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At least 487 records · Page 27

A Fast, Accurate and Sensitive GC-FID Method for the Analyses of Glycols in Water and Urine

Glycols, specifically ethylene glycol and 1,2-propanediol, are some of the major organic compounds found in the humidity condensate samples collected on the International Space Station. The current analytical method for glycols is a GC/MS method with direct sample injection. This method is simple and fast, but it is not very sensitive. Reporting limits for ethylene glycol and 1,2-propanediol are only 1 ppm. A much more sensitive GC/FID method was developed, in which glycols were derivatized with benzoyl chloride for 10 minutes before being extracted with hexane. Using 1,3-propanediol as an internal standard, the detection limits for the GC/FID method was determined to be 50 ppb and the analysis only takes 7 minutes. Data from the GC/MS and the new GC/FID methods shows excellent agreement with each other. Factors affecting the sensitivity, including sample volume, NaOH concentration and volume, volume of benzoyl chloride, reaction time and temperature, were investigated. Interferences during derivatization and possible method to reduce interferences were also investigated.

Kuo, C. Mike↗

An Immersed Boundary Method for Solving the Compressible Navier-Stokes Equations with Fluid Structure Interaction

An immersed boundary method for the compressible Navier-Stokes equation and the additional infrastructure that is needed to solve moving boundary problems and fully coupled fluid-structure interaction is described. All the methods described in this paper were implemented in NASA's LAVA solver framework. The underlying immersed boundary method is based on the locally stabilized immersed boundary method that was previously introduced by the authors. In the present paper this method is extended to account for all aspects that are involved for fluid structure interaction simulations, such as fast geometry queries and stencil computations, the treatment of freshly cleared cells, and the coupling of the computational fluid dynamics solver with a linear structural finite element method. The current approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems in 2D and 3D. As part of the validation procedure, results from the second AIAA aeroelastic prediction workshop are also presented. The current paper is regarded as a proof of concept study, while more advanced methods for fluid structure interaction are currently being investigated, such as geometric and material nonlinearities, and advanced coupling approaches.

Equations↗

A Statistical Method for Reducing Sidelobe Clutter for the Ku-Band Precipitation Radar on Board the GPM Core Observatory

A statistical method to reduce the sidelobe clutter of the Ku-band precipitation radar (KuPR) of the Dual-Frequency Precipitation Radar (DPR) on board the Global Precipitation Measurement (GPM) Core Observatory is described and evaluated using DPR observations. The KuPR sidelobe clutter was much more severe than that of the Precipitation Radar on board the Tropical Rainfall Measuring Mission (TRMM), and it has caused the misidentification of precipitation. The statistical method to reduce sidelobe clutter was constructed by subtracting the estimated sidelobe power, based upon a multiple regression model with explanatory variables of the normalized radar cross section (NRCS) of surface, from the received power of the echo. The saturation of the NRCS at near-nadir angles, resulting from strong surface scattering, was considered in the calculation of the regression coefficients.The method was implemented in the KuPR algorithm and applied to KuPR-observed data. It was found that the received power from sidelobe clutter over the ocean was largely reduced by using the developed method, although some of the received power from the sidelobe clutter still remained. From the statistical results of the evaluations, it was shown that the number of KuPR precipitation events in the clutter region, after the method was applied, was comparable to that in the clutter-free region. This confirms the reasonable performance of the method in removing sidelobe clutter. For further improving the effectiveness of the method, it is necessary to improve the consideration of the NRCS saturation, which will be explored in future work.

Atm/Ocean Structure/ Phenomena; Precipitation; Obs↗

Evaluation of Alternative Altitude Scaling Methods for Thermal Ice Protection System in NASA Icing Research Tunnel

A test was conducted at NASA Icing Research Tunnel to evaluate altitude scaling methods for thermal ice protection system. Two scaling methods based on Weber number were compared against a method based on the Reynolds number. The results generally agreed with the previous set of tests conducted in NRCC Altitude Icing Wind Tunnel. The Weber number based scaling methods resulted in smaller runback ice mass than the Reynolds number based scaling method. The ice accretions from the Weber number based scaling method also formed farther upstream. However there were large differences in the accreted ice mass between the two Weber number based scaling methods. The difference became greater when the speed was increased. This indicated that there may be some Reynolds number effects that isnt fully accounted for and warrants further study.

thermal scaling↗

Evaluation of Alternative Altitude Scaling Methods for Thermal Ice Protection System in NASA Icing Research Tunnel

A test was conducted at NASA Icing Research Tunnel to evaluate altitude scaling methods for thermal ice protection system. Two new scaling methods based on Weber number were compared against a method based on Reynolds number. The results generally agreed with the previous set of tests conducted in NRCC Altitude Icing Wind Tunnel where the three methods of scaling were also tested and compared along with reference (altitude) icing conditions. In those tests, the Weber number-based scaling methods yielded results much closer to those observed at the reference icing conditions than the Reynolds number-based icing conditions. The test in the NASA IRT used a much larger, asymmetric airfoil with an ice protection system that more closely resembled designs used in commercial aircraft. Following the trends observed during the AIWT tests, the Weber number based scaling methods resulted in smaller runback ice than the Reynolds number based scaling, and the ice formed farther upstream. The results show that the new Weber number based scaling methods, particularly the Weber number with water loading scaling, continue to show promise for ice protection system development and evaluation in atmospheric icing tunnels.

upwind schemes↗

Comparison of Aircraft Conceptual Design Weight Estimation Methods to the Flight Optimization System

Weight estimation is critical in the aircraft conceptual design process. The Flight Optimization System (FLOPS) is an aircraft conceptual design tool that has been the primary aircraft synthesis software used by the Systems Analysis and Concepts Directorate at NASA Langley Research Center. FLOPS includes multiple modules that represent aircraft design disciplines. The FLOPS weight module includes estimation methods that are similar in nature to other regression based aircraft preliminary weight estimation methods, however the FLOPS methods were created to use a minimum number of input parameters to limit the effort required by the designer to apply it. As FLOPS has recently been made publically available, this work compares the FLOPS weight estimation methods with several similar methods with the goal of explaining the differences in FLOPS, providing conceptual designers with a brief introduction to the method before attempting to apply it, and providing a reference to inform the development of future weight estimating relationships. In this paper, the Boeing 737-200 is used as a test case to highlight to differences and similarities in the methods.

Horvath, Bryce L.↗

Demonstration of Two Extended Visual Line of Sight Methods for Urban UAV Operations

This report describes two extended visual line of sight (EVLOS) methods developed and utilized during two flight campaigns over the campus of NASA Langley Research Center (LaRC): a chase vehicle method and a radio controlled (RC) pilot handoff method. These campaigns were performed to (a) evaluate small unmanned aerial system (sUAS) flight beyond the visual line of sight (BVLOS) of the ground control station operator and (b) test technologies under development to enable a transition from EVLOS to BVLOS operations. While an autonomous waypoint-based operational approach enabled minimal pilot intervention in both methods, range containment was enforced (a) manually via continual pilot visual monitoring and (b) autonomously via on-board contingency landing autonomy triggerable at the boundary of stay-in geofences. In the thirty-nine flights which utilized the chase vehicle, the pilot followed the sUAS flying a 1.2 km path at 40m altitude over urban streets. In the fifteen flights which utilized pilot handoff, a pilot at one end of a 1.5 km path initiated the flight at 120m altitude over buildings and trees, and at the midway point of the path transferred radio control to a pilot at the other end. In comparison, the chase vehicle method requires less ground crew and simpler avionics, while the pilot handoff method avoids schedule risk arising from street traffic congestion but better replicates actual direct routing for BVLOS flights. Collision risk with another aircraft was introduced in both campaigns and mitigated with the same manual and autonomous methods. Results from these campaigns serve as a basis for planned BVLOS operations at NASA LaRC.

Nicholas Rymer↗

High-Order Shock Fitting with Finite Element Methods

A moving-grid, shock-tracking, finite element method has been implemented that can achieve high-order accuracy for flow simulations with shocks. In this approach, element edges in the computational mesh are fitted to the shock front and moved with the shock throughout the simulation. The Euler equations are solved on the moving mesh in an arbitrary Lagrangian-Eulerian framework. Three different methods for specifying the shock motion have been tested,and the order of accuracy of the resulting solutions was verified. It was found that one of the methods is applicable only for problems with a constant upstream flow state, whereas the other two methods converge to the expected solution for general shock problems. When using a finite element method with polynomial degree p, the two general shock motion methods converged with the expected order of accuracy of (p+1). Finally, accurate solutions are obtained for supersonic nozzle and blunt body bow shock problems. Based on the results, it is concluded that the shock tracking method can preserve high-order solution accuracy in the vicinity of a shock wave.

Luke D'Aquila↗

Culture-Independent Microbial Air Profiling using a Spaceflight-Compatible Nanopore Sequencing Method

Microbial monitoring of spacecraft air is critical toward assessing the efficacy of microbial controls within the environmental control and life support systems to protect the crew and vehicle environment. Currently, onboard the International Space Station (ISS), the air is monitored every quarter using an impaction air sampler. With this method, microbial cells and spores are pulled onto plates containing a growth medium. Following onboard incubation, the crew reports approximate microbial levels to the ground, but sample return is required for identification. Upon return of the plates, the isolates present are identified for crew health risk assessments. As NASA moves beyond low-Earth orbit, sample return will be impractical, and a near real-time monitoring capability is essential. Significant strides have been made in recent years to utilize a molecular-based method for microbial profiling of ISS surfaces. The developed method is independent of microbial culture, thus removing the bias toward detecting only culturable organisms, eliminating the need for sample return, and reducing the risk to crew health from exposure to high microbial levels. The work described here details the evaluation of three different air sampling platforms whose product is amenable to downstream molecular processing. The three samplers were compared in terms of mass and power requirements, ease of use, and the resulting data. For the two highest-ranking samplers, a basic concept of operations was developed to transfer the sample into the already established preparation and sequencing process. Using these concepts of operations, an in-depth comparison of the molecular data generated was compared to the historical culture-based method. Data from both methods detailed similar microbial profiles, while the molecular method detailed microbial identifications that were lacking from the culture data. The developed method will enable the generation of near real-time microbial profiles of the spacecraft atmosphere.

Brandon Dunbar↗

Harvesting Microgreens in Microgravity: Analysis of Six Different Methods

In long duration space missions, crops will be used to supplement the astronaut diet. One such proposed crop type is microgreens, the young seedlings of edible plants that are known for their high nutritional levels, intense flavors, colorful appearance, and variety of textures. While these characteristics make microgreens a great candidate for space crop production, their small size presents a unique challenge within the microgravity environment. To ensure that astronauts will be able to harvest microgreens in microgravity with ease while avoiding the introduction of debris to the spacecraft cabin, multiple harvesting methods were developed by the Space Crop Production Team at NASA’s Kennedy Space Center. Three parabolic flights were conducted in November and December of 2021 and during those flights three different microgreen cutting methods (guillotine, pepper grinder, scissors) as well as two different bagging methods (attached and manual) were tested. In each flight, the microgreens were contained inside of a glovebox and footage of all the microgreen harvests was recorded. The cutting and bagging method combination that introduced the lowest average number of particulates into the glovebox was the scissors with attached bagging, closely followed by the pepper grinder with attached bagging. However, the scissors with attached bagging may had introduced fewer particulates into the glovebox because on average, 27% of the microgreens were never cut using the scissors method, so there were fewer free-floating particulates generated. The cutting and bagging method combination that left the lowest average percentage of microgreens remaining on the hardware post-harvest was the pepper grinder with an attached bag. Future directions include involving microgreen harvests in analog environments and further development of the different microgreen cutting and bagging methods. This research was funded by multiple NASA grants at the Kennedy Space Center.

Haley O Boles↗

Micrometer to Atomic Scale Characterisation of Primitive Astromaterials Using A Novel Method, Metis-Fa: A Coordinated Atom Probe Tomography, Transmission Electron Microscopy and NanoSIMS Approach

Introduction: Presolar grains preserve isotopic, chemical and microstructural records of physical and chemical processing, and formation mechanisms within a vast range of evolved stellar systems, the interstellar medium, solar nebula and their parent bodies. These evolutionary records are preserved at the micrometric to atomic scale, requiring coordinated studies to expand our understanding of evolutionary processes occurringthroughout ours and external stellar systems [1]. NanoSIMS enabled rapid in situ identification and isotopic characterisation of presolar grains and their stellar origins using 17O/16O and 18O/16O, and 13C/12C isotopic ratios [1]. Coordination with transmission electron microscopy (TEM) revealed crystallographic and localised contextual relationships and quantitively constrained their major and minor compositions [1]. However, trace elements cannot be quantified, the most sensitive geochemical tracers of environmental conditions, essential to unravelling the chemical record of their evolutionary pathway and parent stellar systems [2-3] . Furthermore, owing to the combination of technical limitations (only 5 – 7 isotopes can be measured per NanoSIMS run) and their small grain sizes of 100 nm < 3 μm (with rare exceptions in nanodiamonds (2 nm ≤) and SiC (< 40 μm)), the number of measurable isotopes per grain volume is limited [1,3] . Through more comprehensive isotopic studies of presolar grains, NanoSIMS studies have shown the importance of the latter, identifying Fe and Mg as important indicators of nuclear synthetic processing and their stellar origins, respectively [4- 5]. Coordination of NanoSIMS and Atom Probe Tomography (APT) revealed morphological signatures, and isotopic and chemical signatures at major to trace levels without requirements for preselection of elements [6]. However, crystallographic signatures in localized contextual relationships cannot be measured. Consequently, coordination of NanoSIMS, TEM and APT is essential to gain access to almost all contextual, structural and geochemical signatures within each presolar grain.Transmission electron microscopy requires a 100 nm thin lamella which is unstable in APT and would not produce any viable data. Atom probe tomography requires a needle-shaped specimen which when measured in TEM removes the local context, impacts the quality of the TEM diffraction images due to the shank angle of the needle, and can alter the chemistry of beam sensitive materials from the higher degree of surface exposure at the tip. To address these issues, we developed METIS-Fa (Multi-technical measurements of Electron Transparent materials using an Indium Sandwich - a FIB approach). A novel method which enables coordination of NanoSIMS, TEM and APT for generalized and targeted studies of individual grains, including beam sensitive materials, without compromising sample preparation requirements for TEM and APT. This method requires only indium and a Focus Ion Beam (FIB), minimizing the movement of fragile materials while still enabling preparation of TEM lamella into APT needles. Samples: Initial experimental development and testing of the method occurred at Astromaterials Research and Exploration Science (ARES), Johnson Space Centre (JSC), NASA and APT measurements and needle preparation occurred at JdLC, Curtin University. Synthetic silicate samples were used as analogs for presolar silicates when performing a trial run of the method. Samples were extracted from a polished thin section created at JSC, NASA, comprised of 38 wt.% Si, 17 wt.% FeO, 13 wt.% MgO, 12 wt.% Al, 11 wt.% Ca based on electron microprobe analysis (EMPA) [8] . Experimental details, pressure and temperature conditions were presented in [8] and references therein. Testing of the capability to target individual grains in mineral matrices using this method for acquisition in APT, measured matrix regions in meteoritic thin sections of primitive meteorites. These meteorites and their identified presolar grains for future targeted studies are detailed in [9]. Techniques: The TEM-FIB lamella were prepared using a FIB. An e-beam assisted pt deposition was used as a protective coating for the synthetic and meteoritic samples. When targeting individual grains, a secondary e-beam assisted pt deposition button is placed over the desired grain before the protective coating to denote its location. A JEOL 2500SE field-emission TEM was used for high-resolution imaging, energy-dispersive X-ray (EDX) and electron diffraction data.TheMETIS-Fa method was experimentally designed, tested and executed using a FIB at ARES, JSCNASA. Needles for APT were prepared using the Tescan Lyra3 GM Dual Beam Focus Ion Beam (FIB) Field Emission SEM (FE-SEM) at the JdLC, Curtin University. Atom probe tomography measurements were conducted using a CAMECA Local Electrode Atom Probe, LEAP 4000X HR. Two pure indium needles were analyzed initially to constraining acquisition parameters and stability under the beam. Manual acquisition was required to maintain evaporation of specimen’s at the apex and monitor interactions with measurement parameters. Experimental Design: Indium foil is pressed onto an Al stub with a pneumatic press and mounted into the FIB adjacent to the TEM-FIB lamella of interest. Using a FIB, two indium slices (5 μm x ~300 nm x 3 μm) are extracted from indium foil and aligned with the TEM-FIB lamella before touching the TEM-FIB lamella. Each slice is then attached through cold welding to the FIB-TEM lamella. This approach eliminates the need for chemical treatments and proved effective for aligning the Indium within the region of interest for APT, holding it in place for up to 4 days during testing.Once both indium slices are attached within their pre-determined region per grain targeting requirements, they are gradually melted onto the FIB-TEM lamella.When targeting a specific grain, measurements should be taken of the pt button and its distance from edge to edge of the lamella before and after sandwiching. A secondary button should be placed over the same region after the Indium slices have been attached to improve precision when preparing APT needles. Results: Figure 1 shows two indium slices melted onto a FIB-TEM lamella, adding additional bulk for preparation into APT needles as shown in Figure 2 [7] . The latter was essential so samples could be measured in TEM and APT without compromising sample preparation requirements and consequently data quality and acquisition stability. METIS-Fa proved effective forimproving geometry. Figure 3 shows a successful APTrun of the synthetic silicate. EMPA, TEM and APTshowed no chemical alterations. During targetingtesting, a solar silicate grain was successfully identifiedand measured in TEM, and prepared into an APTneedle. However, the indium was melted too long during sample preparation, causing expansion andformation of internal porosity leading to sample loss.Conclusion: METIS-Fa greatly expands the number of isotopic and chemical signatures measured per grain volume, and enables measurements of contextual, structural, crystallographic, isotopic and geochemical signatures within individual grains. Gaining access to such a vast range of evolutionary signatures required for expanding our understanding of external stellar and planetary systems and the evolution of our solar system. This method was designed for application to a vast range of phases including being sensitive materials and thus provides a way for coordination of NanoSIMS, TEM and APT not just for the study of presolar grains and by extension primitive astromaterials, but studies in a vast range of other fields including the geosciences and material sciences.Acknowledgments: Thankyou to ARES, JSC, NASA; JdLC Curtin University and Space Science Technology Centre for the use of laboratory facilities and funding [confirm].

Nicole D Nevill↗

Towards Aerodynamic Shape Optimization Using an Immersed Boundary Overset Grid Method

Traditional Reynolds-averaged Navier-Stokes grid methods applied to aerodynamic shapeoptimization can struggle with the deformation of surface and volume grids at componentintersections, such as at wing-fuselage junctions. To overcome this, we propose an approachwhich utilizes curvilinear overset grids for the discretization of the domain, with the presenceof the body modeled using an immersed boundary method. This approach handles complexgeometries without the need for their explicit integration into the grid. The goal of this approachis to reduce grid generation time and allow for greater geometric freedom for component-basedaerodynamic shape optimization. Two different methods are presented: a source-term-basedand a ghost-node-based immersed boundary method. Flow analyses and adjoint solutionsobtained using the proposed methods show promising comparisons with standard body-fittedgrid methods. Preliminary aerodynamic shape optimization results obtained using one of theimmersed boundary methods are also presented.

TTT↗

Fail-safe reactivity compensation method for a nuclear reactor

The present invention relates generally to the field of compensation methods for nuclear reactors and, in particular to a method for fail-safe reactivity compensation in solution-type nuclear reactors. In one embodiment, the fail-safe reactivity compensation method of the present invention augments other control methods for a nuclear reactor. In still another embodiment, the fail-safe reactivity compensation method of the present invention permits one to control a nuclear reaction in a nuclear reactor through a method that does not rely on moving components into or out of a reactor core, nor does the method of the present invention rely on the constant repositioning of control rods within a nuclear reactor in order to maintain a critical state.

Nygaard, Erik T.↗

Qualitative and Quantitative Evaluation for Representative Human Reliability Analysis Methods

The Korea Institute of Nuclear Safety (KINS) is the regulatory expert organization established by the Korean government to strengthen the nation’s technical capabilities relating to nuclear safety regulation. KINS oversees the technical aspects of nuclear safety regulation, including safety reviews, inspections, education, and safety research—all conducted based on technical knowledge and accumulated regulatory experience. In 2023, KINS requested that Idaho National Laboratory (INL) validates representative human reliability analysis (HRA) methods used throughout the world, thus affording KINS with a basis for determining an HRA method adequate for its domestic regulatory purposes. The present paper mainly examines INL’s efforts in this regard. The resulting INL study covered four representative HRA methods widely used by nuclear utilities and regulatory institutes. These methods were qualitatively evaluated by applying specific evaluation criteria and determining how well each method reflected critical HRA issues. For this assessment, INL benchmarked the Halden International HRA Empirical Study. Using the Halden empirical data, along with information on human failure events (HFEs), the present study employed the selected HRA methods to estimate human error probabilities (HEPs) for the HFEs. It also performed statistical analyses to compare the HEPs predicted via the HRA methods against those from the Halden empirical data.

99 - GENERAL AND MISCELLANEOUS↗

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗

Using Filter Methods to Guide Convergence for ADMM, with Applications to Nonnegative Matrix Factorization Problems

Nonconvex, nonlinear optimization problems arise naturally in parameter fitting and machine learning. While augmented Lagrangian methods have demonstrated robust convergence for classes of these problems, their convergence for block updates has been relatively unexplored outside of the context of the alternating direction method of multipliers (ADMM). ADMM has seen extensive use in these applications, but may exhibit uncertain convergence behavior in many practical nonconvex settings, and struggles with general nonlinear constraints. In contrast, filter methods have proved effective in enforcing convergence for sequential quadratic programming methods and interior point methods with feasibility criteria. We develop an ADMM-filter method for highly nonlinear and nonconvex problems. Here, we show convergence under mild assumptions for several types of coordinate descent schemes, and demonstrate our algorithm on nonnegative matrix factorization and completion problems in imaging and chemical spectrum analysis.

Nonconvex optimization↗

On High-Order/Low-Order and Micro-Macro Methods for Implicit Time-Stepping of the BGK Model

In this paper, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the Bhatnagar–Gross–Krook (BGK) equation for gas dynamics. The MM formulation represents a kinetic distribution as the sum of a local Maxwellian and a perturbation. In highly collisional regimes, the perturbation away from initial and boundary layers is small and can be compressed to reduce the overall storage cost of the distribution. The convergence behavior of the MM methods, the usual HOLO method, and the standard source iteration method is analyzed on a linear BGK model. Both the HOLO and MM methods are implemented using a discontinuous Galerkin (DG) discretization in phase space, which naturally preserves the consistency between high- and low-order models required by the HOLO approach. Furthermore, the accuracy and performance of these methods are compared on the Sod shock tube problem and a sudden wall heating boundary layer problem. Overall, the results demonstrate the robustness of the MM and HOLO approaches and illustrate the compression benefits enabled by the MM formulation when the kinetic distribution is near equilibrium.

BGK model↗

A review of high order strong stability preserving two-derivative explicit, implicit, and IMEX methods

High order strong stability preserving time discretizations ensure the nonlinear non-inner-product strong stability properties of spatial discretizations suited for the stable simulation of hyperbolic PDEs in a wide variety of application areas including fluid dynamics, magnetohydrodynamics, semiconductor devices, electromagnetics, and astrophysics. Over the past decade multiderivative time-stepping have been increasingly used for the time-evolution hyperbolic PDEs, so that the strong stability properties of these methods have become important. In this work we review sufficient conditions for a two-derivative multistage method to preserve the strong stability properties of spatial discretizations in a forward Euler and different conditions on the second derivative. In particular we present the strong stability preserving theory for explicit and implicit two-derivative Runge–Kutta schemes, including a special condition on the second derivative under which these implicit methods may be unconditionally strong stability preserving. This special condition is natural for the stiff component of wide range of plasma physics problems, and can be useful in the context of strong stability preserving implicit-explicit multi-derivative Runge–Kutta schemes, where the time-step restriction is then independent of the stiff term. Lastly, we present the strong stability preserving theory for implicit-explicit multi-derivative general linear methods, and some novel second and third order methods where the time-step restriction is independent of the stiff term.

97 MATHEMATICS AND COMPUTING↗