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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

Quantitative measurement of transverse injector and free stream interaction in a nonreacting SCRAMJET combustor using laser-induced iodine fluorescence

A preliminary quantitative study of the compressible flowfield in a steady, nonreacting model SCRAMJET combustor using laser-induced iodine fluorescence (LIIF) is reported. Measurements of density, temperature, and velocity were conducted with the calibrated, nonintrusive, optical technique for two different combustor operating conditions. First, measurements were made in the supersonic flow over a rearward-facing step without transverse injection for comparison with calculated pressure profiles. The second configuration was staged injection behind the rearward-facing step at an injection dynamic pressure ratio of 1.06. These experimental results will be used to validate computational fluid dynamic (CFD) codes being developed to model supersonic combustor flowfields.

Fletcher, D. G.↗

Quantitative characterization of a nonreacting, supersonic combustor flowfield using unified, laser-induced iodine fluorescence

A calibrated, nonintrusive optical technique, laser-induced iodine fluorescence (LIIF) was used to quantify the steady, compressible flowfield of a nonreacting, supersonic combustor. The combustor was configured with single and staged, transverse-air injection into a supersonic-air freestream behind a rearward-facing step. Pressure, temperature, two-velocity components, and injectant mole fraction were measured with high spatial resolution in the three-dimensional flowfields. These experimental results provide a benchmark set of data for validation of computational fluid dynamic (CFD) codes being developed to model supersonic combustor flowfields.

Fletcher, D. G.↗

Simultaneous measurements of temperature and density in air flows using UV laser spectroscopy

The simultaneous measurement of temperature and density using laser-induced fluorescence of oxygen in combination with Q-branch Raman scattering of nitrogen and oxygen is demonstrated in a low-speed air flow. The lowest density and temperature measured in the experiment correspond to the freestream values at Mach 5 in the Ames 3.5-Foot Hypersonic Wind Tunnel for stagnation conditions of 100 atm and 1000 K. The experimental results demonstrate the viability of the optical technique for measurements that support the study of compressible turbulence and the validation of numerical codes in supersonic and hypersonic wind tunnel flows.

Fletcher, D. G.↗

Numerical simulation of icing, deicing, and shedding

An algorithm has been developed to numerically model the concurrent phenomena of two-dimensional transient heat transfer, ice accretion, ice shedding and ice trajectory which arise from the use of electrothermal pad. The Alternating Direction Implicit method is used to simultaneously solve the heat transfer and accretion equations occurring in the multilayered body covered with ice. In order to model the phase change between ice and water, a technique was used which assumes a phase for each node. This allows the equations to be linearized such that a direct solution is possible. This technique requires an iterative procedure to find the correct phase at each node. The computer program developed to find this solution has been integrated with the NASA-Lewis flow/trajectory code LEWICE.

Wright, W. B.↗

Some partial-unit-memory convolutional codes

The results of a study on a class of error correcting codes called partial unit memory (PUM) codes are presented. This class of codes, though not entirely new, has until now remained relatively unexplored. The possibility of using the well developed theory of block codes to construct a large family of promising PUM codes is shown. The performance of several specific PUM codes are compared with that of the Voyager standard (2, 1, 6) convolutional code. It was found that these codes can outperform the Voyager code with little or no increase in decoder complexity. This suggests that there may very well be PUM codes that can be used for deep space telemetry that offer both increased performance and decreased implementational complexity over current coding systems.

Abdel-Ghaffar, K.↗

An image compression technique for use on token ring networks

A low complexity technique for compression of images for transmission over local area networks is presented. The technique uses the synchronous traffic as a side channel for improving the performance of an adaptive differential pulse code modulation (ADPCM) based coder.

Gorjala, B.↗

Modifications of the Griesmer bound

The Griesmer bound is a classical technique (developed in 1960) for estimating the minimum length n required for a binary linear code with a given dimension k and minimum distance d. In this article, a unified derivation of the Griesmer bound and two new variations on it are presented. The first variation deals with linear codes which contain the all-ones vector; such codes are quite common and are useful in practice because of their 'transparent' properties. The second variation deals with codes that are constrained to contain a word of weight greater than or equal to M. In both cases these constraints (the all-ones word or a word of high weight) can increase the minimum length of a code with given k and d.

Mceliece, R. J.↗

Benchmark Data for Evaluation of Aeroacoustic Propagation Codes With Grazing Flow

Increased understanding of the effects of acoustic treatment on the propagation of sound through commercial aircraft engine nacelles is a requirement for more efficient liner design. To this end, one of NASA s goals is to further the development of duct propagation and impedance reduction codes. A number of these codes have been developed over the last three decades. These codes are typically divided into two categories: (1) codes that use the measured complex acoustic pressure field to reduce the acoustic impedance of treatment that is positioned along the wall of the duct, and (2) codes that use the acoustic impedance of the treatment as input and compute the sound field throughout the duct. Clearly, the value of these codes is dependent upon the quality of the data used for their validation. Over the past two decades, data acquired in the NASA Langley Research Center Grazing Incidence Tube have been used by a number of researchers for comparison with their propagation codes. Many of these comparisons have been based upon Grazing Incidence Tube tests that were conducted to study specific liner technology components, and were incomplete for general propagation code validation. Thus, the objective of the current investigation is to provide a quality data set that can be used as a benchmark for evaluation of duct propagation and impedance reduction codes. In order to achieve this objective, two parallel efforts have been undertaken. The first of these is the development of an enhanced impedance eduction code that uses data acquired in the Grazing Incidence Tube. This enhancement is intended to place the benchmark data on as firm a foundation as possible. The second key effort is the acquisition of a comprehensive set of data selected to allow propagation code evaluations over a range of test conditions.

Jones, Michael G.↗

Evaluation of Variable-Depth Liner Configurations for Increased Broadband Noise Reduction

This paper explores the effects of variable-depth geometry on the amount of noise reduction that can be achieved with acoustic liners. Results for two variable-depth liners tested in the NASA Langley Grazing Flow Impedance Tube demonstrate significant broadband noise reduction. An impedance prediction model is combined with two propagation codes to predict corresponding sound pressure level profiles over the length of the Grazing Flow Impedance Tube. The comparison of measured and predicted sound pressure level profiles is sufficiently favorable to support use of these tools for investigation of a number of proposed variable-depth liner configurations. Predicted sound pressure level profiles for these proposed configurations reveal a number of interesting features. Liner orientation clearly affects the sound pressure level profile over the length of the liner, but the effect on the total attenuation is less pronounced. The axial extent of attenuation at an individual frequency continues well beyond the location where the liner depth is optimally tuned to the quarter-wavelength of that frequency. The sound pressure level profile is significantly affected by the way in which variable-depth segments are distributed over the length of the liner. Given the broadband noise reduction capability for these liner configurations, further development of impedance prediction models and propagation codes specifically tuned for this application is warranted.

Jones, M. G.↗

Streaming authentication and multi-level security for communications networks using quantum cryptography

Message authenticators for quantum-secured communications facilitate low-latency authentication with assurances of security. Low-latency message authenticators are especially valuable in infrastructure systems where security and latency constraints are difficult to satisfy with conventional non-quantum cryptography. For example, a message transmitter receives a message and derives an authentication tag for the message based at least in part on an authenticator that uses one or more quantum keys. The message transmitter outputs the message and its authentication tag. A message receiver receives a message and authentication tag for the message. The message receiver derives a comparison tag for the message based at least in part on an authenticator that uses one or more quantum keys. The message receiver checks whether the message is authentic based on a comparison of the authentication tag and the comparison tag. In example implementations, the authenticator uses stream-wise cyclic redundancy code operations.

Hughes, Richard J.↗

Illustration of bunch merge simulation in AGS

Following are examples of a 4 to 2 to 1 merge of proton bunches in AGS obtained by running the simulation code ags2mrg23. As the code runs, the user is prompted to enter several numbers. For these examples, RF harmonic number 12.0 is entered. An RF frequency of 4.453 913 448 73 MHz at this harmonic is entered. This gives proton G γ = 45.5. The merge simulation starts with a uniform distribution of unbunched protons. 2.0 eV-s is entered for the longitudinal emittance of the distribution. The code will recommend a voltage to capture the unbunched protons into 4 harmonic 12 buckets. A capture voltage of 0.0527 kV is recommended. 0.053 kV is entered. It is desirable to capture the protons as “adiabatically” as possible. Because of the long synchrotron period (372 ms), a capture time of 74,707 ms is recommended by the code. A shorter time, 10,000 ms, is entered to reduce the running time of the code. A 4 to 2 merge time of 37,353 ms is recommended by the code. 4000.0 ms is entered. A 2 to 1 merge time twice that of the 4 to 2 merge is recommended by the code. 8000.0 ms is entered. The code requests a “time fraction” FQMRG to be entered. This is a number (from 0.1 to 1.0) that determines the time at which data are recorded during the 4 to 2 merge. The number 0.5 is entered. This encodes the recording of data halfway through the 4 to 2 merge.

43 PARTICLE ACCELERATORS↗

Generalized minimum distance decoding.

Generalized minimum distance decoding that permits likelihood information to be used, yielding same probability of error as maximum likelihood decoding

DISTANCE MEASURING EQUIPMENT↗

Quantitative metrics for evaluating thermonuclear design codes and physics models applied to the National Ignition Campaign

In this study, physics models and design codes for hot dense plasmas undergoing thermonuclear burn are evaluated objectively using statistical metrics that compare the difference between calculations and data relative to the experimental uncertainties. The analysis is applied to the National Ignition Campaign (NIC) because it is relevant, comprehensive, and well documented. The statistics confirm that a key process afflicting NIC performance is mix driven by hydrodynamic instabilities as approximated here using the KL model [G. Dimonte and R. Tipton, Phys. Fluids 18, 085101 (2006)]. New physics models are also presented for instability-driven magnetic fields [B. Srinivasan et al., Phys. Rev. Lett. 108, 165002 (2012)] and the Coulomb logarithm for electron–ion thermal relaxation [G. Dimonte and J. Daligault, Phys. Rev. Lett. 101, 135001 (2008)]. The plasma-generated magnetic fields improve the agreement between code and data in a statistically significant manner by reducing the electron thermal conduction in the hot-spot via the Hall term. The Coulomb logarithm is presented in a numerically practical form that incorporates recent theoretical advances. However, it does not improve the agreement between the code and data because the thermal relaxation is so fast in non-ignited NIC plasmas that the typical 20% error does not change the tight coupling between electrons and ions. Even with these improved physics models, the one-dimensional simulations presented here are not able to describe the high-convergence NIC implosions in a statistically acceptable manner. Of the heroic multi-dimensional simulations of Clark et al. [Phys. Plasmas 23, 056302 (2016)], only those in three-dimensions satisfy the statistical acceptance criterion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Combined Mesonet and Tracker

Title: Combined Mesonet and Trackers (UNL Mobile Mesonets) Authors University of Nebraska PI: Adam Houston, UNL Professor (ahouston2@unl.edu) Mailing Address: 126 Bessey Hall P.O. Box 880340 Lincoln, NE 68588-0340 CoMeT Overview The University of Nebraska-Lincoln operates three Combined Mesonet and Tracker (CoMeTs). CoMeTs are Ford Explorers (model years 2015, 2017, and 2019) with forward-mounted suites of meteorological sensors and dual moonroofs, combining the capability of a mobile mesonet to collect near-surface observations with the capability of an unmanned aircraft systems (UAS) tracker vehicle, which enables an observer in the second row of seats to see the aircraft and maintain compliance with Federal Aviation Administration policies on UAS operation. The CoMeTs collect observations of slow temperature and humidity at ~2 m above ground level (AGL) using a Vaisala HMP155A, fast temperature at ~2 m AGL using a Campbell Scientific 109SS-L thermistor, pressure at ~2.5 m AGL using a Vaisala PTB210, wind speed and direction at ~3.25 m AGL using an R.M. Young 05103 propeller anemometer, and vehicle heading using a KVH Industries C-100 fluxgate compass (Barbieri et al. 2019). The HMP155A and 109SS-L thermistor are shielded and aspirated within a U-tube (Waugh and Frederickson 2010; Houston et al. 2016). This list of sensors is also included in the CoMeT data file metadata. Manufacturer specifications for these instruments are given in Table 1 of Hanft and Houston (2018). The reported measured quantities are summarized below.CoMeT-3 was funded through an equipment allocation included in the NSF TORUS award (AGS-1824649). Instrument Description The specific sensors included on each CoMeT are summarized in the table at the end of this section. In general each CoMeT collects observations of slow temperature and humidity at ~2 m above ground level (AGL) using a Vaisala HMP155, fast temperature at ~2 m AGL using a Campbell Scientific 109SS-L thermistor, pressure at ~2.5 m AGL using a Vaisala PTB210 barometer with a Gill pressure port, wind speed and direction at ~3.25 m AGL using an R.M. Young 05103 propeller anemometer, position using a Garmin 19x HVS receiver, and vehicle heading using a KVH Industries C-100 fluxgate compass. The HMP155 and 109SS are shielded and aspirated within a U-tube (Waugh and Frederickson 2010; Houston et al. 2016). Fast temperature and corrected RH measurements (using sensors housed within the U-tube) have a time constant of 10-12 s based on data collected across a temperature and RH shock during the CLOUD-MAP 2017 calibration/validation tests on June 26, 2017. Vehicle speed was < 10 kts for this test. CoMeT-1 CoMeT-2 CoMeT-3 Slow Temperature Slow RH Vaisala HMP155A-L20-PT Part #: 22280-7 Vaisala HMP155E Part #: E1AA11A0B1A1A0A Vaisala HMP155E Part #: E1AA11A0B1A1A0A Fast temperature Campbell Scientific 109SS-L20-PT Part #: 21448-3 Campbell Scientific 109SS-L12-PW Part #: 21448-109 Campbell Scientific 109SS-L12-PW Part #: 21448-150 Pressure Vaisala PTB-210 Part #: A1A1B Gill Pressure Port Part #: 61002 Vaisala PTB-210 Part #: A1A1B Gill Pressure Port Part #: 61002 Vaisala PTB-210 Part #: A1A1B Gill Pressure Port Part #: 61002 Wind RM Young 05103-L20-PT Part #: 18435-310 RM Young 05103-L20-PW Part #: 18435-244 RM Young 05103-L20-PW Part #: 18435-244 GPS Garmin GPS 19x HVS (NMEA 0183) Part #: 010-01010-00 Garmin GPS 19x HVS (NMEA 0183) Part #: 010-01010-00 Garmin GPS 19x HVS (NMEA 0183) Part #: 010-01010-00 Compass KVH C-100 Part #: 01-0177-15 KVH C-100 Part #: 01-0177-15 KVH C-100 Part #: 01-0177-15 Logger Campbell Scientific CR6-NA-XT-SW Part #: 28385-9 Campbell Scientific CR6-WIFI-XT-SW Part #: 28385-6 Campbell Scientific CR6-WIFI-XT-SW Part #: 28385-6 Data Collection and Real-Time Processing The reported measured quantities are summarized in the table below. Quantity Units Source Epoch time Seconds GPS Latitude and longitude Degrees GPS Altitude m GPS Pressure hPa PTB210 Temperature (fast) deg C 109SS-L Temperature (slow) deg C HMP155 RH (slow) % HMP155 Vehicle speed m/s GPS Vehicle heading deg C-100 and GPS In addition to the measured variables, several derived variables are calculated. Corrected/fast relative humidity (%) Relative humidity is adjusted to the fast temperature following Richardson et al. (1998) and Houston et al. (2016). Water vapor mixing ratio (g/kg) Dew point temperature (&deg;C) Potential temperature (Kelvin) Virtual potential temperature (Kelvin) Equivalent potential temperature (Kelvin) Regular intercomparisons between all three CoMeTs were performed during TORUS 2019. Comparisons were also conducted between CoMeT-1 and CoMeT-2 during LAPSE-RATE (2018) on 14 July. In these intercomparisons, the vehicles were parked adjacent to each other aligned perpendicular to (and facing into) the wind. To minimize engine heating effects, intercomparisons were only conducted when the wind speed was >10 kts. Data Format Original data files for each deployment are saved as text files and then converted to NetCDF. NetCDF versions have units that are CF compliant and may not match the original units in the txt files. The naming convention for the NetCDF files is as follows: UNL.CoMeT3.{deployment date YYYYMMDD}.{start time of observation collection in UTC HHMM}.L2.{post-processing codes}.cdf example: UNL.CoMeT3.20190627.1931.L2.g1.f1.cdf Post-processing codes are included to track modifications to the raw data. These codes are closely connected to error flags associated with each record. Each letter corresponds to a particular instrument: g: GPS p: Barometer tf: Fast temperature ts: Slow temperature rh: Relative humidity f: Compass w: Wind monitor a: All instruments Each number corresponds to a particular post-processing action described more below. Measured and derived variables are included in the following table. Variable Heading Standard Name Units time Time seconds since 00:00:00, 01-01-1970 Alt Altitude meters lat Latitude degrees north lon Longitude degrees east fast_temp Air Temperature kelvin slow_temp Air Temperature kelvin pressure Air Pressure pascals logger_RH Relative Humidity percent calc_corr_RH Relative Humidity percent wind_speed Wind Speed meters per second wind_dir Wind From Direction degrees vehicle_dir Vehicle Direction degrees dewpoint Dew Point Temperature kelvin mixing_ratio Humidity Mixing Ratio g/g theta Air Potential Temperature kelvin theta_v Virtual Potential Temperature kelvin theta_e Equivalent Potential Temperature Kelvin error_flag The error_flag variable is a string that matches the post-processing codes listed above. All instruments will have an associated code, but will have a &ldquo;0&rdquo; if the datum is unchanged from the initial processed value. Error Codes The following table summarizes the error codes for data collected before 2020: Error Code Relevant CoMeT Description g1 1,2,3 Exact correction. GPS position and time reprocessed from raw data g2 1 As far as we can tell this is an exact correction to an error in the GPS time. During the correct time periods the time suddenly went backwards ~250s and stayed at this offset for 750s when it corrected itself. The offset was applied to the &ldquo;time warp&rdquo; period. p1 2 Approximate correction. Hole in the pressure tube connecting the pressure port to the barometer. Resulted in erroneously low air pressure measurements when the vehicle was in motion. Derived variables recalculated (dew point temperature [e depends on qv and p], water vapor mixing ratio, potential temperature, virtual potential temperature, equivalent potential temperature) a1 3 Exact correction. Missing data reprocessed from raw data a2 1 Bug fix to bias correction for ts1, ts2, and rh1: water vapor mixing ratio was off by a factor of 10 and virtual potential temperature was wrong because of this. f1 3 No correction, missing data. Fluxgate compass inoperable. Wind speed and direction calculated using GPS-derived vehicle heading instead. rh1 1 Approximate correction. Constant bias of +1.7% removed from relative humidity. Derived variables recalculated (corrected/fast relative humidity, dew point temperature, water vapor mixing ratio, virtual potential temperature, equivalent potential temperature) ts1 1 Approximate correction. Constant bias of +0.6 K removed from slow temperature. Derived variables recalculated (corrected/fast relative humidity, dew point temperature, water vapor mixing ratio, virtual potential temperature, equivalent potential temperature) ts2 1 Approximate correction. Constant bias of +1.0 K removed. Derived variables recalculated (corrected/fast relative humidity, dew point temperature, water vapor mixing ratio, virtual potential temperature, equivalent potential temperature) References Bolton, D., 1980: The Computation of Equivalent Potential Temperature. Mon. Wea. Rev., 108, 1046&ndash;1053, https://doi.org/10.1175/1520-0493(1980)108<1046:TCOEPT>2.0.CO;2. Hanft, W., and A. L. Houston, 2018: An Observational and Modeling Study of Mesoscale Air Masses with High Theta-E. Mon. Wea. Rev., 146, 2503&ndash;2524, https://doi.org/10.1175/MWR-D-17-0389.1.Wexler Houston, A. L., R. J. Laurence III, T. W. Nichols, S. Waugh, B. Argrow, and C. L. Ziegler, 2016: Intercomparison of unmanned aircraft-borne and mobile mesonet atmospheric sensors. Journal of Atmospheric and Oceanic Technology. 33, 1569-1582, doi: 10.1175/JTECH-D-15-0178.1. Lowe, P. R., 1977: An Approximating Polynomial for the Computation of Saturation Vapor Pressure. J. Applied Meteorology, 16, 100&ndash;103. Richardson, S. J., S. E. Frederickson, F. V. Brock, and J. A. Brotzge, 1998: Combination temperature and relative humidity probes: Avoiding large air temperature errors and associated relative humidity errors. Preprints, 10th Symp. On Meteorological Observations and Instrumentation, Phoenix, AZ, Amer. Meteor. Soc., 278&ndash;283. Waugh, S., and S. E. Frederickson, 2010: An improved aspirated temperature system for mobile meteorological observations, especially in severe weather. 25th Conf. on Severe Local Storms, Denver, CO, Amer. Meteor. Soc., P5.2. [Available online at https://ams.confex.com/ams/25SLS/techprogram/paper_176205.htm.]

54 ENVIRONMENTAL SCIENCES↗

Numerical Analysis of Temperature Gradients and Interface Shape During Directional Solidification of Al and Al-Cu Alloy Under Microgravity Conditions

Numerical modeling was undertaken to analyze the influence of radial thermal gradient on solid/liquid (s/1) interface shape and convection patterns during solidification of pure Al and Al-4 wt% Cu alloy. The objective of the numerical task was to predict the influence of convective velocity on an insoluble particle near a s/l interface. These predictions would then be used to define the minimum gravity level (g) required to investigate the fundamental physics of interaction between a particle and a s/I interface. To satisfy this objective, steady state calculations were performed for different gravity levels and orientations with the gravity vector. ne furnace configuration used in this analysis is the proposed International Space Station Furnace, Quench Module Insert (QMI) 1. Results from a thermal model of the furnace core were used as initial boundary conditions for solidification modeling. General model of binary alloy solidification was based on the finite element code FIDAP. It was found that for the worst case orientation of 90 degrees with the gravity vector and a g level of 10(exp -4)g(sub o) (g(sub o) = 9.8 m/s(exp 2)) the dominant forces acting on the particle would be the fundamental drag and interfacial forces.

Bune, Andris V.↗

Sphingobium lignivorans sp. nov., isolated from river sediment downstream of a paper mill

Here, a bacterial isolate, B1D3A T , was isolated from river sediment collected from the Hiwassee River near Calhoun, TN, by enrichment culturing with a model 5–5' lignin dimer, dehydrodivanillate, as its sole carbon source. B1D3A T was also shown to utilize several model lignin-derived monomers and dimers as sole carbon sources in a variety of minimal media. Cells were Gram-stain-negative, aerobic, motile, rod-shaped and formed yellow/cream-coloured colonies on rich agar. Optimal growth occurred at 30°C, pH 7–8, and in the absence of NaCl. The major fatty acids of B1D3A T were C 18:1 ω7c and C 17:1 ω6c. The predominant hydroxy fatty acids were C 14: 0 2-OH and C 15:0 2-OH. The polar lipid profile consisted of a mixture of phosphatidylethanolamine, phosphatidylglycerol, diphosphatidylglycerol, phosphatidyldimethylethanolamine and sphingoglycolipid. B1D3A T contained spermidine as the only major polyamine. The major isoprenoid quinone was Q-10 with minor amounts of Q-9 and Q-11. The genomic DNA G+C content of B1D3A T was 65.6mol%. Phylogenetic analyses based on 16S rRNA gene sequences and coding sequences of 49 core, universal genes defined by Clusters of Orthologous Groups gene families indicated that B1D3A T was a member of the genus Sphingobium. B1D3A T was most closely related to Sphingobium sp. SYK-6, with a 100% 16S rRNA gene sequence similarity. B1D3A T showed 78.1–89.9%average nucleotide identity and 19.5–22.2% digital DNA–DNA hybridization identity with other type strains from the genus Sphingobium. On the basis of phenotypic and genotypic properties and phylogenetic inference, strain B1D3A T should be classified as representing a novel species of the genus Sphingobium, for which the name Sphingobium lignivorans sp. nov. is proposed. The type strain is strain B1D3A T (ATCC TSD-279 T =DSM 111877 T ).

59 BASIC BIOLOGICAL SCIENCES↗

A modern concept of Lagrangian hydrodynamics

Here, we offer a modern interpretation of Lagrangian hydrodynamics as employed in Lagrangian simulations of compressible fluid flow. Our main result is to show that artificial viscosity, traditionally viewed as a numerical artifice to control unphysical oscillations in flows with shocks, actually represents a physical process and is necessary to derive accurate simulations in any compressible flow. We begin by reviewing the origins of two numerical devices, artificial viscosity and finite-volume methods. We proceed to construct a mathematical (PDE) model that incorporates those numerics and in which a new length scale, the observer, arises representing the discretization. Associated with that length scale, there are new inviscid fluxes that are the artificial viscosity as first formulated by Richtmyer and an artificial heat flux postulated by Noh but typically not included in Lagrangian codes. We discuss the connection of our results to bivelocity hydrodynamics. We conclude with some speculation as to the direction of future developments in multidimensional Lagrangian codes as computers get faster and have larger memories.

97 MATHEMATICS AND COMPUTING↗