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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 1,603 records · Page 89
All sourcesNASA NTRSDOE OSTI
NASA NTRS2023

X-57 Maxwell Airworthiness Validation Plan

This report is a Final Airworthiness Validation Plan (AVP) and describes how an aircraft like X-57 does (and does not) meet current airworthiness standards. The objective of this report is to create an example certification basis, associated means of compliance (MoC), and method of compliance for a distributed electric propulsion airplane under 14 Code of Federal Regulations (CFR) Part 21, “Certification Procedures for Products and Articles,” and its associated relevant sections of 14 CFR for “Airworthiness Standards” of Part 23, “Normal Category Airplanes,” Part 33 “Aircraft Engines,” and Part 35 “Propellers.” The approach to meet the objective is to use NASA’s X-57 Modification (Mod) IV flight demonstrator as an example and categorize its applicability to the regulations and standards according to the following three conditions: 1. Identify, where applicable, that the MoC and methods of compliance can be associated with existing Standard Specifications and Standard Practices of (ASTM) Committee F39 on Aircraft Systems and ASTM Committee F44 on General Aviation Aircraft; 2. If relevant ASTM standards do not exist, identify means and-or methods of compliance from appropriate Federal Aviation Administration (FAA) Advisory Circulars and other sources to use for the X-57 Mod IV vehicle; or 3. If no relevant certification rule, MoC, or method of compliance exists, highlight this omission and provide recommendations.

Herbert W Schlickenmaier↗
NASA NTRS1985

Numerical investigation of internal high-speed viscous flows using a parabolic technique

A feasibility study has been conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves are present. A set of test problems with weak shock and expansion waves have been analyzed with this modified ADD method and stable and accurate solutions were demonstrated provided the streamwise step size was maintained at levels larger than the boundary layer displacement thickness. Calculations made with further reductions in step size encountered departure solutions consistent with strong interaction theory. Calculations were also performed for a flow field with a flame front in which a specific heat release was imposed to simulate a SCRAMJET combustor. In this case the flame front generated relatively thick shear layers which aggravated the departure solution problem. Qualitatively correct results were obtained for these cases using a marching technique with the convective terms in the normal momentum equation suppressed. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required.

Anderson, O. L.↗
NASA NTRS1975

Steady subsonic flow around finite-thickness wings

The general method for analyzing steady subsonic potential aerodynamic flow around a lifting body having arbitrary shape is presented. By using the Green function method, an integral representation for the potential is obtained. Under small perturbation assumption, the potential at any point, P, in the field depends only upon the values of the potential and its normal derivative on the surface of the body. Hence if the point P approaches the surface of the body, the representation reduces to an integral equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface. The question of uniqueness is examined and it is shown that, for thin wings, the operator becomes singular as the thickness approaches zero. This fact may yield numerical problems for very thin wings. However, numerical results obtained for a rectangular wing in subsonic flow show that these problems do not appear even for thickness ratio tau = .001. Comparison with existing results shows that the proposed method is at least as fast and accurate as the lifting surface theories.

Kuo, C. C.↗
NASA NTRS1993

Resonant frequencies of irregularly shaped microstrip antennas using method of moments

This paper describes an application of the method of moments to determine resonant frequencies of irregularly shaped microstrip patches embedded in a grounded dielectric slab. For analysis, the microstrip patch is assumed to be excited by a linearly polarized plane wave that is normal to the patch. The surface-current density that is induced on the patch because of the incident field is expressed in terms of subdomain functions by dividing the patch into identical rectangular subdomains. The amplitudes of the subdomain functions, as a function of frequency, are determined using the electric-field integral equation (EFIE) approach in conjunction with the method of moments. The resonant frequencies of the patch are then obtained by selecting the frequency at which the amplitude of the surface-current density is real. The resonant frequencies of the equilateral triangular and other nonrectangular patches are computed using the present technique, and these frequencies are compared with measurements and other independent calculations.

Deshpande, Manohar D.↗
NASA NTRS2003

Calibrating Laser Gas Measurements by Use of Natural CO2

An improved method of calibration has been devised for instruments that utilize tunable lasers to measure the absorption spectra of atmospheric gases in order to determine the relative abundances of the gases. In this method, CO2 in the atmosphere is used as a natural calibration standard. Unlike in one prior calibration method, it is not necessary to perform calibration measurements in advance of use of the instrument and to risk deterioration of accuracy with time during use. Unlike in another prior calibration method, it is not necessary to include a calibration gas standard (and the attendant additional hardware) in the instrument and to interrupt the acquisition of atmospheric data to perform calibration measurements. In the operation of an instrument of this type, the beam from a tunable diode laser or a tunable quantum-cascade laser is directed along a path through the atmosphere, the laser is made to scan in wavelength over an infrared spectral region that contains one or two absorption spectral lines of a gas of interest, and the transmission (and, thereby, the absorption) of the beam is measured. The concentration of the gas of interest can then be calculated from the observed depth of the absorption line(s), given the temperature, pressure, and path length. CO2 is nearly ideal as a natural calibration gas for the following reasons: CO2 has numerous rotation/vibration infrared spectral lines, many of which are near absorption lines of other gases. The concentration of CO2 relative to the concentrations of the major constituents of the atmosphere is well known and varies slowly and by a small enough amount to be considered constant for calibration in the present context. Hence, absorption-spectral measurements of the concentrations of gases of interest can be normalized to the concentrations of CO2. Because at least one CO2 calibration line is present in every spectral scan of the laser during absorption measurements, the atmospheric CO2 serves continuously as a calibration standard for every measurement point. Figure 1 depicts simulated spectral transmission measurements in a wavenumber range that contains two absorption lines of N2O and one of CO2. The simulations were performed for two different upper-atmospheric pressures for an airborne instrument that has a path length of 80 m. The relative abundance of CO2 in air was assumed to be 360 parts per million by volume (approximately its natural level in terrestrial air). In applying the present method to measurements like these, one could average the signals from the two N2O absorption lines and normalize their magnitudes to that of the CO2 absorption line. Other gases with which this calibration method can be used include H2O, CH4, CO, NO, NO2, HOCl, C2H2, NH3, O3, and HCN. One can also take advantage of this method to eliminate an atmospheric-pressure gauge and thereby reduce the mass of the instrument: The atmospheric pressure can be calculated from the temperature, the known relative abundance of CO2, and the concentration of CO2 as measured by spectral absorption. Natural CO2 levels on Mars provide an ideal calibration standard. Figure 2 shows a second example of the application of this method to Mars atmospheric gas measurements. For sticky gases like H2O, the method is particularly powerful, since water is notoriously difficult to handle at low concentrations in pre-flight calibration procedures.

Webster, Chris↗
NASA NTRS2008

Using LDPC Code Constraints to Aid Recovery of Symbol Timing

A method of utilizing information available in the constraints imposed by a low-density parity-check (LDPC) code has been proposed as a means of aiding the recovery of symbol timing in the reception of a binary-phase-shift-keying (BPSK) signal representing such a code in the presence of noise, timing error, and/or Doppler shift between the transmitter and the receiver. This method and the receiver architecture in which it would be implemented belong to a class of timing-recovery methods and corresponding receiver architectures characterized as pilotless in that they do not require transmission and reception of pilot signals. Acquisition and tracking of a signal of the type described above have traditionally been performed upstream of, and independently of, decoding and have typically involved utilization of a phase-locked loop (PLL). However, the LDPC decoding process, which is iterative, provides information that can be fed back to the timing-recovery receiver circuits to improve performance significantly over that attainable in the absence of such feedback. Prior methods of coupling LDPC decoding with timing recovery had focused on the use of output code words produced as the iterations progress. In contrast, in the present method, one exploits the information available from the metrics computed for the constraint nodes of an LDPC code during the decoding process. In addition, the method involves the use of a waveform model that captures, better than do the waveform models of the prior methods, distortions introduced by receiver timing errors and transmitter/ receiver motions. An LDPC code is commonly represented by use of a bipartite graph containing two sets of nodes. In the graph corresponding to an (n,k) code, the n variable nodes correspond to the code word symbols and the n-k constraint nodes represent the constraints that the code places on the variable nodes in order for them to form a valid code word. The decoding procedure involves iterative computation of values associated with these nodes. A constraint node represents a parity-check equation using a set of variable nodes as inputs. A valid decoded code word is obtained if all parity-check equations are satisfied. After each iteration, the metrics associated with each constraint node can be evaluated to determine the status of the associated parity check. Heretofore, normally, these metrics would be utilized only within the LDPC decoding process to assess whether or not variable nodes had converged to a codeword. In the present method, it is recognized that these metrics can be used to determine accuracy of the timing estimates used in acquiring the sampled data that constitute the input to the LDPC decoder. In fact, the number of constraints that are satisfied exhibits a peak near the optimal timing estimate. Coarse timing estimation (or first-stage estimation as described below) is found via a parametric search for this peak. The present method calls for a two-stage receiver architecture illustrated in the figure. The first stage would correct large time delays and frequency offsets; the second stage would track random walks and correct residual time and frequency offsets. In the first stage, constraint-node feedback from the LDPC decoder would be employed in a search algorithm in which the searches would be performed in successively narrower windows to find the correct time delay and/or frequency offset. The second stage would include a conventional first-order PLL with a decision-aided timing-error detector that would utilize, as its decision aid, decoded symbols from the LDPC decoder. The method has been tested by means of computational simulations in cases involving various timing and frequency errors. The results of the simulations ined in the ideal case of perfect timing in the receiver.

Jones, Christopher↗
DOE OSTI2021

Quantitative Evaluation of Top Coal Caving Methods at the Working Face of Extra‐Thick Coal Seams Based on the Random Medium Theory

Adopting an effective top coal caving method is the key to enhancing coal recovery and reducing gangue content for the fully mechanized top coal caving working face with extra‐thick coal seams. In this study, the movement of coal particles generated during top coal caving is considered to follow a normal distribution. Then, the caving body and coal‐rock settlement along the working face during the caving process are studied based on both the random media theory and probability theory. Accordingly, the optimal caving interval and caving sequences are determined, and a novel interval symmetrical coal caving method is proposed. The proposed method is systematically verified with results from physical similarity tests, and different caving methods are assessed by field tests. The results show the following: (1) The coal‐rock settlement and the caving body demonstrate clear axial symmetrical features along the working face; the size of the caving body increases as the caving height grows and its shape turns progressively from semicircular to semielliptical with a lower foot of the coal‐rock settlement. (2) The caving interval is derived using the sum of the radii of the coal‐rock settlement curves formed by the two largest caving bodies. (3) The symmetrical caving approach provides a symmetrical space for the subsequent movement of the broken top coal, which enables a uniform development of the caving body. (4) Compared with the traditional sequential coal caving method with the same number of supports, the interval symmetrical caving method results in a 21.7% of coal production increase, 17% caving rate promotion, and a shortened caving time by 23.4%. (5) The interval symmetrical caving method is found to improve the controllability of the caving process at the fully mechanized top coal caving working face. In general, this work presents a theoretical approach to select the optimal caving methods for the fully mechanized caving working face in extra‐thick coal seams for an improved production efficiency of the work face. The results of this study can also provide theoretical significance and referencing value for quantitative analyses of the coal caving methods for work faces with similar geological conditions.

Jiulin, Shi (ORCID:0000000155819062)↗
NASA NTRS2012

Launch Method for Kites in Low-Wind or No-Wind Conditions

Airborne observations using lightweight camera systems are desirable for a variety of applications. This system was contemplated as a method to provide a simple remote sensing aerial platform. Kites have been successfully employed for aerial observations, but have historically required natural wind or towing to become airborne. This new method negates this requirement, and widens the applicability of kites for carrying instrumentation. Applicability is primarily limited by the space available on the ground for launching. The innovation is a method for launching kites in low-wind or no-wind conditions. This method will enable instrumentation to be carried aloft using simple (or complex) kite-based systems, to obtain observations from an aerial perspective. This technique will provide access to altitudes of 100 meters or more over any area normally suited for kite flying. The duration of any observation is dependent on wind strength; however, the initial altitude is relatively independent. The system does not require any electrical or combustion-based elements. This technology was developed to augment local-scale airborne measurement capabilities suitable for Earth science research, agricultural productivity, and environmental observations. The method represents an extension of techniques often used in aeronautical applications for launching fixed-wing aircraft, such as sailplanes, using mechanical means not incorporated in the aircraft itself. The innovation consists of an elastic cord (for propulsive force), a tether extension (optional, for additional height), and the kite (instrumentation optional). Operation of the system is accomplished by fixing the elastic cord to ground (or equivalent), attaching the cord with/or without a tether extension to the kite, tensioning the system to store energy, and releasing the kite. The kite will climb until energy is dissipated.

Bland, Geoffrey↗
NASA NTRS2011

Temperature-Sensitive Coating Sensor Based on Hematite

A temperature-sensitive coating, based on hematite (iron III oxide), has been developed to measure surface temperature using spectral techniques. The hematite powder is added to a binder that allows the mixture to be painted on the surface of a test specimen. The coating dynamically changes its relative spectral makeup or color with changes in temperature. The color changes from a reddish-brown appearance at room temperature (25 C) to a black-gray appearance at temperatures around 600 C. The color change is reversible and repeatable with temperature cycling from low to high and back to low temperatures. Detection of the spectral changes can be recorded by different sensors, including spectrometers, photodiodes, and cameras. Using a-priori information obtained through calibration experiments in known thermal environments, the color change can then be calibrated to yield accurate quantitative temperature information. Temperature information can be obtained at a point, or over an entire surface, depending on the type of equipment used for data acquisition. Because this innovation uses spectrophotometry principles of operation, rather than the current methods, which use photoluminescence principles, white light can be used for illumination rather than high-intensity short wavelength excitation. The generation of high-intensity white (or potentially filtered long wavelength light) is much easier, and is used more prevalently for photography and video technologies. In outdoor tests, the Sun can be used for short durations as an illumination source as long as the amplitude remains relatively constant. The reflected light is also much higher in intensity than the emitted light from the inefficient current methods. Having a much brighter surface allows a wider array of detection schemes and devices. Because color change is the principle of operation, the development of high-quality, lower-cost digital cameras can be used for detection, as opposed to the high-cost imagers needed for intensity measurements with the current methods. Alternative methods of detection are possible to increase the measurement sensitivity. For example, a monochrome camera can be used with an appropriate filter and a radiometric measurement of normalized intensity change that is proportional to the change coating temperature. Using different spectral regions yields different sensitivities and calibration curves for converting intensity change to temperature units. Alternatively, using a color camera, a ratio of the standard red, green, and blue outputs can be used as a self-referenced change. The blue region (less than 500 nm) does not change nearly as much as the red region (greater than 575 nm), so a ratio of color intensities will yield a calibrated temperature image. The new temperature sensor coating is easy to apply, is inexpensive, can contour complex shape surfaces, and can be a global surface measurement system based on spectrophotometry. The color change, or relative intensity change, at different colors makes the optical detection under white light illumination, and associated interpretation, much easier to measure and interpret than in the detection systems of the current methods.

Bencic, Timothy J.↗
NASA NTRS2009

Space Systems - Safety and Compatibility of Materials - Method to Determine the Flammability Thresholds of Materials

Spacecraft fire safety emphasizes fire prevention, which is achieved primarily through the use of fire-resistant materials. Materials selection for spacecraft is based on conventional flammability acceptance tests, along with prescribed quantity limitations and configuration control for items that are non-pass or questionable. ISO 14624-1 and -2 are the major methods used to evaluate flammability of polymeric materials intended for use in the habitable environments of spacecraft. The methods are upward flame-propagation tests initiated in static environments and using a well-defined igniter flame at the bottom of the sample. The tests are conducted in the most severe flaming combustion environment expected in the spacecraft. The pass/fail test logic of ISO 14624-1 and -2 does not allow a quantitative comparison with reduced gravity or microgravity test results; therefore their use is limited, and possibilities for in-depth theoretical analyses and realistic estimates of spacecraft fire extinguishment requirements are practically eliminated. To better understand the applicability of laboratory test data to actual spacecraft environments, a modified ISO 14624 protocol has been proposed that, as an alternative to qualifying materials as pass/fail in the worst-expected environments, measures the actual upward flammability limit for the material. A working group established by NASA to provide recommendations for exploration spacecraft internal atmospheres realized the importance of correlating laboratory data with real-life environments and recommended NASA to develop a flammability threshold test method. The working group indicated that for the Constellation Program, the flammability threshold information will allow NASA to identify materials with increased flammability risk from oxygen concentration and total pressure changes, minimize potential impacts, and allow for development of sound requirements for new spacecraft and extravehicular landers and habitats. Furthermore, recent research has shown that current normal gravity materials flammability tests do not correlate with flammability in ventilated, micro- or reduced-gravity conditions. Currently, the materials selection for spacecraft is based on the assumption of commonality between ground flammability test results and spacecraft environments, which does not appear to be valid. Materials flammability threshold data acquired in normal gravity can be correlated with data obtained in microgravity or reduced-gravity experiments, and consequently a more accurate assessment of the margin of safety of the material in the real environment can be made. In addition, the method allows the option of selecting better or best space system materials, as opposed to what would be considered just acceptable from a flammability point of view and realistic assessment of spacecraft fire extinguishment needs, which could result in significant weight savings. The knowledge afforded by this technique allows for limited extrapolations of flammability behavior to conditions not specifically tested and that could potentially result in significant cost and time savings. The intent of this Technical Specification is to bring to the attention of International Aerospace Community the importance of correlating laboratory test data with real-life space systems applications. The method presented is just one of the possibilities that are believed will lead to better understanding the applicability of laboratory aerospace materials flammability test data. International feedback on improving the proposed method, as well as suggestions for correlating other laboratory aerospace test data with real-life applications relevant to space systems are being sought.

Hirsch, David↗
DOE OSTI2020

Low synchronization Gram–Schmidt and generalized minimal residual algorithms

The Gram–Schmidt process uses orthogonal projection to construct the A = QR factorization of a matrix. When Q has linearly independent columns, the operator P = I - Q(QTQ)-1QT defines an orthogonal projection onto Q⊥. In finite precision, Q loses orthogonality as the factorization progresses. A family of approximate projections is derived with the form P = I - QTQT, with correction matrix T. When T = (QTQ)-1, and T is triangular, it is postulated that the best achievable orthogonality is $\mathcal{O}(ε)\mathcal{K}(A)$. We present new variants of modified (MGS) and classical Gram–Schmidt algorithms that require one global reduction step. An interesting form of the projector leads to a compact WY representation for MGS. In particular, the inverse compact WY MGS algorithm is equivalent to a lower triangular solve. Our main contribution is to introduce a backward normalization lag into the compact WY representation, resulting in a $\mathcal{O}(ε)\mathcal{K}[r_0, AV_m])$ stable Generalized Minimal Residual Method (GMRES) algorithm that requires only one global reduce per iteration. Finally, further improvements in performance are achieved by accelerating GMRES on GPUs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Correlations between thermal history and keyhole porosity in laser powder bed fusion

Additive manufacturing has the potential to revolutionize the production of metallic components as it yields near net shape parts with complex geometries and minimizes waste. At the present day, additively manufactured components face qualification and certification challenges due to the difficulty in controlling defects. This has driven a significant research effort aimed at better understanding and improving processing controls – yielding a plethora of in-situ measurements aimed at correlating defects with material quality metrics of interest. In this work, we develop machine-learning methods to learn correlations between thermal history and subsurface porosity for a variety of print conditions in laser powder bed fusion. Un-normalized surface temperatures (in the form of black-body radiances) are obtained using high-speed infrared imaging and porosity formation is observed in the sample cross-section through synchrotron x-ray imaging. To demonstrate the predictive power of these features, we present four statistical machine-learning models that correlate temperature histories to subsurface porosity formation in laser fused Ti-6Al4V powder.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Controlling T c of iridium films using the proximity effect

A superconducting Transition-Edge Sensor (TES) with low-$T_c$ is essential in a high resolution calorimetric detection. With a motivation of developing sensitive calorimeters for applications in cryogenic neutrinoless double beta decay searches, we have been investigating methods to reduce the $T_c$ of an Ir film down to 20 mK. Utilizing the proximity effect between a superconductor and a normal metal, we found two room temperature fabrication recipes of making Ir-based low-$T_c$ films. In the first approach, an Ir film sandwiched between two Au films, a Au/Ir/Au trilayer, has a tunable $T_c$ in the range of 20-100 mK depending on the relative thicknesses. In the second approach, a paramagnetic Pt thin film is used to create Ir/Pt bilayer with a tunable $T_c$ in the same range. We present detailed study of fabrication and characterization of Ir-based low-$T_c$ films, and compare the experimental results to theoretical models. We show that Ir-based films with predictable and reproducible critical temperature can be consistently fabricated for use in large scale detector applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Structure of a chaotic tangle of quantum vortices in turbulent superfluid liquids and in a Bose – Einstein condensate

Based on the theory of the thermodynamic equilibrium in a system of quantum vortices in superfluid liquids and in a Bose – Einstein condensate in the presence of a counterflow of normal and superfluid components, we investigate the structure of a chaotic tangle of quantum vortices in turbulent superfluid liquids. Using the characteristic functional method, the properties of hydrodynamic vortex filaments are examined. It is shown that the average curvature of the vortex lines is on the order of the intervortex distance, with the proportionality coefficient being independent of the counterflow velocity. It is found that the degree of anisotropy of the vortex loops does not depend on the applied counterflow velocity. The obtained results explain the origin of the anisotropy as well as the relationship between the curvature of the lines and the intervortex space and their dependence on the parameters of the problem. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Graph convolutional networks applied to unstructured flow field data

Abstract Many scientific and engineering processes produce spatially unstructured data. However, most data-driven models require a feature matrix that enforces both a set number and order of features for each sample. They thus cannot be easily constructed for an unstructured dataset. Therefore, a graph based data-driven model to perform inference on fields defined on an unstructured mesh, using a graph convolutional neural network (GCNN) is presented. The ability of the method to predict global properties from spatially irregular measurements with high accuracy is demonstrated by predicting the drag force associated with laminar flow around airfoils from scattered velocity measurements. The network can infer from field samples at different resolutions, and is invariant to the order in which the measurements within each sample are presented. The GCNN method, using inductive convolutional layers and adaptive pooling, is able to predict this quantity with a validation R 2 above 0.98, and a Normalized Mean Squared Error below 0.01, without relying on spatial structure.

Ogoke, Francis (ORCID:0000000224327783)↗
DOE OSTI2021

MgPd 2 Sb : A Mg-based Heusler-type superconductor

Here, we report the synthesis and physical properties of a full Heusler compound, MgPd 2 Sb, which we found to show superconductivity below T c = 2.2 K . MgPd 2 Sb was obtained by a two-step solid-state reaction method and its purity and cubic crystal structure [Fm-3m, a = 6.4523(1) Å ] were confirmed by powder x-ray diffraction. Normal and superconducting states were studied by electrical resistivity, magnetic susceptibility, and heat capacity measurements. The results show that MgPd 2 Sb is a type-II, weak coupling superconductor ( λ e-p = 0.53 ). The observed pressure dependence of T c (ΔT c /p ≈ -0.23 K / GPa ) is one of the strongest reported for a superconducting Heusler compound. The electronic structure, phonons, and electron-phonon coupling in MgPd 2 Sb were theoretically investigated. The obtained results are in agreement with the experiment, confirming the electron-phonon coupling mechanism of superconductivity. We compare the superconducting parameters to those of all reported Heusler-type superconductors.

36 MATERIALS SCIENCE↗
DOE OSTI2020

sta-imex (scripts to investigate stability of IMEX methods)

Set of Matlab scripts to investigate properties of IMEX time stepping methods. Scripts include discretization of a system of linearized equations. One script plots numerical dispersion against analytical dispersion of the system. Another set of scripts uses the system to break it into stiff and non stiff part to investigate stability of Implicit-Explicit Runge-Kutta methods. Scripts are based on Thuburn, J. and Woollings, T. J., Vertical Discretizations for Compressible Euler Equation Atmospheric Models Giving Optimal Representation of Normal Modes , 2005 and Lock, S.-J. and Wood, N. and Weller, H., Numerical analyses of Runge-Kutta implicit-explicit schemes for horizontally explicit, vertically implicit solutions of atmospheric models, 2014 expanding ideas from these two papers. Scripts are used to develop IMEX schemes. SAND2020-12594 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.

Guba, Oksana↗