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NASA NTRS2013

Autonomous Control of Space Nuclear Reactors

Nuclear reactors to support future robotic and manned missions impose new and innovative technological requirements for their control and protection instrumentation. Long-duration surface missions necessitate reliable autonomous operation, and manned missions impose added requirements for failsafe reactor protection. There is a need for an advanced instrumentation and control system for space-nuclear reactors that addresses both aspects of autonomous operation and safety. The Reactor Instrumentation and Control System (RICS) consists of two functionally independent systems: the Reactor Protection System (RPS) and the Supervision and Control System (SCS). Through these two systems, the RICS both supervises and controls a nuclear reactor during normal operational states, as well as monitors the operation of the reactor and, upon sensing a system anomaly, automatically takes the appropriate actions to prevent an unsafe or potentially unsafe condition from occurring. The RPS encompasses all electrical and mechanical devices and circuitry, from sensors to actuation device output terminals. The SCS contains a comprehensive data acquisition system to measure continuously different groups of variables consisting of primary measurement elements, transmitters, or conditioning modules. These reactor control variables can be categorized into two groups: those directly related to the behavior of the core (known as nuclear variables) and those related to secondary systems (known as process variables). Reliable closed-loop reactor control is achieved by processing the acquired variables and actuating the appropriate device drivers to maintain the reactor in a safe operating state. The SCS must prevent a deviation from the reactor nominal conditions by managing limitation functions in order to avoid RPS actions. The RICS has four identical redundancies that comply with physical separation, electrical isolation, and functional independence. This architecture complies with the safety requirements of a nuclear reactor and provides high availability to the host system. The RICS is intended to interface with a host computer (the computer of the spacecraft where the reactor is mounted). The RICS leverages the safety features inherent in Earth-based reactors and also integrates the wide range neutron detector (WRND). A neutron detector provides the input that allows the RICS to do its job. The RICS is based on proven technology currently in use at a nuclear research facility. In its most basic form, the RICS is a ruggedized, compact data-acquisition and control system that could be adapted to support a wide variety of harsh environments. As such, the RICS could be a useful instrument outside the scope of a nuclear reactor, including military applications where failsafe data acquisition and control is required with stringent size, weight, and power constraints.

Merk, John↗

NASA NTRS1980

Moon and earth - Compositional differences inferred from siderophiles, volatiles, and alkalis in basalts

A comparison of RNAA analyses of 18 trace elements in 25 low-Ti lunar and 10 terrestrial oceanic basalts indicated that the volatiles such as Ag, Bi, and Br are depleted in lunar basalts by nearly constant factors of 0.026 relative to terrestrial basalts. This constancy is not consistent with models that derive the moon's volatiles from partial recondensation of the earth's mantle or from partial degassing of a captured body; it is consistent with models which derive planetary volatiles from a thin veneer of C-chondrite material. Chalcogens (Se and Te) have almost constant and identical abundances in lunar and terrestrial basalts; siderophiles show abundant Ni in lunar basalts, while Ir, Re, Ge, and Au are depleted.

Wolf, R.↗

NASA NTRS1988

Determination of the Venus flyby orbits of the Soviet Vega probes using VLBI techniques

In December 1984, the Soviet Union launched two identical Vega spacecraft with the dual objective of exploring Venus and continuing to rendezvous with the comet Halley. The two Vega spacecraft encountered Venus in mid-June 1985 and successfully deployed entry probes and wind-measuring balloons into the Venus atmosphere. An objective of the Venus Balloon experiment was to measure the Venus winds using differential VLBI from the balloon and the flyby bus. NASA's Deep Space 64 meter subnet was part of a world wide network organized to collect data from the Vega probes and balloons. A critical element of this experiment was an accurate determination of the Venus relative flyby orbits of the Vega spacecraft during the 46 hour balloon lifetime. Venus flyby solutions were independently determined by the Soviets using two-way range and Doppler from Soviet stations and by JPL using one-way Doppler and VLBI data collected from the DSN. The Vega flyby solutions determined by the Soviets using a sparse two-way tracking strategy with JPL solutions using the DSN VLBI data to complement the Soviet data and with solutions using only one-way data collected by the DSN were compared.

Ellis, J.↗

NASA NTRS2006

Developmental Flight Instrumentation System for the Crew Launch Vehicle

The National Aeronautics and Space Administration is developing a new launch vehicle to replace the Space Shuttle. The Crew Launch Vehicle (CLV) will be a combination of new design hardware and heritage Apollo and Space Shuttle hardware. The current CLV configuration is a 5 segment solid rocket booster first stage and a new upper stage design with a modified Apollo era J-2 engine. The current schedule has two test flights with a first stage and a structurally identical, but without engine, upper stage. Then there will be two more test flights with a full complement of flight hardware. After the completion of the test flights, the first manned flight to the International Space Station is scheduled for late 2012. To verify the CLV's design margins a developmental flight instrumentation (DFI) system is needed. The DFI system will collect environmental and health data from the various CLV subsystem's and either transmit it to the ground or store it onboard for later evaluation on the ground. The CLV consists of 4 major elements: the first stage, the upper stage, the upper stage engine and the integration of the first stage, upper stage and upper stage engine. It is anticipated that each of CLVs elements will have some version of DFI. This paper will discuss a conceptual DFI design for each element and also of an integrated CLV DFI system.

Crawford, Kevin↗

NASA NTRS1982

Operator split methods in the numerical solution of the finite deformation elastoplastic dynamic problem

The spatial formulation of the elastoplastic dynamic problem for finite deformations is considered. A thermodynamic argument leads to an additive decomposition of the spatial rate of deformation tensor and allows an operator split of the evolutionary equations of the problem into elastic and plastic parts. This operator split is taken as the basis for the definition of a global product algorithm. In the context of finite element discretization the product algorithm entails, for every time step, the solution of a nonlinear elastodynamic problem followed by the application of plastic algorithms that operate on the stresses and internal variables at the integration points and bring in the plastic constitutive equations. Suitable plastic algorithms are discussed for the cases of perfect and hardening plasticity and viscoplasticity. The proposed formalism does not depend on any notion of smoothness of the yield surface and is applicable to arbitrary convex elastic regions, with or without corners. The stabiity properties of the global product algorithm are shown to be identical to those of the algorithm used for the integration of the nonlinear elastodynamic problem. Numerical examples illustrate the accuracy of the method.

Pinsky, P. M.↗

NASA NTRS2016

Modeling Fatigue Damage Onset and Progression in Composites Using an Element-Based Virtual Crack Closure Technique Combined With the Floating Node Method

A new methodology is proposed to model the onset and propagation of matrix cracks and delaminations in carbon-epoxy composites subject to fatigue loading. An extended interface element, based on the Floating Node Method, is developed to represent delaminations and matrix cracks explicitly in a mesh independent fashion. Crack propagation is determined using an element-based Virtual Crack Closure Technique approach to determine mixed-mode energy release rates, and the Paris-Law relationship to obtain crack growth rate. Crack onset is determined using a stressbased onset criterion coupled with a stress vs. cycle curve and Palmgren-Miner rule to account for fatigue damage accumulation. The approach is implemented in Abaqus/Standard® via the user subroutine functionality. Verification exercises are performed to assess the accuracy and correct implementation of the approach. Finally, it was demonstrated that this approach captured the differences in failure morphology in fatigue for two laminates of identical stiffness, but with layups containing θdeg plies that were either stacked in a single group, or distributed through the laminate thickness.

De Carvalho, Nelson V.↗

NASA NTRS1993

B-DNA to Z-DNA structural transitions in the SV40 enhancer: stabilization of Z-DNA in negatively supercoiled DNA minicircles

During replication and transcription, the SV40 control region is subjected to significant levels of DNA unwinding. There are three, alternating purine-pyrimidine tracts within this region that can adopt the Z-DNA conformation in response to negative superhelix density: a single copy of ACACACAT and two copies of ATGCATGC. Since the control region is essential for both efficient transcription and replication, B-DNA to Z-DNA transitions in these vital sequence tracts may have significant biological consequences. We have synthesized DNA minicircles to detect B-DNA to Z-DNA transitions in the SV40 enhancer, and to determine the negative superhelix density required to stabilize the Z-DNA. A variety of DNA sequences, including the entire SV40 enhancer and the two segments of the enhancer with alternating purine-pyrimidine tracts, were incorporated into topologically relaxed minicircles. Negative supercoils were generated, and the resulting topoisomers were resolved by electrophoresis. Using an anti-Z-DNA Fab and an electrophoretic mobility shift assay, Z-DNA was detected in the enhancer-containing minicircles at a superhelix density of -0.05. Fab saturation binding experiments demonstrated that three, independent Z-DNA tracts were stabilized in the supercoiled minicircles. Two other minicircles, each with one of the two alternating purine-pyrimidine tracts, also contained single Z-DNA sites. These results confirm the identities of the Z-DNA-forming sequences within the control region. Moreover, the B-DNA to Z-DNA transitions were detected at superhelix densities observed during normal replication and transcription processes in the SV40 life cycle.

Non-NASA Center↗

NASA NTRS1979

Path dependence of J in three numerical examples

Three cracked geometries are studied with the aid of a new finite element model. The procedure employs a variable singularity at the crack tip that tracks changes in the material response during the loading process. Two of the problems are tension-loaded center-crack panels and the other is a three-point bend specimen. Results usually agree with other numerical and analytical analyses, except the finding that J is path dependent as a substantial plastic zone develops. Credible J values are obtained near the crack tip and J shows a significant increase as the radius of J path increases over two orders of magnitude. Incremental and deformation theories are identical provided the stresses exhibit proportionality found in the far field stresses but not near the tip.

Karabin, M. E., Jr.↗

NASA NTRS2001

Inherent and Apparent Scattering Properties of Coated or Uncoated Spheres Embedded in an Absorbing Host Medium

The conventional Lorenz-Mie formalism is extended to the scattering process associated with a coated sphere embedded in an absorbing medium. It is shown that apparent and inherent scattering cross sections of a scattering particle, which are identical in the case of transparent host medium, are different if the host medium is absorptive. Here the inherent single-scattering properties are derived from the near-field information whereas the corresponding apparent counterparts are derived from the far-field asymptotic form of the scattered wave with scaling of host absorption that is assumed to be in an exponential form. The formality extinction and scattering efficiencies defined in the same manner as in the conventional sense can be unbounded. For a nonabsorptive particle embedded in an absorbing medium, the effect of host absorption on the phase matrix elements associated with polarization is significant. This effect, however, is largely reduced for strongly absorptive particles such as soot. For soot particles coated with water, the impurity can substantially reduce the single-scattering albedo of the particle if the size parameter is small. For water-coating soot and hollow ice spheres, it is shown that the phase matrix elements -P(sub 12)/P(sub 11) and P(sub 33)/P(sub 11) are unique if the shell is thin, as compared with the case for thick shell. Furthermore, the radiative transfer equation regarding a multidisperse particle system in an absorbing medium is discussed. It is illustrated that the conventional computation algorithms can be applied to solve the multiple scattering process if the scaled apparent single-scattering properties are applied.

Yang, P.↗

NASA NTRS2017

The Amorphous Composition of Three Mudstone Samples from Gale Crater: Implications for Weathering and Diagenetic Processes on Mars

The Mars Science Laboratory rover, Curiosity, is exploring the lowermost formation of Gale crater's central mound. Within this formation, three samples named Marimba, Quela, and Sebina have been analyzed by the CheMin X-ray diffractometer and the Alpha Particle X-ray Spectrometer (APXS) to determine mineralogy and bulk elemental chemistry, respectively. Marimba and Quela were also analyzed by the SAM (Sample Analysis at Mars) instrument to characterize the type and abundance of volatile phases detected in evolved gas analyses (EGA). CheMin data show similar proportions of plagioclase, hematite, and Ca-sulfates along with a mixture of di- and trioctahedral smectites at abundances of approximately 28, approximately 16, and approximately 18 wt% for Marimba, Quela, and Sebina. Approximately 50 wt% of each mudstone is comprised of X-ray amorphous and trace crystalline phases present below the CheMin detection limit (approximately 1 wt%). APXS measurements reveal a distinct bulk elemental chemistry that cannot be attributed to the clay mineral variation alone indicating a variable amorphous phase assemblage exists among the three mudstones. To explore the amorphous component, the calculated amorphous composition and SAM EGA results are used to identify amorphous phases unique to each mudstone. For example, the amorphous fraction of Marimba has twice the FeO wt% compared to Quela and Sebina yet, SAM EGA data show no evidence for Fe-sulfates. These data imply that Fe must reside in alternate Fe-bearing amorphous phases (e.g., nanophase iron oxides, ferrihydrite, etc.). Constraining the composition, abundances, and proposed identity of the amorphous fraction provides an opportunity to speculate on the past physical, chemical, and/or diagenetic processes which produced such phases in addition to sediment sources, lake chemistry, and the broader geologic history of Gale crater.

Achilles, C. N.↗

NASA NTRS1988

Thermal cycling of tungsten-fibre-reinforced superalloy composites

The thermal cycling of a tungsten-fiber-reinforced superalloy (TFRS) composite is typical of its application in high-temperature engine environments. The mismatch in thermal expansion coefficients between fiber and matrix causes substantial longitudinal (0 deg) stresses in the composite, which can produce inelastic damage-producing matrix strains. The case of thermal fatigue is explored as a "worst case" of the possible matrix damage, in comparison with specimens which are also mechanically loaded in tension. The thermally generated cyclic stresses and the attendant matrix plasticity may be estimated using a nonlinear finite-element program, by proposing a physical analog to the micromechanics equations. A damage metric for the matrix is proposed using the Coffin-Manson criterion, which metric can facilitate comparisons of damage among different candidate materials, and also comparisons for a given material subjected to different temperature cycles. An experimental program was carried out for thermal cycling of a 37 vol pct TFRS composite to different maximum temperatures. The results confirm the prediction that thermal cycling produces matrix degradation and composite strength reduction, which become more pronounced with increasing maximum cyclic temperature. The strength of the fiber is shown to be identical for the as-fabricated and thermally cycled specimens, suggesting that the reduction in composite strength is due to the loss of matrix contribution and also to notching effects of the matrix voids on the fiber.

Wetherhold, Robert C.↗

NASA NTRS2007

Not So Rare Earth? New Developments in Understanding the Origin of the Earth and Moon

A widely accepted model for the origin of the Earth and Moon has been a somewhat specific giant impact scenario involving an impactor to proto-Earth mass ratio of 3:7, occurring 50-60 Ma after T(sub 0), when the Earth was only half accreted, with the majority of Earth's water then accreted after the main stage of growth, perhaps from comets. There have been many changes to this specific scenario, due to advances in isotopic and trace element geochemistry, more detailed, improved, and realistic giant impact and terrestrial planet accretion modeling, and consideration of terrestrial water sources other than high D/H comets. The current scenario is that the Earth accreted faster and differentiated quickly, the Moon-forming impact could have been mid to late in the accretion process, and water may have been present during accretion. These new developments have broadened the range of conditions required to make an Earth-Moon system, and suggests there may be many new fruitful avenues of research. There are also some classic and unresolved problems such as the significance of the identical O isotopic composition of the Earth and Moon, the depletion of volatiles on the lunar mantle relative to Earth's, the relative contribution of the impactor and proto-Earth to the Moon's mass, and the timing of Earth's possible atmospheric loss relative to the giant impact.

Righter, Kevin↗

NASA NTRS1990

Optimum structural design of robotic manipulators with fiber reinforced composite materials

High-speed robotic arms with advanced structural characteristics can be fabricated from optimally tailored fiber reinforced composites. An integrated design methodology is presented for the optimal structural synthesis of composite robotic manipulators. Optimum configurations of ply angles and ply thicknesses are predicted for maximum structural end-effector stiffness and maximum end-effector load carrying capacity, without altering the geometric dimensions of the links. Multiple posture finite element-based static performance criteria are implemented. A new finite element has been developed for the modeling of tubular composite links. Unique features are the inclusion of shear effects and coupling between stretching and flexure. Numerical solutions are obtained via an efficient optimization algorithm. Applications to an existing SCARA-class manipulator illustrate the effectiveness of the method and demonstrate the dramatic influence of the multi-postural design criteria on the optimal design. For a filament wound structure using a high strength carbon fiber in a thermoplastic matrix, the resultant optimum ply configurations have increased the specific stiffness and specific load capacity by factors of 1.5 and 16, respectively, in comparison to identically sized aluminum links.

Saravanos, D. A.↗

NASA NTRS2019

TPSAS-NF1676L-32920-DND

In June 2019, a full-scale crash test of a Fokker F28 Fellowship aircraft will be conducted at NASA Langley Research Center?s Landing and Impact Research (LandIR) Facility. The F28 is a high-performance twin-turbo fan narrow-body aircraft with seating in a 3+2 configuration. The MK4000 variant, used in this test, is capable of carrying up to 85 passengers on medium range routes. The F28 was first type certified by the Federal Aviation Administration (FAA) in 1969 and now the majority of the F28 fleet has retired from service in the United States. In 2016, the FAA and NASA Langley Research Center (LaRC) signed an interagency agreement for conducting a research program to obtain test data that will support the development of airframe level crash requirements for transport category airplanes [1]. The objectives of the full-scale crash test can be divided into six categories: (1) To compare and contrast responses in identical aircraft undergoing vertical only to combined vertical and horizontal loading conditions, (2) To examine the effects of horizontal loading on aircraft structure during a crash event, (3) To generate data for the use in calibration of computer modelling efforts, (4) To generate data from onboard Anthropomorphic Test Devices (ATDs) for the evaluation of injury, (5) To obtain data from experimental seats, and (6) To obtain data from new and novel ATD designs including Warrior Injury Assessment MANikin (WIAMan) [2], Test device for Human Occupant Response (THOR), and other newly developed child ATDs. The focus of this presentation will be to document finite element model development of the full-scale F28 aircraft and to present preliminary test-analysis predictions. NASA obtained the full-scale F28 aircraft, plus three fuselage sections and two sets of wings with funding through the NASA Aviation Safety Program in 1998. In addition to the hardware, NASA purchased a full NASTRAN model of the airframe that had been developed by the Dutch manufacturer, Fokker. Beginning in 2016, the NASTRAN model was converted to LS-DYNA? [4, 5] format and modified by combining parts, adding missing parts of internal structure, and including ballast for loading weights, etc. It contains: 89,223 nodes; 24,065 beam elements; 55,404 shell elements; 29,044 solid elements; 740 parts; 80 material definitions; and, 46 Constrained Nodal Rigid Bodies (CNRBs). The aircraft model will be executed in LSDYNA to simulate the test article impact onto a 2-ft.-high bed of soil under combined velocity conditions of 70-ft/s forward and 30-ft/s vertical velocity. Pre-test simulation predictions will be generated and correlated with test data.

Karen E Jackson↗

NASA NTRS2009

The GLACE-2 Experiment

A major motivation for the study of the coupled land-atmosphere system is the idea that soil moisture anomalies may affect future meteorological variables through their effects on future surface energy and water budgets. If true, the accurate initialization of soil moisture in a subseasonal or seasonal forecast system may improve forecast skill, making the forecast products more valuable to society. The Global Land-Atmosphere Coupling Experiment (GLACE-2) project is examining, with a wide variety of models, the degree to which subseasonal (out to two months) precipitation and air temperature forecasts improve through the realistic initialization of soil moisture. For the first time ever, a global consensus should emerge regarding the value of land initialization for forecasts, perhaps motivating national forecast centers to make full use of land moisture initialization in their operations. Participants in GLACE-2 perform two series of forecasts, each consisting of 100 2-month forecast ensembles (10 members per ensemble) covering ten boreal spring and summer start-dates in each of the years 1986-1995. Series 1 utilizes realistic land surface state initialization, provided through a decadal offline simulation using realistic meteorological forcing, as provided by the Global Soil Wetness Project - Phase 2 (GSWP-2), a research activity of the Global Land-Atmosphere System Study (GLASS) of GEWEX. Series 2 is identical to Series 1 in every way except for the fact that it does not benefit from realistic land state initialization. Through the comparison of Series 1 and 2, we isolate the impact of land initialization on the forecasts. Optional extensions to these base runs include forecasts covering additional years, using alternative meteorological forcing for the land initialization. To date, GLACE-2 has garnered participation from eleven modeling groups, covering 13 atmospheric models. Analysis of available results is already well underway, both at the individual modeling institutions and at the NASA Goddard Space Flight Center, which is coordinating the project. Analysis focuses on two elements of the forecast problem: (i) the quantification of model-specific "predictability" (i.e., the degree to which simulated atmospheric chaos will foil a forecast, even under the assumption of"perfect" model physics, initialization data, and validation data) and its decay with time; and (ii) the quantification of forecast skill, determined through a comparison of predicted precipitation and air temperature against observations. Indeed, the specific contribution of land initialization to both these elements is isolated through a comparison of the Series 1 and 2 forecasts. We examine the two elements at four different forecast leads: 1-15, 16-30, 31-45, and 46-60 days. Statistics-based approaches for enhancing skill (essentially using observational statistics to reduce the impact of the models' climatic biases) are also tested. In the present talk, we provide an update of progress in GLACE-2, featuring quantifications of predictability and forecast skill for a number of the participating models and providing a "first look" at the desired consensus view of land impacts on subseasonal forecasts.

Koster, Randal↗

NASA NTRS2005

High-Aperture-Efficiency Horn Antenna

A horn antenna (see Figure 1) has been developed to satisfy requirements specific to its use as an essential component of a high-efficiency Ka-band amplifier: The combination of the horn antenna and an associated microstrip-patch antenna array is required to function as a spatial power divider that feeds 25 monolithic microwave integrated-circuit (MMIC) power amplifiers. The foregoing requirement translates to, among other things, a further requirement that the horn produce a uniform, vertically polarized electromagnetic field in its patches identically so that the MMICs can operate at maximum efficiency. The horn is fed from a square waveguide of 5.9436-mm-square cross section via a transition piece. The horn features cosine-tapered, dielectric-filled longitudinal corrugations in its vertical walls to create a hard boundary condition: This aspect of the horn design causes the field in the horn aperture to be substantially vertically polarized and to be nearly uniform in amplitude and phase. As used here, cosine-tapered signifies that the depth of the corrugations is a cosine function of distance along the horn. Preliminary results of finite-element simulations of performance have shown that by virtue of the cosine taper the impedance response of this horn can be expected to be better than has been achieved previously in a similar horn having linearly tapered dielectric- filled longitudinal corrugations. It is possible to create a hard boundary condition by use of a single dielectric-filled corrugation in each affected wall, but better results can be obtained with more corrugations. Simulations were performed for a one- and a three-corrugation cosine-taper design. For comparison, a simulation was also performed for a linear- taper design (see Figure 2). The three-corrugation design was chosen to minimize the cost of fabrication while still affording acceptably high performance. Future designs using more corrugations per wavelength are expected to provide better field responses and, hence, greater aperture efficiencies.

Pickens, Wesley↗

NASA NTRS1997

Study of the solid-phase thermal decomposition of NTO using Simultaneous Thermogravimetric Modulated Beam Mass Spectrometry (STMBMS)

The solid phase thermal reaction chemistry of NTO between 190 and 250 C is presently being evaluated by utilizing STMBMS, a technique that enables the authors to measure the vapor pressure of NTO and to explore the reaction mechanisms and chemical kinetics associated with the NTO thermal decomposition process. The vapor pressure of NTO is expressed as Log(sub 10) p(torr) = 12.5137 + 6,296.553(1/t(k)) and the Delta-H(sub subl) = 28.71 +/- 0.07 kcal/mol (120.01 +/- 0.29 kJ/mol). The pyrolysis of NTO results in the formation of gaseous products and a condensed-phase residue. The identity of the major gaseous products and their origin from within the NTO molecules are determined based on the results from pyrolysis of NTO, NTO-3-C-13, NTO-1,2- (15)N2 and NTO-(2)H2. Identification of the products show the major gaseous products to be N2, CO2, NO, HNCO, H2O and some N2O, CO, HCN and NH3. The N2 is mostly derived from the N-1 and N-2 positions with some being from the N-4 and N-1 or N-2 positions. The CO2 is derived from both carbons in the NTO molecule in comparable amounts. The residue has an elemental formula of C(2.1)H(.26)N(2.9)O and FTIR analysis suggests that the residue is polyurea- and polycarbamate- like in nature. The temporal behaviors of the rates of formation of the gaseous products indicate that the overall thermal decomposition of NTO in the temperature range evaluated involves four major processes: (1) NTO sublimation; (2) an apparent solid-solid phase transition between 190 and 195 C; (3) a decomposition regime induced by the presence of exogenous H2O at the onset of decomposition; and (4) a decomposition regime that occurs at the onset of decomposition and continues until the depletion of NTO. Decomposition pathways that are consistent with the data are presented.

Minier, L.↗

NASA NTRS1995

The Method of Space-time Conservation Element and Solution Element: Development of a New Implicit Solver

The method of space-time conservation element and solution element is a nontraditional numerical method designed from a physicist's perspective, i.e., its development is based more on physics than numerics. It uses only the simplest approximation techniques and yet is capable of generating nearly perfect solutions for a 2-D shock reflection problem used by Helen Yee and others. In addition to providing an overall view of the new method, we introduce a new concept in the design of implicit schemes, and use it to construct a highly accurate solver for a convection-diffusion equation. It is shown that, in the inviscid case, this new scheme becomes explicit and its amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, its principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.

Chang, S. C.↗