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DOE OSTI2026

Ultra-low thermal resistance and pressure drop copper and copper-tungsten diamond-shaped pin fin cold plates for liquid cooling of electronics

Modern and future data centers face increasing cooling challenges due to increasing chip thermal design power and die size, along with the need to reduce energy consumption used for cooling. High performance cooling solutions that maintain a low chip junction temperature are needed to ensure electronics reliability. This work develops an ultra-low thermal resistance and low pressure drop 75 mm × 75 mm cold plate, intended for next-generation electronics cooling. The cold plate features an array of diamond-shaped pin fins and integrated copper tungsten heat spreader, selected for its low coefficient of thermal expansion which reduces thermomechanical deformation and allows for closer integration of the cold plate with silicon dies. Starting with 300 candidate designs, three-dimensional computational fluid dynamics simulations predict the thermal-hydraulic performance of cold plate subsections. The highest performing geometries are evaluated with high fidelity simulations. Four cold plates are manufactured for experiments: three with diamond-shaped pin fins and one with straights fins for comparison purposes. The cold plates are fabricated from copper-tungsten (CuW), copper (Cu), or aluminum-silicon-magnesium alloy (AlSi10Mg). The diamond-shaped pin fins achieve a roughly 15 % lower thermal resistance compared to the conventional straight fin microchannel. The highest performing design achieves a chip-to-coolant (including thermal interface material) thermal resistance of 9.0 K/kW in CuW and 6.9 K/kW in Cu under a 1 kW heat load with an inlet-to-outlet pressure drop of 9.0 kPa and water as the working fluid. This work demonstrates ultra-low thermal resistance and pressure drop cold plates for large die, high heat load applications, and shows that CuW is an attractive cold plate material for improved reliability in next generation data center cooling.

Coefficient of thermal expansion↗

NASA NTRS1991

Transient response of a high-capacity heat pipe for Space Station Freedom

High-capacity heat pipe radiator panels have been proposed as the primary means of heat rejection for Space Station Freedom. In this system, the heat pipe would interface with the thermal bus condensers. Changes in system heat load can produce large temperature and heat load variations in individual heat pipes. Heat pipes could be required to start from an initially cold state, with heat loads temporarily exceeding their low-temperature transport capacity. The present research was motivated by the need for accurate prediction of such transient operating conditions. In this work, the cold startup of a 6.7-meter long high-capacity heat pipe is investigated experimentally and analytically. A transient thermohydraulic model of the heat pipe was developed which allows simulation of partially-primed operation. The results of cold startup tests using both constant temperature and constant heat flux evaporator boundary conditions are shown to be in good agreement with predicted transient response.

Ambrose, J. H.↗

NASA NTRS1997

Ion-Atom Cold Collisions and Atomic Clocks

Collisions between ultracold neutral atoms have for some time been the subject of investigation, initially with hydrogen and more recently with laser cooled alkali atoms. Advances in laser cooling and trapping of neutral atoms in a Magneto-Optic Trap (MOT) have made cold atoms available as the starting point for many laser cooled atomic physics investigations. The most spectacularly successful of these, the observation of Bose-Einstein Condensation (BEC) in a dilute ultra-cold spin polarized atomic vapor, has accelerated the study of cold collisions. Experimental and theoretical studies of BEC and the long range interaction between cold alkali atoms is at the boundary of atomic and low temperature physics. Such studies have been difficult and would not have been possible without the development and advancement of laser cooling and trapping of neutral atoms. By contrast, ion-atom interactions at low temperature, also very difficult to study prior to modern day laser cooling, have remained largely unexplored. But now, many laboratories worldwide have almost routine access to cold neutral atoms. The combined technologies of ion trapping, together with laser cooling of neutrals has made these studies experimentally feasible and several very important, novel applications might come out of such investigations . This paper is an investigation of ion-atom interactions in the cold and ultra-cold temperature regime. Some of the collisional ion-atom interactions present at room temperature are very much reduced in the low temperature regime. Reaction rates for charge transfer between unlike atoms, A + B(+) approaches A(+) + B, are expected to fall rapidly with temperature, approximately as T(sup 5/2). Thus, cold mixtures of atoms and ions are expected to coexist for very long times, unlike room temperature mixtures of the same ion-atom combination. Thus, it seems feasible to cool ions via collisions with laser cooled atoms. Many of the conventional collisional interactions, exploited as a useful tool at room temperature and higher, are greatly enhanced at low energy. For example, collisional spin transfer from one species of polarized atoms to another has long been a useful method for polarizing a sample of atoms where no other means was available. Because optical pumping cannot be used to polarize the nuclear spin of Xe-129 or He-3 (for use in nmr imaging of the lungs), the nuclear spins are polarized via collisions with an optically pumped Rb vapor in a cell containing both gases. In another case, a spin polarized thermal Cs beam was used to polarize the hyperfine states of trapped He(+)-3 ions in order to measure their hyperfine clock transition frequency. The absence of an x-ray light source to optically pump the ground state of the He(+)-3 ion necessitated this alternative state preparation. Similarly, Cd(+) and Sr(+) ions were spin-oriented via collisions in a cell with optically pumped Rb vapor. Resonant RF spin changing transitions in the ground state of the ions were detected by changes in the Rb resonance light absorption. Because cold collision spin exchange rates scale with temperature as T(sup -1/2) this technique is expected to be a far more powerful tool than the room temperature counterpart. This factor of 100 or more enhancement in spin exchange reaction rates at low temperatures is the basis for a novel trapped ion clock where laser cooled neutrals will cool, state select and monitor the ion clock transition. The advantage over conventional direct laser cooling of trapped ions is that the very expensive and cumbersome UV laser light sources, required to excite the ionic cooling transition, are effectively replaced by simple diode lasers.

Prestage, John D.↗

DOE OSTI2025

Ray-Tracing Simulations Characterizing the Performance of the Proposed 2028 HFIR HB4 Main Shutter

The Main Shutter at HB4 will serve two purposes after the HFIR Beryllium Reflector Replacement, planned to take place in 2028. First as the primary certified safety control permitting the passage of neutrons from the cold source in the HFIR pressure vessel into the cold guide hall, and second as the first set of reflecting surfaces used to guide neutrons from the source and into the individual guide starts for each instrument in the cold guide hall. This report outlines a the simulations and analyses used to conclude that the HB4 Main Shutter Insert alignment is critical to associated instrument performance. In general, the alignment of these surfaces to within +/-0.25 millimeters and +/-0.05° across all dimensions will ensure losses are no worse than 1% for any of the guide starts.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

Ray-Tracing Simulations Characterising the Performance of the Proposed 2024 HFIR HB4 Main Shutter

The Main Shutter at HB4 will serve two purposes after the HFIR Beryllium Reflector Replacement planned to take place in 2024. First as the primary certified safety control controlling the passage of neutrons from the cold source in the HFIR pressure vessel into the cold guide hall, and second as the first set of reflecting surfaces used to guide neutrons from the source and into the individual guide starts for each instrument in the cold guide hall.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1985

Chemistry in dynamically evolving clouds

A unified model of chemical and dynamical evolution of isolated, initially diffuse and quiescent interstellar clouds is presented. The model uses a semiempirically derived dependence of the observed cloud temperatures on the visual extinction and density. Even low-mass, low-density, diffuse clouds can collapse in this model, because the inward pressure gradient force assists gravitational contraction. In contrast, previous isothermal collapse models required the low-mass diffuse clouds to be unrealistically cold before gravitational contraction could start. Theoretically predicted dependences of the column densities of various atoms and molecules, such as C and CO, on visual extinction in diffuse clouds are in accord with observations. Similarly, the predicted dependences of the fractional abundances of various chemical species (e.g., CO, H2CO, HCN, HCO(+)) on the total hydrogen density in the core of the dense clouds also agree with observations reported to date in the literature. Compared with previous models of interstellar chemistry, the present model has the potential to explain the wide spectrum of chemical and physical properties of both diffuse and dense clouds with a common formalism employing only a few simple initial conditions.

Tarafdar, S. P.↗

NASA NTRS1933

Engine performance with a hydrogenated safety fuel

This report presents the results of an investigation to determine the engine performance obtained with a hydrogenated safety fuel developed to eliminate fire hazard. The tests were made on a single-cylinder universal test engine at compression ratios of 5.0, 5.5, and 6.0. Most of the tests were made with a fuel-injection system, although one set of runs was made with a carburetor when using gasoline to establish comparative performance. The tests show that the b.m.e.p. obtained with safety fuel when using a fuel-injection system is slightly higher than that obtained with gasoline when using a carburetor, although the fuel consumption with safety fuel is higher. When the fuel-injection system is used with each fuel and with normal engine temperatures the b.m.e.p. with safety fuel is from 2 to 4 percent lower than with gasoline and the fuel consumption about 25 to 30 percent higher. However, a few tests at an engine coolant temperature of 250 F have shown a specific fuel consumption approximating that obtained with gasoline with only a slight reduction in power. The idling of the test engine was satisfactory with the safety fuel. Starting was difficult with a cold engine but could be readily accomplished when the jacket water was hot. It is believed that the use of the safety fuel would practically eliminate crash fires.

Schey, Oscar W↗

NASA NTRS2009

Nozzle Side Load Testing and Analysis at Marshall Space Flight Center

Realistic estimates of nozzle side loads, the off-axis forces that develop during engine start and shutdown, are important in the design cycle of a rocket engine. The estimated magnitude of the nozzle side loads has a large impact on the design of the nozzle shell and the engine s thrust vector control system. In 2004 Marshall Space Flight Center (MSFC) began developing a capability to quantify the relative magnitude of side loads caused by different types of nozzle contours. The MSFC Nozzle Test Facility was modified to measure nozzle side loads during simulated nozzle start. Side load results from cold flow tests on two nozzle test articles, one with a truncated ideal contour and one with a parabolic contour are provided. The experimental approach, nozzle contour designs and wall static pressures are also discussed

Ruf, Joseph H.↗

NASA NTRS2014

Combustion Stability Characteristics of the Project Morpheus Liquid Oxygen / Liquid Methane Main Engine

The project Morpheus liquid oxygen (LOX) / liquid methane (LCH4) main engine is a Johnson Space Center (JSC) designed ~5,000 lbf-thrust, 4:1 throttling, pressure-fed cryogenic engine using an impinging element injector design. The engine met or exceeded all performance requirements without experiencing any in- ight failures, but the engine exhibited acoustic-coupled combustion instabilities during sea-level ground-based testing. First tangential (1T), rst radial (1R), 1T1R, and higher order modes were triggered by conditions during the Morpheus vehicle derived low chamber pressure startup sequence. The instability was never observed to initiate during mainstage, even at low power levels. Ground-interaction acoustics aggravated the instability in vehicle tests. Analysis of more than 200 hot re tests on the Morpheus vehicle and Stennis Space Center (SSC) test stand showed a relationship between ignition stability and injector/chamber pressure. The instability had the distinct characteristic of initiating at high relative injection pressure drop at low chamber pressure during the start sequence. Data analysis suggests that the two-phase density during engine start results in a high injection velocity, possibly triggering the instabilities predicted by the Hewitt stability curves. Engine ignition instability was successfully mitigated via a higher-chamber pressure start sequence (e.g., ~50% power level vs ~30%) and operational propellant start temperature limits that maintained \cold LOX" and \warm methane" at the engine inlet. The main engine successfully demonstrated 4:1 throttling without chugging during mainstage, but chug instabilities were observed during some engine shutdown sequences at low injector pressure drop, especially during vehicle landing.

Melcher, John C.↗

DOE OSTI2024

Cold Weather Impacts on Battery-Electric Transit Buses

Transit fleets exploring the adoption of battery-electric buses (BEBs) can start here to learn about the effects of cold weather and how to enhance bus performance in low temperatures.

ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2024

Tuning austenite stability through prior microstructure control in a low-alloy Q&P steel

Quenching and partitioning (Q&P) processing is a widely accepted heat treatment methodology for creating high strength steels consisting of ferrite, martensite, and austenite, while maintaining relatively low manufacturing costs. Though the research on effects of prior microstructure is limited, an understanding of the heat treatment response of different starting microstructures is critical to processing and creating steels with complex microstructures that contain retained austenite and may afford opportunities to further optimize properties. This study investigates the influence of starting microstructure (ferrite/pearlite versus martensite) and prior levels of cold work (38 verses 58 %) on the microstructural development and mechanical properties of a 0.2 C-2.0 Mn-1.5 Si (wt.%) steel exposed to Q&P processing. Samples with a starting martensitic microstructure resulted in higher retained austenite fractions and a more homogeneous microstructure after Q&P processing compared to a starting microstructure of ferrite-pearlite. Starting martensitic microstructures also displayed higher work hardening rates and higher uniform elongations. Larger cold reductions saw accelerated dissolution kinetics and austenite formation during intercritical annealing, resulting in more similar final microstructures from the ferrite-pearlite and martensitic starting microstructures. Finally, the results presented here indicate that varying prior processing can be a route to manipulate and control austenite stability in a Q&P processed steel.

36 MATERIALS SCIENCE↗

NASA NTRS2012

Characterization of the Vectron PX-570 Crystal Oscillator for Use in Harsh Environments

Computing hardware, data-acquisition systems, communications systems, and many electronic control systems require well-controlled timing signals for proper and accurate operation. These signals are, in most cases, provided by circuits that employ crystal oscillators due to availability, cost, ease of operation, and accuracy. In some cases, the electronic systems are expected to survive and operate under harsh conditions that include exposure to extreme temperatures. These applications exist in terrestrial systems as well as in aerospace products. Well-logging, geothermal systems, and industrial process control are examples of ground-based applications, while distributed jet engine control in aircraft, space-based observatories (such as the James Webb Space Telescope), satellites, and lunar and planetary landers are typical environments where electronics are exposed to harsh operating conditions. To ensure these devices produce reliable results, the digital heartbeat from the oscillator must deliver a stable signal that is not affected by external temperature or other conditions. One such solution is a recently introduced commercial-off-the-shelf (COTS) oscillator, the PX-570 series from Vectron International. The oscillator was designed for high-temperature applications and as proof, the crystal oscillator was subjected to a wide suite of tests to determine its ruggedness for operation in harsh environments. The tests performed by Vectron included electrical characterization under wide range of temperature, accelerated life test/aging, shock and vibration, internal moisture analysis, ESD threshold, and latch-up testing. The parametric evaluation was performed on the oscillator's frequency, output signal rise and fall times, duty cycle, and supply current over the temperature range of -125 C to +230 C. The evaluations also determined the effects of thermal cycling and the oscillator's re-start capability at extreme hot and cold temperatures. These thermal cycling and restart tests were performed at the NASA Glenn Research Center. Overall, the crystal oscillator performed well and demonstrated very good frequency stability. This paper will discuss the test procedures and present details of the performance results.

Li, Jacob↗

DOE OSTI2023

Overview on Shielding Analyses for the VENUS Instrument at SNS

VENUS, a world‐class versatile neutron imaging instrument, is under construction and is expected to be completed and ready to start commissioning in 2023. The range of cold to epithermal neutrons at SNS will give users of VENUS access to novel imaging methods, as well as to significantly improved existing methods. The instrument is being built on beam line 10 at Spallation Neutron Source (SNS) First Target Station (FTS) facing a decoupled poisoned hydrogen moderator. Instrument design, which includes optics, Front-End components and instrument enclosure components and shape started over 10 years ago and during this time had significant changes. All changes were supported by neutronics analyses to provide adequate shielding for both Front-End and instrument enclosure.Final optics design will provide the field of view (FOV) at the detector position (where the image is formed) to be as high as 0.20 by 0.20 m. Both the beam, which contains a large fraction of high-energy neutrons, and the desire for a large footprint on the detector are challenges for shielding design and budget, because the driving cost for the instrument is the beam line and enclosure shielding. For cost reason VENUS baseline design is optimized with respect to both the instrument cave footprint and its wall thickness, and Front-End shielding is tailored along the beam. Analyses are performed with the Monte Carlo particle transport code MCNPX version 2.7.0 to make choices on materials, thicknesses and configurations of the shielding. Numerous calculations are performed to meet space and coast constrain and to satisfy instrument physics needs and to comply with radiation protection requirements.

Gallmeier, Franz X.↗

DOE OSTI2020

RELAP5-3D Modeling of High Temperature Test Facility (HTTF) Test PG-26

The High Temperature Test Facility (HTTF) at Oregon State University (OSU) is a scaled integral effects experiment designed to investigate transient behavior in high-temperature gas-cooled nuclear reactors with prismatic fuel and reflector blocks. Several tests have been completed, and more are still planned to at the HTTF, including depressurized conduction cooldown (DCC) and pressurized conduction cooldown (PCC) transients. This report analyses test PG-26, a progression of the Double Ended Inlet-Outlet Crossover Duct Break transient that is referred to as a DCC. PG-26 has been performed at the HTTF between May 30 and June 30, 2019. Core initial conditions (i.e., before the DCC started) have been met using low power (<100 kW) and two of ten available electric heaters. The DCC transient was initiated during the 50 th hour of the test. The break valves were opened, and hot helium from the core and cold helium from the reactor cavity simulation tank (RCST) started mixing. The gases flowed in a countercurrent fashion, where the top half of the hot duct contained hot helium that flowed in one direction and cold helium that flowed in the other direction in the bottom half of the duct. After the pressure and density reached equilibrium, the event entered a diffusion mode. The onset of a reverse natural circulation was not observed during the DCC period of the test. Version 4.4.2ie of the RELAP5-3D computer code has been used to model the HTTF PG-26 test, and results have been compared to available high-quality measured data. The model used in this study is the quality-controlled HTTF RELAP5-3D model (HTTF base 2018-04-19 QA), originally developed by P. Bayless. The report includes RELAP5-3D results of the “base calculations” as well as some sensitivities to important uncertain model inputs, such as primary helium mass flow rate, core ceramic thermal properties, as well as heat evacuation and loop friction models. Using the base RELAP5-3D model predicts a countercurrent helium flow in the hot duct observed at the beginning of the DCC, but instead of going into a molecular diffusion mode, the model predicts the onset of natural convection. Increasing friction in the core and hot duct prevents the natural convection from happening in some of the simulations. Although some temperatures are well predicted (and even overpredicted), the general tendency is to underpredict the ceramic and helium temperatures and heat removal rates during the DCC, resulting in many of the assessment findings being in minimal or insufficient agreement with the data. It is worth noting that the described discrepancies between measured data and RELAP5-3D predictions are not RELAP5-3D code limitations. More so, they reflect limitations in boundary condition and thermal property knowledge. While the RELAP5-3D calculations of the test provide some insights into what happens during the transient, and point to missing or potentially uncertain data to which the experimenters can direct their attention, the principal conclusion is that the PG-26 test data are insufficient for a system code assessment.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Modeling of HTTF test PG-26 using RELAP5-3D and SAM

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2000

Geoscience Laser Altimeter System (GLAS) Final Test Report of DM LHP TV Testing

Two loop heat pipes (LHPs) are to be used for thermal control of the Geoscience Laser Altimeter System (GLAS), planned for flight in 2001. One LHP will be used to transport 100 W from a laser to the radiator, the other will transport 210 W from electronic boxes to the radiator. In order to verify the LHP design for the GLAS application, an LHP Development Model has been fabricated, and ambient and thermal vacuum tested. Two aluminum blocks of 15 kg and 30 kg, respectively, were attached to the LHP to simulate the thermal masses connected to the heat sources. A 20 W starter heater was installed on the evaporator to aid the loop startup. A new concept to thermally couple the vapor and liquid line was also incorporated in the LHP design. Such a thermal coupling would reduce the power requirement on the compensation chamber in order to maintain the loop set point temperature. To avoid freezing of the liquid in the condenser during cold cases, propylene was selected as the working fluid. The LHP was tested under reflux mode and with adverse elevation. Tests conducted included start-up, power cycle, steady state and transient operation during hot and cold cases, and heater power requirements for the set point temperature control of the LHP. Test results showed very successful operation of the LHP under all conditions. The 20 W starter heater proved necessary in order to start the loop when a large thermal mass was attached to the evaporator. The thermal coupling between the liquid line and the vapor line significantly reduced the heater power required for loop temperature control, which was less than 5 watts in all cases, including a cold radiator. The test also demonstrated successful operation with a propylene working fluid, with successful startups with condenser temperatures as low as 100 C. Furthermore, the test demonstrated accurate control of the loop operating temperature within +/- 0.2 C, and a successful shutdown of the loop during the survival mode of operation.

Baker, Charles↗

DOE OSTI2023

Self-Powered Autonomous Sensing System for Arctic Ocean using a Frequency-multiplied Cylindrical Triboelectric Nanogenerator

An autonomous sensing system for collecting environmental observations in the Arctic region is critical for the estimation and prediction of climate change. Ocean waves are a great source of energy for these sensing systems but there has been limited research done on small-scale energy harvesting applications in the Arctic Ocean (subsea or surface). The available wave energy in the Arctic Ocean is lower than the typical ocean wave energy due to the low wave frequency, height, and operating months. Although the available wave energy depends on the specific location in the Arctic Ocean, the wave height decreases everywhere during the winter (Jan-March) [1]. Our target location in this work is the Beaufort and Chukchi Seas, which are ice covered for about 195 days per year leaving only a few months (June-November) for wave energy harvesting [2]. During these few months, the average wave frequency is 0.2 Hz and the most common wave frequency is around 0.15 Hz. Many energy harvesting methods are unsuitable for use in the Arctic Ocean because of to the cold temperature, low wave frequency, and low wave height. Triboelectric nanogenerators (TENG) are one of the few energy harvesting methods that excel in these conditions. Zhong et al. [3] designed a stacked pendulum-structured TENG for low-frequency ocean wave energy and reported the device generated a peak power density of 11.2 W/m3 under the low wave frequency of 0.2 Hz. The autonomous sensing system we developed for the Arctic Ocean, the Arctic-TENG, is based on a frequency-multiplied cylindrical TENG (FMC-TENG) which is an optimized TENG configuration for Arctic Ocean conditions due to the high power density under low-frequency wave conditions [4]. Figure 1 shows an FMC-TENG with multiple pairs of free-standing triboelectric-layer mode materials (Aluminum and FEP). The mass and magnet attached to the rotor store gravitational potential energy which is released as kinetic energy when the potential energy overcomes the repulsive magnetic force generated by the opposing magnet attached to the stator. This force unbalance triggers a sudden rotation and swinging motion of the mass which increases the angular velocity of the system and therefore enhances the output power of the TENG system. The main components of the Arctic-TENG are a 3D-printed rotor and stator, electric and dielectric material adhesive tape, and bearings. All these materials were cold-soaked and tested at -40 °C in a chest freezer. Both the 3D-printed parts and adhesives were confirmed to have a minimal effect from the cold temperature. Multiple bearings were tested and the starting torque of each one was compared both at room temperature and -40 °C. The bearing with the lowest starting torque at -40 °C was selected for use in the Arctic-TENG. The Arctic-TENG was tested using an out-of-water motor-driven wave simulator (Figure 2). The wave simulator allows for controlled testing at a wave height of 0.2 m and frequencies between 0.1 Hz to 0.5 Hz. This wave simulator was used for both room temperature and -40 °C testing. The Arctic-TENG generated significantly more power at -40 °C compared to room temperature for each frequency tested. The system stored energy in a supercapacitor via a power management circuit, and the amount of energy stored per day was calculated at different wave frequencies. Based on the conditions at the proposed deployment location (days of non-ice-covered ocean and wave frequency), the amount of stored energy per year from Arctic-TENG was calculated to be enough energy for two transmissions every day. Durability testing was completed on the Arctic-TENG at room temperature to determine the lifetime. The rotor of the Arctic-TENG was attached to a DC motor and spun continuously for several millions of cycles without degradation of the electrical output, demonstrating the feasibility for long-term operation.

Jung, Hyunjun↗

NASA NTRS1994

A comparison of cosmological hydrodynamic codes

We present a detailed comparison of the simulation results of various hydrodynamic codes. Starting with identical initial conditions based on the cold dark matter scenario for the growth of structure, with parameters h = 0.5 Omega = Omega(sub b) = 1, and sigma(sub 8) = 1, we integrate from redshift z = 20 to z = O to determine the physical state within a representative volume of size L(exp 3) where L = 64 h(exp -1) Mpc. Five indenpendent codes are compared: three of them Eulerian mesh-based and two variants of the smooth particle hydrodynamics 'SPH' Lagrangian approach. The Eulerian codes were run at N(exp 3) = (32(exp 3), 64(exp 3), 128(exp 3), and 256(exp 3)) cells, the SPH codes at N(exp 3) = 32(exp 3) and 64(exp 3) particles. Results were then rebinned to a 16(exp 3) grid with the exception that the rebinned data should converge, by all techniques, to a common and correct result as N approaches infinity. We find that global averages of various physical quantities do, as expected, tend to converge in the rebinned model, but that uncertainites in even primitive quantities such as (T), (rho(exp 2))(exp 1/2) persists at the 3%-17% level achieve comparable and satisfactory accuracy for comparable computer time in their treatment of the high-density, high-temeprature regions as measured in the rebinned data; the variance among the five codes (at highest resolution) for the mean temperature (as weighted by rho(exp 2) is only 4.5%. Examined at high resolution we suspect that the density resolution is better in the SPH codes and the thermal accuracy in low-density regions better in the Eulerian codes. In the low-density, low-temperature regions the SPH codes have poor accuracy due to statiscal effects, and the Jameson code gives the temperatures which are too high, due to overuse of artificial viscosity in these high Mach number regions. Overall the comparison allows us to better estimate errors; it points to ways of improving this current generation ofhydrodynamic codes and of suiting their use to problems which exploit their best individual features.

Kang, Hyesung↗