle, walked around the cone making a 180° left turn, returned to the chair, and sat down in the chair. Other tasks included a tandem stance on rails, jump down from a 30cm platform, recovery from fall (prone to stand), and limits of stability tasks. Data were collected using inertial measurement units (Opal V2, APDM, Portland, OR) worn on the head and trunk, heart rate monitors (Polar, Finland), and a force plate (Bertec, Columbus, OH). During the jump down and limits of stability tasks, falls were recorded if subjects took extra steps, lifted their heels/toes, or used their arms to recover balance. RESULTS Gravity level had a significant effect on performance, with the greatest changes from 1g tending to be at the 0.25g level (Table 1). Lower gravity levels were associated with increased times to complete the seat egress and walk task and the recovery from fall task, increased head-trunk coordination, decreased tandem stance rail balance times, decreased change in heart rate during the recovery from fall task, and increased cone of stability distance in the anterior-posterior direction. In addition, there were significantly more falls recorded at the lower gravity levels: 31 falls at 0.25g, 14 falls at 0.5g, 6 falls at 0.75g, and 6 falls at 1g. DISCUSSION These data suggest that there is a dose-response relationship between gravity level and functional task performance. The largest changes in performance were expected at the lowest gravity level (0.25g) because subjects would no longer be able to use the gravitational reference for the perception of upright. Understanding the extent of performance deficits informs the risks and design of countermeasures for exploration spaceflight missions.

T R Macaulay↗

Localization of Ad-Hoc Lunar Constellations in Communication Failure Modes for Distributed Spacecraft Autonomy

As lunar missions increase in complexity inspired by NASA’s Artemis Program, they will require reliable and sufficient capability of the Position, Navigation, and Timing (PNT) system to support their scientific objectives. In addition, NASA's Commercial Lunar Payload Services (CLPS) program initiates the proliferation of public and private exploration partnerships using small satellites from commercial and private organizations, expanding traditionally confined low Earth orbit to be used for missions beyond geosynchronous orbit (Zucherman et al., 2022). Therefore, the Lunar PNT system is also required to provide navigation services compatible with the smaller platforms being sent by the public and private sectors, like CubeSats. However, traditional approaches to deep space missions’ navigation based on ground radio facilities have difficulties in providing sufficient support for the increasing number of users and communication at a distance from the Earth (Kaplev et al., 2022). In particular, the existing Lunar navigation technologies such as weak signal global positioning system (GPS) and deep space network (DSN) are not able to ensure operations of the upcoming small-scale Lunar missions due to their limitations in localization performance as well as capacity aspects. Another way to provide Lunar PNT service is to create a dedicated Lunar global navigation satellite system (GNSS) constellation, like GNSS systems on Earth. Space agencies like NASA, ESA, and JAXA are now developing the lunar communications relay and navigation systems (LCRNS) and Lunar navigation satellite systems (LNSS). In their systems, satellites will be deployed in moon orbits to provide the communication, positioning, navigation, and timing (CPNT) service at the lunar south pole region where the Artemis base camp will be expected (Murata et al., 2022). Meanwhile, common challenges considered in lunar PNT research arise from poor geometry of the terrestrial GNSS satellites when seen from the lunar user, highly perturbed lunar orbits, and limitations in power, size, and cost of the equipment on lunar satellites (Iiyama et al., 2023). It is also not clear if there will be enough Lunar users to support the cost and resources this would require as the Low-cost surface missions may not be able to support the large power, mass, and weight requirements that these navigation solutions entail (Niemoeller et al., 2022). As an alternative, existing Lunar science and exploration assets could be used to create a low-cost, autonomous, ad-hoc, and on-demand mission-centric Lunar PNT swarm capable of providing PNT services to these low-cost lunar missions (Hagenau et al., 2021). Introducing the non-dedicated and ad-hoc Lunar navigation constellation gives a way to provide PNT services on-demand. The non-dedicated swarm assets of Lunar constellations are designed to localize themselves with minimal interaction with Earth by adding cooperative autonomous localization to lunar missions, freeing up valuable bandwidth and ground segment resources. An autonomous localization of Lunar constellations is based on the concept of the decentralized PNT system with a distributed extended Kalman filter (DEKF) approach to state estimation for minimal onboard operating costs. In the distributed data processing algorithm, computation is broken down and assigned to each satellite, resulting in a considerably decreased computational amount while maintaining the accuracy of the orbit ephemeris and clock offsets as the result of centralized data processing (Wen et al., 2019). The DEKF requires spacecraft to perform two-way ranging operations with each other to communicate simultaneously, leveraging neighbor two-way intersatellite link (ISL) measurements such as pseudoranges to, and relative velocities between, visible satellites as sensor values (Frank et al., 2021). The Lunar autonomous PNT simulation (LAPS) demonstrated the feasibility of orbital asset localization among ad-hoc Lunar small-sat constellations based on the DEKF in Hagenau et al. (2021) and evaluated the matching algorithm proposed by Frank et al. (2021) in scheduling position estimation updates. In previous papers, all assets and measurements are assumed to be always available without consideration of the impact of intermittent and permanent communication failure. This study presents localization performance with increasing levels of network degradation for swarm assets and users to demonstrate the robustness of the decentralized Lunar PNT service in more realistic scenarios. Main issues arising from communication failure include spacecraft permanent or transient loss, antenna failures, message delays, etc. We tested four possible reasons for network degradation for 7 days in 21 satellites frozen with an altitude of 5500 km, evenly spaced around 3 circular, 40 inclination orbital planes where each spacecraft has two directional antennas. As anchor nodes with an independent estimate of their position are required in the DEKF approach, two ground nodes in each pole and one node in the gateway were implemented in the simulation. First, the most probable failure scenario involves the loss of a single spacecraft due to solar interference and technical malfunctions of the assets. Losing the availability of a single spacecraft means losing the two-way ISL measurement of the asset in the DEKF update. In order to provide the best possible quality of PNT service with limited time and resources, the distributed Lunar constellations must schedule the communication activities. The scheduler leverages mixed-integer linear programming (MILP) for the coordination and scheduling of the desired “as-needed” localization service (Niemoeller et al., 2022). We assume the scheduler has completely excluded the spacecraft information before the DEKF update in the failure scenario. When a random spacecraft has been turned off at a specific time, the robustness of the autonomous Lunar PNT system is evaluated. The simulation results give an 11.5% degradation in median position accuracy compared to the idealized performance excluding the asset loss. Second, a large number of assets may vanish due to major hardware problems or meteor strikes around the moon. A multiple spacecraft loss can degrade the localization performance very fast by losing the communication ability to do cross-plane measurements and in-plane measurements in a 3-plane constellation. When the matching-based scheduler is aware of ISL availability, we investigate a large number of in-plane and cross-plane asset vanishments both in close proximity and equally spaced throughout the orbital plane. According to the simulations, the loss of in-plane measurements gives 40.2% degradation while cross-plane measurements degrade 50.5% of asset localization performance among available assets. Therefore, it is concluded that cross-plane measurements are more important in improving the position estimation accuracy. Third, spacecraft failure information can be lost due to the internal message delay, resulting in the DEKF update scheduler to solve the matching problem with unavailable assets. The DEKF update cycle is comprised of network setup, communication, and computations where a global broadcast network and a 2-way ISL network setup take 6 minutes in total (Frank et al., 2021). Once the broadcast network successfully transmits and receives information, a random spacecraft may lose its availability right before solving the matching problem. This means the matching solution is no longer optimal, resulting in degradation in the localization performance. A numerical assessment shows the matching-based scheduler with knowing failure holds 11.5% of position accuracy degradation, whereas the scheduler without knowing failure gives 34% degraded localization performance without asset loss. Fourth, a transient loss of a single or multiple spacecraft may occur due to their antenna outages. After losing the two-way ISL availability for a few DEKF update cycles, the availability of spacecraft can easily be recovered as their states have been independently updated using measurements from anchor nodes. It is likely that the longer failure will result in worse localization performance. We have tested the transient failure of a random single asset for 30 min in the simulation, which is losing 3 update cycles in the DEKF system. From the simulation results, the position accuracy has been degraded to 4.84% which is better than the degraded localization performance of 11.5% from the permanent loss scenario among available assets. In conclusion, the autonomous Lunar PNT system based on the DEKF approach shows the ability to maintain resilience and robustness in the possible communication failure scenarios, ensuring that localization accuracy is preserved across various network degradation and outages. Future studies on investigating user localization performance near the South Pole and the broadcast network system will be continued in the following months.

Yeji Kim↗

Modeling Self-Pressurization and Spray Bar Pressure Control of A Cryogenic Storage Tank in Normal Gravity

This paper presents computational fluid dynamics (CFD) models for simulating self-pressurization and spray-bar pressure control processes in a large-scale liquid hydrogen storage tank under normal gravity conditions. For self-pressurization, the model employs the kinetics-based Schrage equation alongside the volume-of-fluid (VOF) method to account for interfacial mass transfer. The CFD predictions of pressure and temperature are compared with experimental data from the Multipurpose Hydrogen Test Bed (MHTB) experiment, and the predicted interfacial mass transfer rates are also presented. A CFD model simulating pressure control using a spray bar has also been developed. An Eulerian-Lagrangian approach models the interactions between discrete droplets and the continuous ullage (vapor) phase. The spray model is coupled with the VOF method by tracking droplets in the ullage and removing them when they reach the liquid interface. The T-sat model calculates droplet-ullage heat and mass transfer, where droplets warm up to the saturation temperature corresponding to the ullage vapor pressure before evaporating while remaining at the saturation temperature. The evolution of tank pressure, vapor temperature, and liquid temperature predicted by the CFD model is validated against data from the MHTB spray-bar mixing experiment. Overall, the CFD models agree with experimental data, demonstrating their capability to simulate self-pressurization and pressure control processes in large-scale cryogenic storage tanks. These models can be valuable tools for designing and optimizing cryogenic fluid management systems in future applications.

Computational Fluid Dynamics↗

Modeling Self-Pressurization and Spray Bar Pressure Control of A Cryogenic Storage Tank in Normal Gravity

This paper presents computational fluid dynamics (CFD) models for simulating self-pressurization and spray-bar pressure control processes in a large-scale liquid hydrogen storage tank under normal gravity conditions. For self-pressurization, the model employs the kinetics-based Schrage equation alongside the volume-of-fluid (VOF) method to account for interfacial mass transfer. The CFD predictions of pressure and temperature are compared with experimental data from the Multipurpose Hydrogen Test Bed (MHTB) experiment, and the predicted interfacial mass transfer rates are also presented. A CFD model simulating pressure control using a spray bar has also been developed. An Eulerian-Lagrangian approach models the interactions between discrete droplets and the continuous ullage (vapor) phase. The spray model is coupled with the VOF method by tracking droplets in the ullage and removing them when they reach the liquid interface. The T-sat model calculates droplet-ullage heat and mass transfer, wherein droplets warm up to the saturation temperature corresponding to the ullage vapor pressure before evaporating while remaining at the saturation temperature. The evolution of tank pressure, vapor temperature, and liquid temperature predicted by the CFD model is validated against data from the MHTB spray-bar mixing experiment. Overall, the CFD models agree with experimental data, demonstrating their capability to simulate self-pressurization and pressure control processes in large-scale cryogenic storage tanks. These models can be valuable tools for designing and optimizing cryogenic fluid management systems in future applications.

Self-Pressurization↗

The NASA OSIRIS-REx Sample Catalog: Samples Returned from Investigators

OSIRIS-REx is a sample return mission that collected carbon-rich material from B-type asteroid Bennu. After landing on September 24th, 2023, the science canister was transported to NASA Johnson Space Center (JSC) in Houston, Texas where it was opened and samples were processed by the curation team in pristine sample nitrogen gloveboxes. As the sample analysis phase of the OSIRIS-REx mission concludes, the Sample Analysis Team (SAT) has returned the majority of mission samples to NASA JSC curation and will return the remaining samples on a defined timetable. The curation team processed and documented as many of these samples as possible to include in the spring 2026 catalog update and are steadily working to process hundreds of more samples to include in the fall 2026 catalog update.

OSIRIS-REx↗

Performance of Nickel-Cadmium Batteries on the GOES I-K Series of Weather Satellites

The US National Oceanic and Atmospheric Administration (NOAA) operates the Geostationary Operational Environmental Satellite (GOES) spacecraft (among others) to support weather forecasting, severe storm tracking, and meteorological research by the National Weather Service (NWS). The latest in the GOES series consists of 5 spacecraft (originally named GOES I-M), three of which are in orbit and two more in development. Each of five spacecraft carry two Nickel-Cadmium batteries, with batteries designed and manufactured by Space Systems Loral (SS/L) and cells manufactured by Gates Aerospace Batteries (sold to SAFT in 1993). The battery, which consists of 28 cells with a 12 Ah capacity, provides the spacecraft power needs during the ascent phase and during the semi-annual eclipse seasons lasting for approximately 45 days each. The maximum duration eclipses are 72 minutes long which result in a 60 percent depth of discharge (DOD) of the batteries. This paper provides a description of the batteries, reconditioning setup, DOD profile during a typical eclipse season, and flight performance from the 3 launched spacecraft (now GOES 8, 9, and 10) in orbit.

Singhal, Sat P.↗

Performance of Nickel-Cadmium Batteries on the GOES 1-K Series of Weather Satellites

The US National Oceanic and Atmospheric Administration (NOAA) operates the Geostationary Operational Environmental Satellite (GOES) spacecraft (among others) to support weather forecasting, severe storm tracking, and meteorological research by the National Weather Service (NWS). The latest in the GOES series consists of five spacecraft (originally named GOES 1-M), three of which are in orbit and and two more in development. Each of the five spacecraft carries two Nickel-Cadmium battery, with batteries designed by Space Systems Loral (SS/L) and cells manufactured by Gates Aerospace Batteries (sold to SAFT in 1993). The battery, which consists of 28 cells with a 12 Ah capacity, provides the spacecraft power needs during the ascent phase and during the semi-annual eclipse seasons lasting for approximately 45 days each. The maximum duration eclipses are 72 minutes long which result in a 60 percent depth of discharge (DOD) of the batteries. This paper provides a description of the batteries, reconditioning setup, DOD profile during a typical eclipse season, and flight performance from the three launched spacecraft (now GOES 8, 9, and 10) in orbit.

Singhal, Sat P.↗

Performance of Nickel-Cadmium Batteries on the GOES-1 Series of Weather Satellites

This is an errata from an original paper published in the 1997 NASA Aerospace Battery workshop proceedings. A minor change was made to the second equation on page 98 and table 4 was revised during the final preparation of the paper. These changes were inadvertently left out of the final proceedings. These pages are reproduced in their entirety.

Singhal, Sat P.↗

A phase response curve to single bright light pulses in human subjects

The circadian pacemaker is differentially sensitive to the resetting effects of retinal light exposure, depending upon the circadian phase at which the light exposure occurs. Previously reported human phase response curves (PRCs) to single bright light exposures have employed small sample sizes, and were often based on relatively imprecise estimates of circadian phase and phase resetting. In the present study, 21 healthy, entrained subjects underwent pre- and post-stimulus constant routines (CRs) in dim light (approximately 2-7 lx) with maintained wakefulness in a semi-recumbent posture. The 6.7 h bright light exposure stimulus consisted of alternating 6 min fixed gaze (approximately 10 000 lx) and free gaze (approximately 5000-9000 lx) exposures. Light exposures were scheduled across the circadian cycle in different subjects so as to derive a PRC. Plasma melatonin was used to determine the phase of the onset, offset, and midpoint of the melatonin profiles during the CRs. Phase shifts were calculated as the difference in phase between the pre- and post-stimulus CRs. The resultant PRC of the midpoint of the melatonin rhythm revealed a characteristic type 1 PRC with a significant peak-to-trough amplitude of 5.02 h. Phase delays occurred when the light stimulus was centred prior to the critical phase at the core body temperature minimum, phase advances occurred when the light stimulus was centred after the critical phase, and no phase shift occurred at the critical phase. During the subjective day, no prolonged 'dead zone' of photic insensitivity was apparent. Phase shifts derived using the melatonin onsets showed larger magnitudes than those derived from the melatonin offsets. These data provide a comprehensive characterization of the human PRC under highly controlled laboratory conditions.

Randomized Controlled Trial↗

The NASA Earth Science Program and Small Satellites

Earth's changing environment impacts every aspect of life on our planet and climate change has profound implications on society. Studying Earth as a single complex system is essential to understanding the causes and consequences of climate change and other global environmental concerns. NASA's Earth Science Division (ESD) shapes an interdisciplinary view of Earth, exploring interactions among the atmosphere, oceans, ice sheets, land surface interior, and life itself. This enables scientists to measure global and climate changes and to inform decisions by Government, other organizations, and people in the United States and around the world. The data collected and results generated are accessible to other agencies and organizations to improve the products and services they provide, including air quality indices, disaster prediction and response, agricultural yield projections, and aviation safety. ESD's Flight Program provides the spacebased observing systems and supporting infrastructure for mission operations and scientific data processing and distribution that support NASA's Earth science research and modeling activities. The Flight Program currently has 21 operating Earth observing space missions, including the recently launched Global Precipitation Measurement (GPM) mission, the Orbiting Carbon Observatory-2 (OCO-2), the Soil Moisture Active Passive (SMAP) mission, and the International Space Station (ISS) RapidSCAT and Cloud-Aerosol Transport System (CATS) instruments. The ESD has 22 more missions and instruments planned for launch over the next decade. These include first and second tier missions from the 2007 Earth Science Decadal Survey, Climate Continuity missions to assure availability of key climate data sets, and small-sized competitively selected orbital missions and instrument missions of opportunity belonging to the Earth Venture (EV) Program. Small satellites (~500 kg or less) are critical contributors to these current and future satellite missions. Some examples are the aforementioned Orbiting Carbon Observatory-2 (OCO-2), the Gravity Recovery and Climate Experiment Follow On (GRACE FO), and the Cyclone Global Navigation Satellite System (CYGNSS) microsatellite constellation. Small satellites also support ESD in space validation and risk reduction of enabling technologies (components and systems). The status of the ESD Flight Program and the role of small satellites will be discussed.

Earth Science Prog & Small Sat↗

The Moon Burst Energetics All-sky Monitor (MoonBEAM)

MoonBEAM is a SmallSat concept placed in cislunar orbit developed to study the progenitors and multimessenger/multiwavelength signals of transient relativistic jets and outflows and determine the conditions that lead to the launching of a transient relativistic jet. The distinguishing advantage of MoonBEAM is the instantaneous all-sky coverage, maximizing the gamma-ray transients observations and providing upper limits for nondetections. Gamma-ray observatories in low Earth orbit are not able to survey the entire sky at a given time due to Earth blockage as well as detector downtime from the high particle activity in the South Atlantic Anomaly region. The long baseline provided from a cislunar orbit, allows MoonBEAM to constrain the localization annulus when combined with a gamma-ray instrument in low Earth orbit utilizing the timing triangulation technique. Improving the localization precision of a gamma-ray burst aids the gravitational wave follow-up community in reducing the region needed to be searched to locate and identify the afterglow and kilanova emission. Furthermore, by providing a different vantage point for a gamma-ray detection, MoonBEAM can help extend the gravitational wave detection horizon by increasing the confidence of a simultaneous marginal gravitational wave signal. Through the all-sky coverage, MoonBEAM will also provide insight into the conditions that lead to a successful relativistic jet, instead of a shock breakout event, or a completely failed jet in the case of core collapse supernovae.

Gamma-ray Bursts↗

Linking Strategic Astrophysics Missions, Technology Gaps, and Technology Maturation Investments

The National Aeronautics and Space Administration’s (NASA) Astrophysics Division (APD) funds the development of cutting-edge technologies through multiple programs to enable its strategic missions to achieve ambitious and groundbreaking science goals. These technology development efforts are managed by the Cosmic Origins (COR), Exoplanet Exploration (ExE), and Physics of the Cosmos (PhysCOS) programs. The 2020 Astronomy and Astrophysics Decadal Survey, “Pathways to Discovery in Astronomy and Astrophysics for the 2020s,” (Astro2020) recommended a pan-chromatic set of missions, including three Great Observatories (GO) and three Probe-class missions that could collect unprecedented data over the coming decades. We show the correlation between these strategic missions and the current Astrophysics technology gaps, as well as recent and current technology maturation projects funded to help close these technology gaps. We also cover how these investments advanced their Technology Readiness Levels (TRLs) [1] and where they have been infused into missions and projects.

SAT↗

Intrastep, Stage-Value Predictors for Diagonally-Implicit Runge-Kutta Methods

To better identify the necessary attributes of good stage-value predictors (SVPs), numerous SVPs are designed for an existing: ESDIRK4(3)7L[2]SA [26] and a new: ESDIRK4(3)8L[2]SA scheme.1 Both are stifflyaccurate, stage-order two, explicit, singly-diagonally implicit Runge–Kutta (ESDIRK) schemes. Tradeoffs are studied in the parameter spaces enforcing the constraints on accuracy, linear stability, nonlinear stability and coefficient size to determine which objectives correlate with effective predictors. The SVPs are tested on three challenging external aerodynamics problems [107 − 108 degrees of freedom (DoFs)], each with a different level of stiffness. The problems include two 3D airfoils simulations and one canonical turbulence simulation. All simulations use the compressible Navier-Stokes equations (CNSE). An entropy stable spectral collocation formulation is used for discretizing the spatial terms in the equations. Simulations are performed at a wide variety of temporal error tolerances. Problems that are sufficiently stiff (e.g., lax temporal error tolerances) benefit from SVPs designed with second-order accuracy and stability properties: A-stability, and L-stability, rather than high accuracy constraints. Simulations with modest stiffness (e.g., strict error tolerances) are better suited for SVPs designed using high accuracy constraints. Designing SVPs with enhanced stability properties is tedious but worthwhile. Simulation times are reduced with optimal SVPs by as much as 100% on some stages, with combined stepwise improvements of between 50 − 100% for both methods. A comparative study is performed with the two aforementioned methods as well as four other ESDIRKs. The newly designed ESDIRK4(3)8L[2]SA with γ ≈ 1/10, proves to be the most efficient of the six tested ESDIRK schemes simulating the CNSE.

Diagonally-Implicit Runge-Kutta↗