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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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Using Strain in the Vadose Zone During Sinusoidal-Rate Well Tests to Characterize an Aquifer

Well tests with sinusoidal variation in pumping rate are appealing because of the ability to filter competing signals and they also can be set up with no net removal of water, which is an advantage at contaminated sites. Current methods of interpreting sinusoidal-rate well tests analyze the phase lag and amplitude of pressure signals in the aquifer. This approach is restricted by the availability of monitoring wells. An alternative approach could be to measure the stain in the vadose zone instead of pressure in the aquifer. The goal of this research is to evaluate the feasibility of using signals from in-situ sensors in the vadose zone to characterize sinusoidal-rate well tests. Well tests with a variety of periods and amplitudes were performed using a well completed in an unconfined saprolite aquifer with a water table at 9m depth at our test site near Clemson, South Carolina. Vertical strain was measured every meter between 1 to 7 m using a distributed optical fiber sensing technique called coherence length gated microwave photonics interferometry (CMPI). A novel packaging system was designed to couple the optical fiber to the saprolite. The results show that strain measured in the vadose zone during sinusoidal-rate pumping varies periodically with amplitudes from 0.1 to 3 microstrain, depending on the amplitude of the sinusoidal pumping rate. Hydraulic heads at similar radial distances were also periodic with changing amplitudes ranging up to ±0.2 meters. The strain in the vadose zone responds to pressure in the underlying aquifer—the strain is tensile when the pressure is falling, and compressive when the pressure is rising. The phase lag between the pumping rate and the strain was 3 min with a pumping period of 15 minutes, and this gives a hydraulic diffusivity of 0.06 m2/s. This is the same diffusivity obtained by analyzing a constant rate pumping test, and it is slightly larger than the diffusivity (0.044 m2/s) obtained by analyzing the phase lag of the pressure in a nearby monitoring well. Strain measurements in the vadose zone could be made with much less cost and effort than installing a deep monitoring well. These results suggest that strain measurements in the vadose zone could be used to supplement monitoring wells, thereby increasing the resolution, and reducing costs of analyzing well tests.

well test, sinusoidal, periodic pumping, strain↗
DOE OSTI2019

Utah FORGE: InSAR Data 2019

This dataset contains Interferometric Synthetic Aperture Radar (InSAR) data used for ground deformation monitoring during Phase 2C of the Utah FORGE project. The dataset includes measurements of the mean rate of range change and associated standard errors, provided in both CSV and NetCDF formats. Supporting materials include histograms, maps, and MATLAB scripts used for data processing, as well as unit vector information describing the satellite's sensor orientation. Compressed archives contain additional metadata and masked range change data for individual interferometric pairs. A README file is included to provide further details on the dataset's structure and contents.

15 GEOTHERMAL ENERGY↗
NASA NTRS1991

Magnetic field draping at the low-latitude magnetopause

Magnetohydrodynamic simulations are used to investigate the structure of the low-latitude magnetopause for interplanetary magnetic field conditions with a dominant southward component. The structure is self-consistently calculated as an initial-value problem in which the system is allowed to evolve into a quasi-steady state. All components of the 3D velocity and magnetic field as well as compressibility, resistivity, and viscosity are included in the 2D calculation. The simulation model shows that magnetic field draping can occur at the magnetopause boundary when magnetic merging takes place in the presence of a tangential shear flow. For 'normal' (positive Bx) draping, the higher-latitude portion of the field lines are curved toward the sun on the magnetospheric side of the magnetopause and away from the sun on the magnetosheath side. The thickness of the normal draping structure scales with the viscosity. The field-aligned current system that accompanies normal magnetic draping is consistent with the sense of the region 1 currents that flow into the dayside ionosphere.

Richard, R. L.↗
NASA NTRS1986

Fluid flow meter for measuring the rate of fluid flow in a conduit

A tube fluid flow rate meter consists of a reservoir divided by flexible diaphragm into two separate isolated compartments. The incoming and outgoing tubes open into the compartments. The orifice is sized to allow maximum tube fluid flow. Opposing compression springs are secured within the two compartments on opposite sides of the orifice to maintain orifice position when the tube fluid pressure is zero. A tapered element is centered in, and extends through the orifice into the compartment, leaving an annular opening between the element and the perimeter of the oriface. The size varies as the diaphragm flexes with changes in the tube fluid pressure to change the fluid flow through the opening. The light source directs light upon the element which in turn scatters the light through the opening into the compartment. The light detector in the compartment senses the scattered light to generate a signal indicating the amount of fluid.

White, P. R.↗
NASA NTRS2012

Modeling and Detection of Ice Particle Accretion in Aircraft Engine Compression Systems

The accretion of ice particles in the core of commercial aircraft engines has been an ongoing aviation safety challenge. While no accidents have resulted from this phenomenon to date, numerous engine power loss events ranging from uneventful recoveries to forced landings have been recorded. As a first step to enabling mitigation strategies during ice accretion, a detection scheme must be developed that is capable of being implemented on board modern engines. In this paper, a simple detection scheme is developed and tested using a realistic engine simulation with approximate ice accretion models based on data from a compressor design tool. These accretion models are implemented as modified Low Pressure Compressor maps and have the capability to shift engine performance based on a specified level of ice blockage. Based on results from this model, it is possible to detect the accretion of ice in the engine core by observing shifts in the typical sensed engine outputs. Results are presented in which, for a 0.1 percent false positive rate, a true positive detection rate of 98 percent is achieved.

May, Ryan D.↗
NASA NTRS2015

Feasibility Assessment of an EVA Glove Sensing Platform to Evaluate Potential Hand Injury Risk Factors

Injuries to the hands are common among astronauts who train for extravehicular activity (EVA). When the gloves are pressurized, they restrict movement and create pressure points during tasks, sometimes resulting in pain, muscle fatigue, abrasions, and occasionally more severe injuries such as onycholysis. A brief review of the Lifetime Surveillance of Astronaut Health's injury database reveals that 58% of total astronaut hand and arm injuries from NBL training between 1993 and 2010 occurred either to the fingernail, MCP, or fingertip. The purpose of this study was to assess the potential of using small sensors to measure force acting on the fingers and hand within pressurized gloves and other variables such as blood perfusion, skin temperature, humidity, fingernail strain, skin moisture, among others. Tasks were performed gloved and ungloved in a pressurizable glove box. The test demonstrated that fingernails saw greater transverse strain levels for tension or compression than for longitudinal strain, even during axial fingertip loading. Blood perfusion peaked and dropped as the finger deformed during finger presses, indicating an initial dispersion and decrease of blood perfusion levels. Force sensitive resistors to force plate comparisons showed similar force curve patterns as fingers were depressed, indicating suitable functionality for future testing. Strategies for proper placement and protection of these sensors for ideal data collection and longevity through the test session were developed and will be implemented going forward for future testing.

Reid, Christopher R.↗
NASA NTRS1993

Experimental investigations of the time and flow-direction responses of shear-stress-sensitive liquid crystal coatings

Time and flow-direction responses of shearstress-sensitive liquid crystal coatings were explored experimentally. For the time-response experiments, coatings were exposed to transient, compressible flows created during the startup and off-design operation of an injector-driven supersonic wind tunnel. Flow transients were visualized with a focusing Schlieren system and recorded with a 1000 frame/sec color video camera. Liquid crystal responses to these changing-shear environments were then recorded with the same video system, documenting color-play response times equal to, or faster than, the time interval between sequential frames (i.e., 1 millisecond). For the flow-direction experiments, a planar test surface was exposed to equal-magnitude and known-direction surface shear stresses generated by both normal and tangential subsonic jet-impingement flows. Under shear, the sense of the angular displacement of the liquid crystal dispersed (reflected) spectrum was found to be a function of the instantaneous direction of the applied shear. This technique thus renders dynamic flow reversals or flow divergences visible over entire test surfaces at image recording rates up to 1 KHz. Extensions of the technique to visualize relatively small changes in surface shear stress direction appear feasible.

Reda, Daniel C.↗
NASA NTRS1981

Preliminary feasibility analysis of a pressure modulator radiometer for remote sensing of tropospheric constituents

A pressure modulator radiometer operated in a nadir viewing mode from the top of a midlatitude summer model of the atmosphere was theoretically studied for monitoring the mean volumetric mixing ratio of carbon monoxide in the troposphere. The mechanical characteristics of the instrument on the Nimbus 7 stratospheric and mesospheric sounder experiment are assumed and CO is assumed to be the only infrared active constituent. A line by line radiative transfer computer program is used to simulate the upwelling radiation reaching the top of the atmosphere. The performance of the instrument is examined as a function of the mean pressure in and the length of the instrument gas correlation cell. Instrument sensitivity is described in terms of signal to noise ratio for a 10 percent change in CO mixing ratio. Sensitivity to mixing ratio changes is also studied. It is concluded that tropospheric monitoring requires a pressure modulator drive having a larger swept volume and producing higher compression ratios at higher mean cell pressures than the Nimbus 7 design.

Orr, H. D., III↗
NASA NTRS1986

Magnetic configuration of the Venus magnetosheath

A data set consisting of nearly six Venus years of Pioneer Venus Orbiter magnetometer data is analyzed in order to describe the configuration of the magnetosheath. A coordinate system is developed which isolates the effects of the solar wind flow and the interplanetary magnetic field (IMF). The data indicate that the magnetosheath field magnitude is responsive to solar wind dynamic pressure and that the compression of the upstream field is controlled by magnetosonic Mach number. The draping of the field is similar to that predicted by gasdynamic modeling; specific draping features include distinct dependence on the radial and the transverse components of the IMF, and a tendency of the field to encircle the planet at low altitude. Certain features of the processes of mass loading by magnetosheath fluctuations and by the motional electric field are examined. Magnetic fluctuations can dominate the magnetosheath field for periods of low interplanetary cone angle and in general for the magnetosheath regions near the quasi-parallel part of the bow shock. The magnetosheath magnetic field magnitude displays a hemispherical asymmetry; the sense of this asymmetry is controlled by the cross-flow component of the IMF in a manner which indicates that ion pickup by the convective electric field occurs preferentially in one hemisphere. The results of this survey indicate that mass loading is a significant process which should be incorporated into computational models but that a fluid treatment of the planetary ion component may not be appropriate.

Phillips, J. L.↗
DOE OSTI2019

Pressure‐Induced Emission (PIE) and Phase Transition of a Two‐dimensional Halide Double Perovskite (BA) 4 AgBiBr 8 (BA=CH 3 (CH 2 ) 3 NH 3 + )

Abstract Two‐dimensional (2D) halide perovskites have attracted significant attention due to their compositional flexibility and electronic diversity. Understanding the structure–property relationships in 2D double perovskites is essential for their development for optoelectronic applications. In this work, we observed the emergence of pressure‐induced emission (PIE) at 2.5 GPa with a broad emission band and large Stokes shift from initially nonfluorescent (BA) 4 AgBiBr 8 (BA=CH 3 (CH 2 ) 3 NH 3 + ). The emission intensity increased significantly upon further compression up to 8.2 GPa. Moreover, the band gap narrowed from the starting 2.61 eV to 2.19 eV at 25.0 GPa accompanied by a color change from light yellow to dark yellow. Analysis of combined in situ high‐pressure photoluminescence, absorption, and angle‐dispersive X‐ray diffraction data indicates that the observed PIE can be attributed to the emission from self‐trapped excitons. This coincides with [AgBr 6 ] 5− and [BiBr 6 ] 3− inter‐octahedral tilting which cause a structural phase transition. High‐pressure study on (BA) 4 AgBiBr 8 sheds light on the relationship between the structure and optical properties that may improve the material's potential applications in the fields of pressure sensing, information storage and trademark security.

Fang, Yuanyuan↗
DOE OSTI2019

Pressure‐Induced Emission (PIE) and Phase Transition of a Two‐dimensional Halide Double Perovskite (BA) 4 AgBiBr 8 (BA=CH 3 (CH 2 ) 3 NH 3 + )

Abstract Two‐dimensional (2D) halide perovskites have attracted significant attention due to their compositional flexibility and electronic diversity. Understanding the structure–property relationships in 2D double perovskites is essential for their development for optoelectronic applications. In this work, we observed the emergence of pressure‐induced emission (PIE) at 2.5 GPa with a broad emission band and large Stokes shift from initially nonfluorescent (BA) 4 AgBiBr 8 (BA=CH 3 (CH 2 ) 3 NH 3 + ). The emission intensity increased significantly upon further compression up to 8.2 GPa. Moreover, the band gap narrowed from the starting 2.61 eV to 2.19 eV at 25.0 GPa accompanied by a color change from light yellow to dark yellow. Analysis of combined in situ high‐pressure photoluminescence, absorption, and angle‐dispersive X‐ray diffraction data indicates that the observed PIE can be attributed to the emission from self‐trapped excitons. This coincides with [AgBr 6 ] 5− and [BiBr 6 ] 3− inter‐octahedral tilting which cause a structural phase transition. High‐pressure study on (BA) 4 AgBiBr 8 sheds light on the relationship between the structure and optical properties that may improve the material's potential applications in the fields of pressure sensing, information storage and trademark security.

Fang, Yuanyuan↗
NASA NTRS1988

Wave/current interaction model

The wave-current interaction for the application to remote sensing data via numerical simulations and data comparison is modelled. Using the field data of surface current shear, wind condition and ambient wave spectrum, the numerical simulations of directional wave spectrum evolution were used to interpret and to compare with the aircraft data from Radar Ocean Wave Spectrometer (ROWS) and Surface Contour Radar (SCR) across the front during Frontal Air Sea Interaction Experiment (FASINEX). The wave-ice interaction was inspired by the observation of large amplitude waves hundreds of kms inside the ice pack in the Weddell Sea, resulting in breakup of the ice pack. The developed analysis of processes includes the refraction of waves at the pack edge, the effects of pack compression on wave propagation, wave train stability and buckling stability in the ice pack. Sources of pack compression and interaction between wave momentum and pack compression are investigated. Viscous camping of propagating waves in the marginal ice zone are also studied. The analysis suggests an explanation for the change in wave dispersion observed from the ship and the sequence of processes that cause ice pack breakup, pressure ridge formation and the formation of open bands of water.

Liu, A. K.↗
NASA NTRS2000

BOREAS Level-4c AVHRR-LAC Ten-Day Composite Images: Surface Parameters

The BOReal Ecosystem-Atmosphere Study (BOREAS) Staff Science Satellite Data Acquisition Program focused on providing the research teams with the remotely sensed satellite data products they needed to compare and spatially extend point results. Manitoba Remote Sensing Center (MRSC) and BOREAS Information System (BORIS) personnel acquired, processed, and archived data from the Advanced Very High Resolution Radiometer (AVHRR) instruments on the NOAA-11 and -14 satellites. The AVHRR data were acquired by CCRS and were provided to BORIS for use by BOREAS researchers. These AVHRR level-4c data are gridded, 10-day composites of surface parameters produced from sets of single-day images. Temporally, the 10-day compositing periods begin 11-Apr-1994 and end 10-Sep-1994. Spatially, the data cover the entire BOREAS region. The data are stored in binary image format files. Note: Some of the data files on the BOREAS CD-ROMs have been compressed using the Gzip program.

Cihlar, Josef↗
NASA NTRS1998

Constitutive Theory Developed for Monolithic Ceramic Materials

With the increasing use of advanced ceramic materials in high-temperature structural applications such as advanced heat engine components, the need arises to accurately predict thermomechanical behavior that is inherently time-dependent and that is hereditary in the sense that the current behavior depends not only on current conditions but also on the material's thermomechanical history. Most current analytical life prediction methods for both subcritical crack growth and creep models use elastic stress fields to predict the time-dependent reliability response of components subjected to elevated service temperatures. Inelastic response at high temperatures has been well documented in the materials science literature for these material systems, but this issue has been ignored by the engineering design community. From a design engineer's perspective, it is imperative to emphasize that accurate predictions of time-dependent reliability demand accurate stress field information. Ceramic materials exhibit different time-dependent behavior in tension and compression. Thus, inelastic deformation models for ceramics must be constructed in a fashion that admits both sensitivity to hydrostatic stress and differing behavior in tension and compression. A number of constitutive theories for materials that exhibit sensitivity to the hydrostatic component of stress have been proposed that characterize deformation using time-independent classical plasticity as a foundation. However, none of these theories allow different behavior in tension and compression. In addition, these theories are somewhat lacking in that they are unable to capture the creep, relaxation, and rate-sensitive phenomena exhibited by ceramic materials at high temperatures. The objective of this effort at the NASA Lewis Research Center has been to formulate a macroscopic continuum theory that captures these time-dependent phenomena. Specifically, the effort has focused on inelastic deformation behavior associated with these service conditions by developing a multiaxial viscoplastic constitutive model that accounts for time-dependent hereditary material deformation (such as creep and stress relaxation) in monolithic structural ceramics. Using continuum principles of engineering mechanics, we derived the complete viscoplastic theory from a scalar dissipative potential function.

Janosik, Lesley A.↗
NASA NTRS2001

Adaptive Numerical Dissipation Controls for High Order Methods

A numerical scheme for direct numerical simulation of shock-turbulence interactions of high speed compressible flows would ideally not be significantly more expensive than the standard fourth or sixth-order compact or non-compact central differencing scheme. It should be possible to resolve all scales down to scales of order of the Kolmogorov scales of turbulence accurately and efficiently, while at the same time being able to capture steep gradients occurring at much smaller scales efficiently. The goal of this lecture is to review the progress and new development of the low dissipative high order shock-capturing schemes proposed by Yee et al. Comparison on the efficiency and accuracy of this class of schemes with spectral and the fifth-order WENO (weighted essentially nonoscillatory) scheme will be presented. A new approach to dynamically sense the appropriate amount of numerical dissipation to be added at each grid point using non-orthogonal wavelets will be discussed.

Yee, Helen C.↗
DOE OSTI2022

Shape memory in self-adapting colloidal crystals

We report reconfigurable, mechanically responsive crystalline materials are central components in many sensing, soft robotic, and energy conversion and storage devices1,2,3,4. Crystalline materials can readily deform under various stimuli and the extent of recoverable deformation is highly dependent upon bond type1,2,5,6,7,8,9,10. Indeed, for structures held together via simple electrostatic interactions, minimal deformations are tolerated. By contrast, structures held together by molecular bonds can, in principle, sustain much larger deformations and more easily recover their original configurations. In this report we study the deformation properties of well-faceted colloidal crystals engineered with DNA. These crystals are large in size (greater than 100 µm) and have a body-centred cubic (bcc) structure with a high viscoelastic volume fraction (of more than 97%). Therefore, they can be compressed into irregular shapes with wrinkles and creases, and, notably, these deformed crystals, upon rehydration, assume their initial well-formed crystalline morphology and internal nanoscale order within seconds. For most crystals, such compression and deformation would lead to permanent, irreversible damage. The substantial structural changes to the colloidal crystals are accompanied by notable and reversible optical property changes. For example, whereas the original and structurally recovered crystals exhibit near-perfect (over 98%) broadband absorption in the ultraviolet–visible region, the deformed crystals exhibit significantly increased reflection (up to 50% of incident light at certain wavelengths), mainly because of increases in their refractive index and inhomogeneity.

36 MATERIALS SCIENCE↗
DOE OSTI2023

IACMI Project 4.7: Pultruded Textile Carbon Fiber for Spar Caps (Final Report)

The primary objective of this project was to demonstrate the potential to significantly reduce the cost of wind turbine blades with carbon fiber reinforced polymer (CFRP) structure. Applicability of textile carbon fibers (TCF) were evaluated for use in pultruded spar cap (SC) elements as a path to cost reduction for utility scale wind turbine blades. In earlier work for the Department of Energy (DOE) Wind Energy Technologies Office (WETO), a collaboration of Sandia National Laboratory (SNL), Oak Ridge National Laboratory (ORNL), and Montana State University has demonstrated potential for pultruded TCF to compete with infused fiberglass and commercially available carbon fiber pultruded sections for spar cap construction. In the design cases evaluated, the TCF sections fared well when compared on cost per unit composite stiffness and cost per unit composite compressive strength for those designs [1]. Both stiffness and compressive strength tend to be key factors in the design of blade composite Spar Cap which carry the bulk of the blade structural loads in bending. Spar Cap design tends to distribute largely symmetric tensile and compressive stresses to opposite sides of the spar structure, but since carbon fiber composite compressive strength is typically 20-50% lower than tensile strength, the compressive loading reaches failure levels well before the tensile loading. Stiffness is critical in containing the large tip deflection in high wind loading situations. However, materials and process development were very limited in the earlier study and the work in this project was expanded to make the comparative information more representative of what will be required in order to make further inroads towards implementation. Similar to that study, this project team confirmed that the primary materials of interest for pultruded spar cap elements should be thermoset (TS) resins reinforced by carbon fibers, utilizing as high a percentage of TCF as practical to benchmark cost and performance against commercial carbon fibers. To make the closest comparison possible and eliminate specific test article size, resin selection, and equipment/operational nuance effects, the team planned to pultrude sections with 100% commercially available carbon fiber (Panex 35 carbon fiber from Zoltek) as well as samples utilizing high fractions of TCF. The resin system chosen was based on formulations recommended by large wind industry supplier Hexion and consisted of Hexion resin RSL-4597, curing agent CCA-138, and internal mold release additive 117, along with common kaolin filler ASP400P from BASF. As commonly deployed in spar cap configurations, the team had a mold built to pultrude a rectangular spar cap element of 100mm width and 3mm thickness. The extremely limited number of samples produced for the earlier study were produced with a “generic” epoxy utilized for a variety of applications by the pultruder contracted to produce test articles for demonstration purposes. More importantly, those samples were produced at a fiber fraction only slightly over 50%. Based on feedback from our industrial advisory team for that project and strongly recommended by this project team, the consensus is that it is highly desirable to obtain fiber fractions of 65-68% for significant penetration in wind blade spar cap. Although this requirement has yet to be exhaustively confirmed in readily available information, this was established as a project goal and informally decided we needed to exceed 60% fiber fraction to gain serious industry consideration. Previous TCF pultrusion trials have been challenged by the lack of robust TCF packages, resulting in non-uniform tension across and between tows, as well as excess labor and waste for removal of interleaved paper. The non-uniform tension and associated intermingling of tows in textile acrylic fiber tows and associated difficulties created from broken filaments in carbon fiber conversion inhibit the ordered packing necessary to enhance fiber fraction elevation. (These “cross-overs” are not considered undesirable for textile applications and there is some sense that they might be advantageous for those applications). In addition to work that is ongoing at the acrylic fiber manufacturers to improve their formats, The Institute of Advanced Composites Manufacturing Innovation (IACMI) Project 6.12 (report PA16-0349-6.12-01) [2] has developed and demonstrated a more robust packaging and creeling approach that at least partially addresses these issues, thus improving control of the TCF feed into the pultrusion unit. It was hoped that these and other improvements currently being implemented would allow us to achieve fiber fractions at least approaching these fiber fraction targets. During this project, sections utilizing 100% commercially available carbon fiber reinforcement were produced as a baseline, as well as sections reinforced with about 94% TCF and the balance being commercially available fiber for comparison. The most important finding was that similar to results reported in the earlier WETO-funded project and results from tests of TCF reported at IACMI meetings, this work demonstrated that sections pultruded with TCF in an epoxy resin frequently utilized in actual spar cap production had stiffness and compressive strengths largely comparable to similar sections pultruded with a commercially available carbon fiber also frequently utilized in the wind industry. Although the amount of that data is limited, some of the tensile strength results were actually closer than would have been expected based on fiber strength results provided by the TCF and commercial fiber producers. The actual test data are reported and discussed in detail in Section 5. The pultruded sections dominated by TCF reinforcement were approximately 8-10% lower in fiber fraction than for the sections produced using commercial fiber alone, making direct comparison difficult. The COVID-19 project has provided significant insight into the current state-of-the-art with various TCF product forms. The data obtained in this project will guide the planned improvements at the precursor level, especially in attaining uniform tensioning and payout to facilitate enhanced fiber fractions and overall processability of the TCF composites. The project team is providing guidance to stakeholders concerning the attributes, needs, and potential demand for TCF in wind blade spar caps. Results achieved in this project are consistent with findings in the related work cited [1] and support this guidance and the high potential for this product type. TCF precursor-producing partners continue to express interest in enhancing their product forms and the team looks forward to working with these improved materials as they become available.

42 ENGINEERING↗
NASA NTRS1995

Explicit and implicit compact high-resolution shock-capturing methods for multidimensional Euler equations 1: Formulation

Two classes of explicit compact high-resolution shock-capturing methods for the multidimensional compressible Euler equations for fluid dynamics are constructed. Some of these schemes can be fourth-order accurate away from discontinuities. For the semi-discrete case their shock-capturing properties are of the total variation diminishing (TVD), total variation bounded (TVB), total variation diminishing in the mean (TVDM), essentially nonoscillatory (ENO), or positive type of scheme for 1-D scalar hyperbolic conservation laws and are positive schemes in more than one dimension. These fourth-order schemes require the same grid stencil as their second-order non-compact cousins. One class does not require the standard matrix inversion or a special numerical boundary condition treatment associated with typical compact schemes. Due to the construction, these schemes can be viewed as approximations to genuinely multidimensional schemes in the sense that they might produce less distortion in spherical type shocks and are more accurate in vortex type flows than schemes based purely on one-dimensional extensions. However, one class has a more desirable high-resolution shock-capturing property and a smaller operation count in 3-D than the other class. The extension of these schemes to coupled nonlinear systems can be accomplished using the Roe approximate Riemann solver, the generalized Steger and Warming flux-vector splitting or the van Leer type flux-vector splitting. Modification to existing high-resolution second- or third-order non-compact shock-capturing computer codes is minimal. High-resolution shock-capturing properties can also be achieved via a variant of the second-order Lax-Friedrichs numerical flux without the use of Riemann solvers for coupled nonlinear systems with comparable operations count to their classical shock-capturing counterparts. The simplest extension to viscous flows can be achieved by using the standard fourth-order compact or non-compact formula for the viscous terms.

Yee, H. C.↗