Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “solutions center”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20

Rover mast calibration, exact camera pointing, and camara handoff for visual target tracking

This paper presents three technical elements that we have developed to improve the accuracy of the visual target tracking for single-sol approach-and-instrument placement in future Mars rover missions. An accurate, straightforward method of rover mast calibration is achieved by using a total station, a camera calibration target, and four prism targets mounted on the rover. The method was applied to Rocky8 rover mast calibration and yielded a 1.1-pixel rms residual error. Camera pointing requires inverse kinematic solutions for mast pan and tilt angles such that the target image appears right at the center of the camera image. Two issues were raised. Mast camera frames are in general not parallel to the masthead base frame. Further, the optical axis of the camera model in general does not pass through the center of the image. Despite these issues, we managed to derive non-iterative closed-form exact solutions, which were verified with Matlab routines. Actual camera pointing experiments aver 50 random target image paints yielded less than 1.3-pixel rms pointing error. Finally, a purely geometric method for camera handoff using stereo views of the target has been developed. Experimental test runs show less than 2.5 pixels error on high-resolution Navcam for Pancam-to-Navcam handoff, and less than 4 pixels error on lower-resolution Hazcam for Navcam-to-Hazcam handoff.

camera handoff↗

Autonomous Ocean World Exploration: Advancement of a Virtual Testbed

The search for life (extinct or extant) and potentially habitable bodies in our solar system and beyond is one of the 12 priority science questions outlined in the National Acadamies’ 2022 decadal survey [5]. Extraterrestrial destinations containing liquid water present an opportunity to search for life as we know it, and in recent years an increasing number of such locations have been discovered within our solar system. Several Jovian moons—Europa, Ganymede, and Callisto [10]—and the Saturnian moons Enceladus [8] and Titan [9] are known or suspected to harbor massive subsurface oceans. Of these "ocean worlds", Europa is the focus of at least one planned NASA orbiter mission, Europa Clipper [4], and an early lander mission concept, the Europa Lander [2, 3]. Whereas most robotic missions to the Moon and Mars (e.g. orbiters, rovers, landers) to date have had ground controllers on Earth tightly involved in mission operations, missions to more distant worlds will require a high degree of onboard autonomy due to long communication lags and blackouts, harsh environments (radiation, cold), and more limited battery and hardware life. The past decade has seen great advances in both AI technologies and computing scalability and performance that offer promising solutions for spacecraft autonomy and motivate the software system and research programs described in this paper. The Ocean Worlds Autonomy Testbed for Exploration, Research, and Simulation (OceanWATERS) [1], which has been in development at the NASA Ames Research Center since 2018, is a virtual environment for testing lander autonomy solutions. It is built on the Robot Operating System (ROS), runs on consumer-grade Linux workstations, and was released as open source in 2020. OceanWATERS provides a physical and visual simulation of a prototypical lander in a Europa-like environment (Figure 1). The lander was modeled after requirements and specifications made in JPL’s Europa Lander Study of 2016 [3]. Simulated lander systems include stereo cameras and spotlights mounted on an antenna mast that pans and tilts, a 6 degrees of freedom (DoF) robotic arm with a force-torque sensor and two interchangeable end effectors, and a battery pack power system. The environment consists of multiple terrain models including a highly detailed model sourced from the FROST dataset [11], simulation of surrounding planetary bodies based on an ephemeris model, and lighting from the sun with associated surface illumination, reflectance, and shadows. Operations supported by OceanWATERS include panoramic and directed imaging of the environment and lander workspace, Cartesian and joint-level arm commanding, grinding of the terrain surface (e.g. digging a trench), and scooping of ground material (Figure 2) which can be discarded or collected as science samples in a receptacle that can be emptied (science operations themselves are not simulated). These operations are realized as ROS Actions and are complimented by a wide selection of telemetry that is continually produced by each lander subsystem. The power system model is driven by the open-source Generic Software Architecture for Prognostics (GSAP) [11] that predicts the battery’s remaining useful life and other characteristics. As a testbed for high-level autonomy, OceanWATERS provides an execution framework based on PLEXIL [12], an open-source plan specification language and execution engine developed largely at Ames. NASA's initial development of OceanWATERS, as well the Ocean Worlds Lander Autonomy Testbed (OWLAT) [6], a complimentary physical testbed developed at JPL, was the first step in a plan for realizing candidate onboard autonomy solutions for such planetary landers. In 2020 NASA solicited applications for its Autonomous Robotics Research for Ocean Worlds (ARROW) program, and in 2021 the similar Concepts for Ocean worlds Life Detection Technology (COLDTech) program. Collectively six research teams, based in universities and companies across the United States, were awarded grants to develop and demonstrate autonomy solutions on OceanWATERS and OWLAT. These 1–2-year projects have now finished or are nearing completion, and a wide variety of autonomy challenges in ocean world surface missions were addressed. Prototyped and demonstrated solutions have included autonomous discovery, response and adaptation to system faults and unexpected environmental events, world model synthesis through perception, plan synthesis using learned models, methods to optimize sample target selection and prioritize science data transmission, extension of PLEXIL for stochastic decision-making, and an integration of a model of JPL’s mission-ready COLDArm [7]. Technologies used in these projects include many forms of machine learning, causal reasoning, automated planning, Markov decision processes, formal methods, and other advanced techniques. A more detailed summary of the ARROW and COLDTech projects is given herein. OceanWATERS has had significant enhancements since its open-source release in 2020. Many of its new features were driven or shaped by feedback from the ARROW and COLDTech teams and requirements of their projects. In support of enabling autonomous adaptation to spacecraft faults (a specific capability solicited by both programs), a fault injection and detection framework was developed that supports a wide and growing range of fault types such as locked joints, image loss, and battery failures. The power system model was completed and integrated into the simulator, starting as a single-cell battery model and later upgraded to a multi-cell model with associated faults such as cell disconnection. Arm/terrain interaction was improved by adding a force-torque sensor and associated faults, and an analytic dig force model based on the Balovnev bucket force equations. Environment fidelity was increased by modeling terrain deformation resulting from digging and scooping; visual improvements were made in textures, lighting, and shadows. To facilitate interoperation with OWLAT, a unified command and telemetry interface between the testbeds was developed at the ROS level, along with a PLEXIL interface. The number of lander operations was greatly expanded (e.g. with Cartesian-based arm and antenna movement), and a framework was designed for users to build their own lander actions. A GUI for PLEXIL plan selection was created (Figure 3), and an expansive set of plans were added, such as those that illustrate patterns for fault handling. This paper provides a self-contained high-level description of OceanWATERS, focusing on more detailed coverage of the aforementioned enhancements. It provides a high-level summary of the projects undertaken by participants in the ARROW and COLDTech programs and how these efforts have helped shape OceanWATERS. Finally, potential future work and directions for the testbed are listed, as likely informed by the recent planetary science decadal survey [5].

K Michael Dalal↗

Autonomous Formation Flying from Ground to Flight

The cost of on-orbit operations remains a significant and increasingly visible concern in the support of satellite missions. Headway has been made in automating some ground operations; however, increased mission complexity and more precise orbital constraints have compelled continuing human involvement in mission design and maneuver planning operations. AI Solutions, Inc. in cooperation with the National Aeronautics and Space Administration's (NASA) Goddard Space Flight Center (GSFC) has tackled these more complex problems through the development of AutoCon as a tool for an automated solution. NASA is using AutoCon to automate the maneuver planning for the Earth Orbiter-1 (EO-1) mission. AutoCon was developed originally as a ground system tool. The EO-1 mission will be using a scaled version of AutoCon on-board the EO-1 satellite to command orbit adjustment maneuvers. The flight version of AutoCon plans maneuvers based on formation flying algorithms developed by GSFC, JPL, and other industry partners. In its fully autonomous mode, an AutoCon planned maneuver will be executed on-board the satellite without intervention from the ground. This paper describes how AutoCon automates maneuver planning for the formation flying constraints of the EO-1 mission. AutoCon was modified in a number of ways to automate the maneuver planning on-board the satellite. This paper describes how the interface and functionality of AutoCon were modified to support the on-board system. A significant component of this modification was the implementation of a data smoother, based on a Kalman filter, that ensures that the spacecraft states estimated by an on-board GPS receiver are as accurate as possible for maneuver planning. This paper also presents the methodology use to scale the AutoCon functionality to fit and execute on the flight hardware. This paper also presents the modes built that allow the incremental phasing in of autonomy. New technologies for autonomous operations are usually received with significant, and probably appropriate trepidation. A number of safeguards have been designed in both AutoCon and the interfacing systems to alleviate the potential of mission-impacting anomalies from the on-board autonomous system. This paper describes the error checking, input data integrity validation and limits set on maneuvers in AutoCon and the on-board system.

Chapman, Keith B.↗

Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

Coirier, William J.↗

Effective Storage of Electrons in Water by the Formation of Highly Reduced Polyoxometalate Clusters

Aqueous solutions of polyoxometalates (POMs) have been shown to have potential as high-capacity energy storage materials due to their potential for multi-electron redox processes, yet the mechanism of reduction and practical limits are currently unknown. Herein, we explore the mechanism of multi-electron redox processes that allow the highly reduced POM clusters of the form {MO 3 } y to absorb y electrons in aqueous solution, focusing mechanistically on the Wells-Dawson structure X 6 [P 2 W 18 O 62 ], which comprises 18 metal centers and can uptake up to 18 electrons reversibly (y = 18) per cluster in aqueous solution when the countercations are lithium. This unconventional redox activity is rationalized by density functional theory, molecular dynamics simulations, UV-vis, electron paramagnetic resonance spectroscopy, and small-angle X-ray scattering spectra. These data point to a new phenomenon showing that cluster protonation and aggregation allow the formation of highly electron-rich meta-stable systems in aqueous solution, which produce H 2 when the solution is diluted. Finally, we show that this understanding is transferrable to other salts of [P 5 W 30 O 110 ] 15- and [P 8 W 48 O 184 ] 40- anions, which can be charged to 23 and 27 electrons per cluster, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Benchmarking Mixed Mode Failure in Progressive Damage and Failure Analysis Methods

The verification and validation of progressive-damage-analysis finite element methods are difficult but critical tasks to undertake during their development. Verification exercises assess whether a predictive analysis tool produces results that are consistent with the fundamental concepts and assumptions of the tool under evaluation. Ideally, closed-form analytical solutions can be derived for which method verification results can be compared. Problems selected for computational tool verification are often simple and isolate individual features of the tool. In the case of progressive damage finite element methods, verifications should be performed to evaluate the ability of the model to predict the initiation of damage and its growth through the finite element mesh under a variety of conditions. Mabson et al. proposed a test case of a unidirectional, fiber-reinforced plate with a center crack subjected to tensile loads to evaluate matrix crack propagation predictions. The problem was modeled using the Abaqus Hashin continuum damage mechanics (CDM) model for fiber-reinforced composites. Different combinations of matrix strengths and element sizes were used in the simulations, and the results were compared to a closed-form solution based on linear elastic fracture mechanics (LEFM). It was determined that the Abaqus CDM model could predict the LEFM solution of Mode I cracks only when the finite element mesh density met specific requirements based on the material properties. This paper presents closed-form LEFM solutions for a center notch mixed mode (CNMM) verification problem. Parametric finite element analyses were developed using progressive damage analysis methods of both the Discrete Damage Mechanics (DDM) and CDM classes. The progressive damage analysis methods applied in the analyses of the CNMM problem include CompDam and the Floating Node Method. Analyses were conducted with various mode mixities and element sizes to verify that the damage models were working as intended and to identify any limits of applicability.

Leone, Frank↗

Conic state extrapolation

The Conic State Extrapolation Routine provides the capability to conically extrapolate any spacecraft inertial state vector either backwards or forwards as a function of time or as a function of transfer angle. It is merely the coded form of two versions of the solution of the two-body differential equations of motion of the spacecraft center of mass. Because of its relatively fast computation speed and moderate accuracy, it serves as a preliminary navigation tool and as a method of obtaining quick solutions for targeting and guidance functions. More accurate (but slower) results are provided by the Precision State Extrapolation Routine.

Shepperd, S. W.↗

Electric field mill network products to improve detection of the lightning hazard

An electric field mill network has been used at Kennedy Space Center for over 10 years as part of the thunderstorm detection system. Several algorithms are currently available to improve the informational output of the electric field mill data. The charge distributions of roughly 50 percent of all lightning can be modeled as if they reduced the charged cloud by a point charge or a point dipole. Using these models, the spatial differences in the lightning induced electric field changes, and a least squares algorithm to obtain an optimum solution, the three-dimensional locations of the lightning charge centers can be located. During the lifetime of a thunderstorm, dynamically induced charging, modeled as a current source, can be located spatially with measurements of Maxwell current density. The electric field mills can be used to calculate the Maxwell current density at times when it is equal to the displacement current density. These improvements will produce more accurate assessments of the potential electrical activity, identify active cells, and forecast thunderstorm termination.

Maier, Launa M.↗

Time-Lapse Electromagnetic Methods for Monitoring Plume Development in a Carbon Storage Reservoir

Conference presentation at International Meeting for Applied Geoscience & Energy (IMAGE), Houston, Texas, August 25–28, 2025. The Energy & Environmental Research Center (EERC) is leading applied research on electromagnetic (EM) monitoring methods at an active carbon storage site in North Dakota. Injection operations at the site began in February 2024, with a permitted injection rate of up to 2.7 million tonnes of CO 2 annually using six injection wells. CO 2 is captured on-site and injected into the Broom Creek Formation, a predominantly sandstone reservoir and saline aquifer located at a depth of approximately 1800 meters. The EERC led acquisition of multiple active- and passive-source EM techniques between August and October of 2024 to provide a thorough understanding of the resistivity profile at the site.

02 PETROLEUM↗

Unstructured Unsteady Flow Solver Applicable to MSU TURBO and Computational Design

This paper presents numerical simulations for a high-speed transonic compressor rotor, NASA Rotor 35, using an unstructured grid flow solver U2NCLE. It solves Reynolds averaged Navier-Stokes equations using an arbitrary Mach number solution algorithm. Experiments were conducted at the NASA Glen Research Center to investigate compressor stability enhancement using steady and discrete tip injections. The mass injection upstream of the tip of a high- speed axial compressor rotor has shown effectiveness in suppressing stall in tip-critical rotors. This work presents numerical simulations of a high-speed compressor rotor with and without tip injections. Methods to model the flow injection are described. Numerical simulations are conducted at 80 and 100 percent of the design speed. Results show that numerical solutions are consistent with the experimental trends.

Newman, James C., III↗

Autonomous Formation Flying from the Ground to Flight

The cost of on-orbit operations remains a significant and increasingly visible concern in the support of satellite missions. Headway has been made in automating some ground operations; however, increased mission complexity and more precise orbital constraints have compelled continuing human involvement in mission design and maneuver planning operations. AI Solutions, Inc. in cooperation with the National Aeronautics and Space Administration's (NASA) Goddard Space Flight Center (GSFC) has tackled these more complex problems through the development of AutoCon(TM) as a tool for an automated solution. NASA is using AutoCon(TM) to automate the maneuver planning for the Earth Orbiter-1 (EO-1) mission. AutoCon(TM) was developed originally as a ground system tool. The EO-1 mission will be using a scaled version of AutoCon(TM) on-board the EO-1 satellite to command orbit adjustment maneuvers. The flight version of AutoCon(TM) plans maneuvers based on formation flying algorithms developed by GSFC, JPL, and other industry partners. In its fully autonomous mode, an AutoCon(TM) planned maneuver will be executed on-board the satellite without intervention from the ground. This paper describes how AutoCon(TM) automates maneuver planning for the formation flying constraints of the EO-1 mission. AutoCon(TM) was modified in a number of ways to automate the maneuver planning on-board the satellite. This paper describes how the interface and functionality of AutoCon(TM) were modified to support the on-board system. A significant component of this modification was the implementation of a data smoother, based on a Kalman filter, that ensures that the spacecraft states estimated by an on-board GPS receiver are as accurate as possible for maneuver planning. This paper also presents the methodology used to scale the AutoCon(TM) functionality to fit and execute on the flight hardware. This paper also presents the modes built into the system that allow the incremental phasing in of autonomy. New technologies for autonomous operations are usually received with significant, and probably appropriate, trepidation. A number of safeguards have been designed in both AutoCon(TM) and the interfacing systems to alleviate the potential of mission-impacting anomalies from the on-board autonomous system. This paper describes the error checking, input data integrity validation, and limits set on maneuvers in AutoCon(TM) and the on-board system.

Chapman, Keith B.↗

Multidisciplinary computational aerosciences

As the challenges of single disciplinary computational physics are met, such as computational fluid dynamics, computational structural mechanics, computational propulsion, computational aeroacoustics, computational electromagnetics, etc., scientists have begun investigating the combination of these single disciplines into what is being called multidisciplinary computational aerosciences (MCAS). The combination of several disciplines not only offers simulation realism but also formidable computational challenges. The solution of such problems will require computers orders of magnitude larger than those currently available. Such computer power can only be supplied by massively parallel machines because of the current speed-of-light limitation of conventional serial systems. Even with such machines, MCAS problems will require hundreds of hours for their solution. To efficiently utilize such a machine, research is required in three areas that include parallel architectures, systems software, and applications software. The main emphasis of this paper is the applications software element. Examples that demonstrate application software for multidisciplinary problems currently being solved at NASA Ames Research Center are presented. Pacing items for MCAS are discussed such as solution methodology, physical modeling, computer power, and multidisciplinary validation experiments.

Kutler, Paul↗

Open Innovation for a NASA Architecture Library

NASA’s Center of Excellence for Collaborative Innovation (CoECI) uses open innovation, or “crowdsourcing”, to access the global public to find ideas, concepts, designs, or solutions that meet a previously unmet need possibly resulting in significant advances in performance. The Center of Excellence for Collaborative Innovation was launched at the request of the White House Office of Science and Technology Policy. This is both a non-traditional method of innovation and a non-traditional method of outreach to the public to involve them in space technologies and programs. It has been used often for software development and new hardware technology. In this case we applied it to innovate with systems engineering tools for creating space architectures. The challenge was sponsored by NASA Engineering and Safety Center Systems Engineering Technical Fellow as part of a program for NASA’s adoption of MBSE. It was a trial to see if there would be as much participation or quality submissions with this more specialized topic and skill. The challenge sought space architecture representations and decompositions to create a library of modeled parts in a system modeling language (SysML). Mission architects mostly start from scratch to build model elements representing the functional and physical architecture of a system in SysML. There are a few beginning libraries, but these are also local to a program or group. A common library will save system engineers a large amount of time, will allow project stakeholders to recognize common graphics and quickly understand the architecture options. The challenge was promoted internationally, especially through professional organizations and universities with a systems engineering focus. It was open for 4 months, purposefully over the winter holiday break time to allow participants extra time outside of work or school. The challenge was designed so that expertise in space hardware was not necessary but getting to play with models of space architecture could provide motivation to participate. We did not receive as many entries as other broader outreach challenges, but the ones we received were extremely thorough and high quality. Solutions came from individuals and teams, students and professional consultants from the United States and Europe. We learned a few lessons about how to engage with the public and what characteristics of a problem result in good crowdsourcing results. The outreach challenge produced several useful ideas and modeled space elements, and the group will be engaging the winners to learn more about their new approaches.

innovation↗

Accelerated Aging and Evaluation of Hose-In-Hose Transfer Lines in the Hanford Waste Transfer System - 20312

Nonmetallic materials are used in the United States Department of Energy's Hanford Site Tank Farm waste transfer system. These materials include the inner primary hoses in the hose-in-hose transfer lines (HIHTLs), Garlock{sup R} gaskets, ethylene propylene diene monomer (EPDM) O-rings, and other nonmetallic materials. These nonmetallic materials are exposed to β and γ radiation, caustic solutions as well as high temperature and pressure stressors. How the nonmetallic components react to each of these stressors individually has been well established. However, simultaneous exposure of these stressors has not been evaluated and is of great concern to Hanford Site engineers. Florida International University's Applied Research Center engineers worked closely with key Hanford's Washington River Protection Solutions personnel to develop an experimental test plan that determines how these nonmetallic components react to various simultaneous stressor exposures. In this paper, research on the experimental testing of the hose-in-hose transfer lines used in the Hanford tank farm waste transfer system under simultaneous stressor exposures is presented. The stressor exposure experiments consisted of various combinations of simultaneous stressor exposure of caustic solution, high temperature and high pressure stressors. Research efforts focused on evaluating the aging behavior of EPDM by exposing samples of HIHTLs as well as EPDM dog bone shaped specimens to a 25% NaOH solution at (38 deg. C), operating (54 deg. C) and design temperatures (77 deg. C) for 6 months and 12 months. In addition, HIHTL and the EPDM dog-bone specimens were exposed to only hot water at 77 deg. C for a duration of one year. The mechanical and material properties of the samples were characterized and compared with those of the unexposed samples (baseline). Evaluations included burst pressure tests of the EPDM hose-in-hose transfer lines and material tensile strength test of EPDM dog-bone coupons. Both the tensile strength of the EPDM material dog bones and the burst pressure of the HIHTLs significantly decreased with the increasing temperature and increasing exposure time. When compared with the baseline samples, the burst pressure decreased by 28.75% for the sample aged at 77 deg. C after 12 months, in comparison to sample aged at 38 deg. C and 54 deg. C which had about 1.34% and 5.70% loss in burst pressures, respectively, after 12-month exposure. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Near‐Unity Superradiant Emission from Delocalized Frenkel Excitons in a Two‐Dimensional Supramolecular Assembly

Abstract Three general effective strategies are shown to mitigate nonradiative losses in the superradiant emission from supramolecular assemblies. J‐aggregates of 5,5′,6,6′‐tetrachloro‐1,1′‐diethyl‐3,3′‐di(4–sulfobutyl)‐benzimidazolocarbocyanine (TDBC) are used to elucidate the nature of nonradiative processes. Self‐annealing at room temperature (RT), photo‐brightening, and purification of the dye monomers are shown to all lead to substantial increases in emission quantum yields (QYs) and a concomitant lengthening of the emission lifetime, with purification having the largest effect. Structural and optical measurements are used to support a microscopic model that emphasizes the deleterious effects of a small number of impurity and defect sites that serve as nonradiative recombination centers. This understanding has yielded a molecular fluorophore in solution at RT with an unprecedented combination of fast emissive lifetime and high QY. Superradiant emission with a QY of 82% and a lifetime of 174 ps is obtained from J‐aggregates of TDBC in solution at RT. This combination of high QY and fast lifetime at RT makes supramolecular assemblies of purified TDBC a model system for the study of fundamental superradiance phenomena. High QY J‐aggregates are uniquely suited for the development of applications that require high speed and high brightness fluorophores such as devices for high‐speed optical communication.

36 MATERIALS SCIENCE↗

Present obliquity oscillations of Mars - Fourth-order accuracy in orbital e and I

A long period analysis of solar system orbital evolution, correct to fourth order in orbital eccentricities and inclinations (Bretagnon, 1974), and an improved value of the planet's moment of inertia (Reasenberg, 1977) have been incorporated in a recalculation of the obliquity oscillations of Mars. A linearized solution predicts a maximum oscillation amplitude of 13.6 deg centered on a long-term average value of 24.4 deg. A numerical integration of the obliquity for the past 10,000,000 years is also presented. Epochs of minimal oscillation like the present occur at intervals of the order of 4 m.y.

Ward, W. R.↗

Numerical solution for supersonic flow near the trailing edge of a flat plate

In the present study, problems of laminar and turbulent two-dimensional flow of a viscous compressible fluid near the trailing edge of a thin flat plate are considered. The complete set of Navier-Stokes equations is solved by the finite-difference method of MacCormack (MacCormack and Baldwin, 1975). It is an explicit, predictor-corrector, time-splitting method of second order acuracy. The computational mesh employed has sufficient resolution for all the characteristic lengths suggested by theory. In the laminar case, the present results are compared with the triple deck solution of Daniels (1974). This comparison indicates that the asymptotic triple deck theory for supersonic trailing edge flow is accurate within five percent for Reynolds numbers greater than 1000. In the turbulent case, the Prandtl-Van Driest-Clauser algebraic eddy viscosity model is used. The numerical results show that the region of upstream influence is approximately of the order of the boundary layer thickness. The solutions for skin-friction, pressure and wake center-line velocity are presented.

Degani, D.↗

the finite element machine: An experiment in parallel processing

The Finite Element Machine at the NASA Langley Research Center is a prototype computer designed to support parallel solutions to structural analysis problems. The hardware architecture and support software for the machine, initial solution algorithms and test applications, and preliminary results are described. Directions for future work are presented.

Storaasli, O. O.↗