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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 199 records · Page 11
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NASA NTRS1958

Experimental Determination of Effects of Frequency and Amplitude on the Lateral Stability Derivatives for a Delta, a Swept, and Unswept Wing Oscillating in Yaw

Three wing models were oscillated in yaw about their vertical axes to determine the effects of systematic variations of frequency and amplitude of oscillation on the in-phase and out-of-phase combination lateral stability derivatives resulting from this motion. The tests were made at low speeds for a 60 degree delta wing, a 45 degree swept wing, and an unswept wing; the swept and unswept wings had aspect ratios of 4. The results indicate that large changes in the magnitude of the stability derivatives due to the variation of frequency occur at high angles of attack, particularly for the delta wing. The greatest variations of the derivatives with frequency take place for the lowest frequencies of oscillation; at the higher frequencies, the effects of frequency are smaller and the derivatives become more linear with angle of attack. Effects of amplitude of oscillation on the stability derivatives for delta wings were evident for certain high angles of attack and for the lowest frequencies of oscillation. As the frequency became high, the amplitude effects tended to disappear.

Fisher, Lewis R↗
NASA NTRS1994

Effect of delta tabs on mixing and axis switching in jets from asymmetric nozzles

The effect of delta tabs on mixing and the phenomenon of axis switching in free air jets from various asymmetric nozzles was studied experimentally. Flow visualization and Pitot probe surveys were carried out with a set of small nozzles (D = 1.47 cm) at a jet Mach number, Mj = 1.63. Hot wire measurements for streamwise vorticity were carried out with larger nozzles (D = 6.35 cm) at Mj = 0.31. Jet mixing with the asymmetric nozzles, as indicated by the mass fluxes downstream, was found to be higher than that produced by a circular nozzle. The circular nozzle with four delta tabs, however, produced fluxes much higher than that produced by a asymmetric nozzles themselves or by most of the tab configurations tried with them. Even higher fluxes could be obtained with only a few cases, e.g., with 3:1 rectangular nozzle with two large delta tabs placed on the narrow edges. In this case, the jet 'fanned out' at a large angle after going through one axis switch. The axis switching could be either stopped or augmented with suitable choice of the tab configurations. Two mechanisms are identified governing the phenomenon. One, as described in Ref. 12 and referred to here as the omega(sub Theta)-induced dynamics, is due to differential induced velocities of different segments of a rolled up azimuthal vortical structure. The other is the omega(sub x)-induced dynamics due to the induced velocities of streamwise vortex pairs in the flow. While the former dynamics are responsible for rapid axis switching in periodically forced jets, the effect of the tabs is governed mainly by the latter. It is inferred that both dynamics are active in a natural asymmetric jet issuing from a nozzle having an upstream contraction. The tendency for axis switching caused by the omega(sub Theta)-induced dynamics is resisted by the omega(sub x)-induced dynamics, leading to a delayed or no switch over in that case. In jets from orifices and in screeching jets, the omega(sub Theta)-induced dynamics dominate causing a faster switch over.

Zaman, K. B. M. Q.↗
NASA NTRS1992

Electromagnetic scattering calculations on the Intel Touchstone Delta

During the first year's operation of the Intel Touchstone Delta system, software which solves the electric field integral equations for fields scattered from arbitrarily shaped objects has been transferred to the Delta. To fully realize the Delta's resources, an out-of-core dense matrix solution algorithm that utilizes some or all of the 90 Gbyte of concurrent file system (CFS) has been used. The largest calculation completed to date computes the fields scattered from a perfectly conducting sphere modeled by 48,672 unknown functions, resulting in a complex valued dense matrix needing 37.9 Gbyte of storage. The out-of-core LU matrix factorization algorithm was executed in 8.25 h at a rate of 10.35 Gflops. Total time to complete the calculation was 19.7 h-the additional time was used to compute the 48,672 x 48,672 matrix entries, solve the system for a given excitation, and compute observable quantities. The calculation was performed in 64-b precision.

Cwik, Tom↗
NASA NTRS1994

On the measurement of the crack tip stress field as a means of determining Delta K(sub eff) under conditions of fatigue crack closure

The optical method of caustics has been successfully extended to enable stress intensity factors as low as 1MPa square root of m to be determined accurately for central fatigue cracks in 2024-T3 aluminium alloy test panels. The feasibility of using this technique to study crack closure, and to determine the effective stress intensity factor range, Delta K(sub eff), has been investigated. Comparisons have been made between the measured values of stress intensity factor, K(sub caus), and corresponding theoretical values, K(sub theo), for a range of fatigue cracks grown under different loading conditions. The values of K(sub caus) and K(sub theo) were in good agreement at maximum stress, where the cracks are fully open, while K(sub caus) exceeded K(sub theo) at minimum stress, due to crack closure. However, the levels of crack closure and values of Delta K(sub eff) obtained could not account for the variations of crack growth rate with loading conditions. It is concluded that the values of Delta K(sub eff), based on caustic measurements in a 1/square root of r stress field well outside the plastic zone, do not fully reflect local conditions which control crack tip behavior.

Wallhead, Ian R.↗
NASA NTRS1993

CFD flowfield simulation of Delta Launch Vehicles in a power-on configuration

This paper summarizes recent work at McDonnell Douglas Aerospace (MDA) to develop and validate computational fluid dynamic (CFD) simulations of under expanded rocket plume external flowfields for multibody expendable launch vehicles (ELVs). Multi engine reacting gas flowfield predictions of ELV base pressures are needed to define vehicle base drag and base heating rates for sizing external nozzle and base region insulation thicknesses. Previous ELV design programs used expensive multibody power-on wind tunnel tests that employed chamber/nozzle injected high pressure cold or hot-air. Base heating and pressure measurements were belatedly made during the first flights of past ELV's to correct estimates from semi-empirical engineering models or scale model tests. Presently, CFD methods for use in ELV design are being jointly developed at the Space Transportation Division (MDA-STD) and New Aircraft Missiles Division (MDA-NAMD). An explicit three dimensional, zonal, finite-volume, full Navier-Stokes (FNS) solver with finite rate hydrocarbon/air and aluminum combustion kinetics was developed to accurately compute ELV power-on flowfields. Mississippi State University's GENIE++ general purpose interactive grid generation code was chosen to create zonal, finite volume viscous grids. Axisymmetric, time dependent, turbulent CFD simulations of a Delta DSV-2A vehicle with a MB-3 liquid main engine burning RJ-1/LOX were first completed. Hydrocarbon chemical kinetics and a k-epsilon turbulence model were employed and predictions were validated with flight measurements of base pressure and temperature. Zonal internal/external grids were created for a Delta DSV-2C vehicle with a MB-3 and three Castor-1 solid motors burning and a Delta-2 with an RS-27 main engine (LOX/RP-1) and 9 GEM's attached/6 burning. Cold air, time dependent FNS calculations were performed for DSV-2C during 1992. Single phase simulations that employ finite rate hydrocarbon and aluminum (solid fuel) combustion chemistry are currently in progress. Reliable and efficient Eulerian algorithms are needed to model two phase (solid-gas) momentum and energy transfer mechanisms for solid motor fuel combustion products.

Pavish, D. L.↗
NASA NTRS1994

BSA Delta Qualification 2, volume 3, book 1

This report, presented in three volumes, provides the results of a two-motor Delta Qualification 2 program conducted in 1993 to certify the following enhancements for incorporation into booster separation motor (BSM) flight hardware: vulcanized-in-place nozzle aft closure insulation; new iso-static ATJ bulk graphite throat insert material; adhesive EA 9394 for bonding the nozzle throat, igniter grain rod/centering insert/igniter case; deletion of the igniter adapter insulator ring; deletion of the igniter adapter/igniter case interface RTV; and deletion of Loctite from igniter retainer plate threads. The enhancements above directly resulted from (1) the BSM total quality management (TQM) team initiatives to enhance the BSM producibility, and (2) the necessity to qualify new throat insert and adhesive systems to replace existing materials that will not be available. Testing was completed at both the component and motor levels. Component testing was accomplished to screen candidate materials (e.g., throat materials, adhesive systems) and to optimize processes (e.g., aft closure insulator vulcanization approach) prior to their incorporation into the test motors. Motor tests -- consisting of two motors, randomly selected by USBI's on-site quality personnel from production lot AAY, which were modified to accept the enhancements -- were completed to provide the final qualification of the enhancements for incorporation into flight hardware. Volume 3 book 1 provides supporting documentation to the analyses and plans of testing the two Delta Qualification units including thermal cycling planning/data acceptance records, environmental test procedures and pretest temperature conditioning history, Delta Qualification test plan, and specification SE0837 -- mix acceptance test specification.

Source record↗
NASA NTRS1994

BSM Delta Qualification 2, volume 3, book 2

This report, presented in three volumes, provides the results of a two-motor Delta Qualification 2 program conducted in 1993 to certify the following enhancements for incorporation into booster separation motor (BSM0 flight hardware: vulcanized-in-place nozzle aft closure insulation; new iso-static ATJ bulk graphite throat insert material, adhesive EA9394 for bonding the nozzle throat, igniter grain rod/centering insert/igniter case; deletion of the igniter adapter insulator ring; deletion of the igniter adapter/igniter case interface RTV; and deletion of loctite from igniter retainer plate threads. The enhancements above directly resulted from (1) the BSM total quality management (TQM) team initiatives to enhance the BSM producibility, and (2) the necessity to qualify new throat insert and adhesive systems to replace existing materials that will not be available. Testing was completed at both the component and motor levels. Component testing was accomplished to screen candidate materials (e.g., throat materials, adhesive systems) and to optimize processes (e.g., aft closure insulator vulcanization approach) prior to their incorporation into the test motors. Motor testing--consisting of two motors, randomly selected by USBI's on-site quality personnel from production lot AAY, which were modified to accept the enhancements -- was completed to provide the final qualification of the enhancements for incorporation into flight hardware. Volume 3, Book 2 provides various supporting documentation to the previous volumes with regards to the testing of the two Delta qualification units: data acceptance records, thermal conditioning analysis, igniter adapter thermal flake analysis, laboratory adhesive (EA-9394) qualification report, throat insert thermal/structural analysis, Delta Qualification Nonconformance Reports (NCR's), O-ring seating tests, and interim test report for vulcanization process qualification.

Source record↗
NASA NTRS1995

Partitioning of ocean and land uptake of CO2 as inferred by delta C-13 measurements from the NOAA Climate Monitoring and Diagnostics Laboratory Global Air Sampling Network

Using delta C-13 measurements in atmospheric CO2 from a cooperative global air sampling network, we determined the partitioning of the net uptake of CO2 between ocean and land as a function of latitude and time. The majority of delta C-13 measurements were made at the Institute of Arctic and Alpine Research (INSTAAR) of the University of Colorado. We perform an inverse deconvolution of both CO2 and delta C-13 observations, using a two-dimensional model of atmospheric transport. Also, the discrimination against C-13 by plant photosynthesis, as a function of latitude and time, is calculated from global runs of the simple biosphere (SiB) model. Uncertainty due to the longitudinal structure of the data, which is not represented by the model, is studied through a bootstrap analysis by adding and omitting measurement sites. The resulting error estimates for our inferred sources and sinks are of the order of 1 GTC (1 GTC = 10(exp 15) gC). Such error bars do not reflect potential systematic errors arising from our estimates of the isotopic disequilibria between the atmosphere and the oceans and biosphere, which are estimated in a separate sensitivity analysis. With respect to global totals for 1992 we found that 3.2 GTC of carbon dissolved into the ocean and that 1.5 GTC were sequestered by land ecosystems. Northern hemisphere ocean gyres north of 15 deg N absorbed 2.7 GTC. The equatorial oceans between 10 deg S and 10 deg N were a net source to the atmosphere of 0.9 GTC. We obtained a sink of 1.6 GTC in southern ocean gyres south of 20 deg S, although the deconvolution is poorly constrained by sparse data coverage at high southern latitudes. The seasonal uptake of CO2 in the northern gyres appears to be correlated with a bloom of phytoplankton in surface waters. On land, northern temperate and boreal ecosystems between 35 deg N and 65 deg N were found to be a major sink of CO2 in 1992, as large as 3.5 GTC. Northern tropical ecosystems (equator-30 deg N) appear to be a net source to the source to the atmosphere of 2 GTC which could reflect biomass burning. A small sink, 0.3 GTC, was inferred for southern tropical ecosystems (30 deg S-equator).

Ciais, Philippe↗
NASA NTRS1996

Natural Rolling Responses of a Delta Wing in Transonic and Subsonic Flows

The unsteady, three-dimensional, full Navier-Stokes (NS) equations and the Euler equations of rigid-body dynamics are sequentially solved to simulate the natural rolling response of slender delta wings of zero thickness at moderate to high angles of attack, to transonic and subsonic flows. The governing equations of fluid flow and dynamics of the present multi-disciplinary problem are solved using the time-accurate solution of the NS equations with the implicit, upwind, Roe flux-difference splitting, finite-volume scheme and a four-stage Runge-Kutta scheme, respectively. The main focus is to analyze the effect of Mach number and angle of attack on the leading edge vortices and their breakdown, the resultant rolling motion, and overall aerodynamic response of the wing. Three cases demonstrate the natural response of a 65 deg swept, cropped delta wing in a transonic flow with breakdown of the leading edge vortices and an 80 deg swept delta wing in a subsonic flow undergoing either damped or self-excited limit-cycle rolling oscillations as a function of angle of attack. Comparisons with an experimental investigation completes this study, validating the analysis and illustrating the complex details afforded by computational investigations.

Menzies, Margaret A.↗
NASA NTRS1960

Investigation at Mach Numbers of 0.20 to 3.50 of Blended Wing-Body Combinations of Sonic Design with Diamond, Delta, and Arrow Plan Forms

The models had aspect-ratio-2 diamond, delta, and arrow wings with the leading edges swept 45.00 deg, 59.04 deg, and 70.82 deg, respectively. The wing sections were computed by varying the section shape along with the body radii (blending process) to match the prescribed area distribution and wing plan form. The wing sections had an average value of maximum thickness ratio of about 4 percent of the local chords in a streamwise direction. The models were tested with transition fixed at Reynolds numbers of about 4,000,000 to 9,000,0000, based on the mean aerodynamic chord of the wings. The effect of varying Reynolds number was checked at both subsonic and supersonic speeds. The diamond model was superior to the other plan forms at transonic speeds ((L/D)max = 11.00 to 9.52) because of its higher lift-curve slope and near optimum wave drag due to the blending process. For the wing thickness tested with the diamond model, the marked body and wing contouring required for transonic conditions resulted in a large wave-drag penalty at the higher supersonic Mach numbers where the leading and trailing edges of the wing were supersonic. Because of the low sweep of the trailing edge of the delta model, this configuration was less adaptable to the blending process. Removing a body bump prescribed by the Mach number 1.00 design resulted in a good supersonic design. This delta model with 10 percent less volume was superior to the other plan forms at Mach numbers of 1.55 to 2.35 ((L/D)max = 8.65 to 7.24), but it and the arrow model were equally good at Mach numbers of 2.50 to 3.50 ((L/D)max - 6.85 to O.39). At transonic speeds the arrow model was inferior because of the reduced lift-curve slope associated with its increased sweep and also because of the wing base drag. The wing base-drag coefficients of the arrow model based on the wing planform area decreased from a peak value of 0.0029 at Mach number 1.55 to 0.0003 at Mach number 3.50. Linear supersonic theory was satisfactory for predicting the aerodynamic trends at Mach numbers from 1.55 to 3.50 of lift-curve slope, wave drag, drag due to lift, aerodynamic-center location, and maximum lift-drag ratios for each of the models.

Holdaway, George H.↗
NASA NTRS1998

Delta Scuti stars: Theory

The purpose of asteroseismology is not only to derive the internal structure of individual stars from their observed oscillation frequencies, but also to test and extend one's understanding of the physics of matter under the extremes of temperature, density, and pressure found in stellar interiors. In this review, the author hopes to point out what one can learn about the Sun by studying (delta) Scuti stars, as well as what one can learn about stars more massive or evolved than the Sun. He discusses some of the difficulties in theoretical approaches to asteroseismology for (delta) Scuti stars, using FG Vir, (delta) Scuti, and CD-24(degree) 7599 as examples.

Guzik, J. A.↗
NASA NTRS1994

Design Issues of GaAs and AlGaAs Delta-Doped p-i-n Quantum-Well APD's

We examine the basic design issues in the optimization of GaAs delta-doped and AlGAs delta-doped quantum-well avalanche photodiode (APD) structures using a theoretical analysis based on an ensemble Monte Carlo simulation. The devices are variations of the p-i-n doped quantum-well structure previously described in the literature. They have the same low-noise, high-gain and high-bandwidth features as the p-i-n doped quantum-well device. However, the use of delta doping provides far greater control or the doping concentrations within each stage possibly enhancing the extent to which the device can be depleted. As a result, it is expected that the proposed devices will operate at higher gain levels (at very low noise) than devices previously developed.

Wang, Yang↗
NASA NTRS1995

Delta XTE Launch Activities and Scrub (Anomaly) at Cape Canaveral Air Station Complex 17

This NASA Kennedy Space Center video presents launch activities of the Delta X-ray Timing Explorer and scrub aboard a McDonnell Douglas Delta II rocket from Complex 17. The primary objective of the Delta XTE is to study time variability and broadband spectral phenomena in the X-ray emission from astronomical sources. XTE is designed for a required lifetime of two years with a goal of five years and will be inserted into a low-Earth circular orbit at an altitude of 600 km. The launch was postponed due to unfavorable wind conditions aloft.

Source record↗
NASA NTRS1995

Delta XTE Press Briefing

Live coverage of the pre-launch Delta X-Ray Timing Explorer (XTE) press briefing is presented. George Diller, NASA Public Affairs, introduces the panel. The panel consists of Floyd Curington, NASA Launch Manager, Kennedy Space Center; David Mitchell, Launch Vehicle Manager, NASA Goddard Space Flight Center; Dale Schulz, Mission Director, XTE Project Manager Goddard Space Flight Center; Dr. Hale Bradt, XTE Principle Investigator, Massachusetts Institute of Technology (MIT); and Joel Tumbiolo, Launch Weather Officer, Department of the Air Force. The launch of the Delta XTE spacecraft atop the Delta 230 expendable launch vehicle is discussed. Once lofted into orbit, the XTE spacecraft will embark on a two-year mission to carry out an in-depth study of x-ray sources in the universe. Floyd Curington gives the lift-off schedule, fueling, and countdown of the spacecraft. David Mitchell discusses the launch sequence and spacecraft separation. Dale Schulz presents viewcharts of the instrument side of the XTE. Dr. Hale will be studying compact stars such as light dwarfs, neutron stars and quasars. Joel Tumbiolo presents the weather forecast for the December 10, 1995 launch. The press briefing ends with a question and answer period.

Source record↗
NASA NTRS1977

Recent Loads Calibration Experience With a Delta Wing Airplane

Aircraft which are designed for supersonic and hypersonic flight are evolving with delta wing configurations. An integral part of the evolution of all new aircraft is the flight test phase. Included in the flight test phase is an effort to identify and evaluate the loads environment of the aircraft. The most effective way of examining the loads environment is to utilize calibrated strain gages to provide load magnitudes. Using strain gage data to accomplish this has turned out to be anything but a straightforward task. The delta wing configuration has turned out to be a very difficult type of wing structure to calibrate. Elevated structural temperatures result in thermal effects which contaminate strain gage data being used to deduce flight loads. The concept of thermally calibrating a strain gage system is an approach to solving this problem. This paper will address how these problems were approached on a program directed toward measuring loads on the wing of a large, flexible supersonic aircraft. Structural configurations typical of high-speed delta wing aircraft will be examined. The temperature environment will be examined to see how it induces thermal stresses which subsequently cause errors in loads equations used to deduce the flight loads.

Jenkins, Jerald M.↗
NASA NTRS2002

Analysis of Salinity Intrusion in the San Francisco Bay-Delta using a GA- Optimized Neural Net, and Application of the Model to Prediction in the Elkhorn Slough Habitat

The San Francisco Bay Delta is a large hydrodynamic complex that incorporates the Sacramento and San Joaquin Estuaries, the Burman Marsh, and the San Francisco Bay proper. Competition exists for the use of this extensive water system both from the fisheries industry, the agricultural industry, and from the marine and estuarine animal species within the Delta. As tidal fluctuations occur, more saline water pushes upstream allowing fish to migrate beyond the Burman Marsh for breeding and habitat occupation. However, the agriculture industry does not want extensive salinity intrusion to impact water quality for human and plant consumption. The balance is regulated by pumping stations located alone the estuaries and reservoirs whereby flushing of fresh water keeps the saline intrusion at bay. The pumping schedule is driven by data collected at various locations within the Bay Delta and by numerical models that predict the salinity intrusion as part of a larger model of the system. The Interagency Ecological Program (IEP) for the San Francisco Bay/Sacramento-San Joaquin Estuary collects, monitors, and archives the data, and the Department of Water Resources provides a numerical model simulation (DSM2) from which predictions are made that drive the pumping schedule. A problem with this procedure is that the numerical simulation takes roughly 16 hours to complete a C:~ prediction. We have created a neural net, optimized with a genetic algorithm, that takes as input the archived data from multiple stations and predicts stage, salinity, and flow at the Carquinez Straits (at the downstream end of the Burman Marsh). This model seems to be robust in its predictions and operates much faster than the current numerical DSM2 model. Because the system is strongly tidal driven, we used both Principal Component Analysis and Fast Fourier Transforms to discover dominant features within the IEP data. We then filtered out the dominant tidal forcing to discover non-primary tidal effects, and used this to enhance the neural network by mapping input-output relationships in a more efficient manner. Furthermore, the neural network implicitly incorporates both the hydrodynamic and water quality models into a single predictive system. Although our model has not yet been enhanced to demonstrate improve pumping schedules, it has the possibility to support better decision-making procedures that may then be implemented by State agencies if desired. Our intention is now to use this model in the smaller Elkhorn Slough complex near Monterey Bay where no such hydrodynamic model currently exists. At the Elkhorn Slough, we are fusing the neural net model of tidally-driven flow with in situ flow data and airborne and satellite remote sensation data. These further constrain the behavior of the model in predicting the longer-term health and future of this vital estuary.

Thompson, David E.↗
NASA NTRS2002

The Delta x B = 0 Constraint Versus Minimization of Numerical Errors in MHD Simulations

The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. It has previously been shown by Powell et al. (1995) that an 'almost' equivalent MHD system in non-conservative form can be derived. This non-conservative system has a better conditioned eigensystem. Aside from Powell et al., the MHD equations can be derived from basic principles in either conservative or non-conservative form. The Delta x B = 0 constraint of the MHD equations is only an initial condition constraint, it is very different from the incompressible Navier-Stokes equations in which the divergence condition is needed to close the system (i.e., to have the same number of equations and the same number of unknown). In the MHD formulations, if Delta x B = 0 initially, all one needs is to construct appropriate numerical schemes that preserve this constraint at later time evolutions. In other words, one does not need the Delta x B condition to close the MHD system. We formulate our new scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the divergence of the magnetic condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.

Yee, H. C.↗
NASA NTRS2002

The Delta(dot) B = O Constraint vs. Minimization of Numerical Errors in MHD Simulations

The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. On the other hand, the MHD equations can be derived from basic principles in either conservative or non-conservative form. The non-conservative system has a better conditioned eigensystem. The Delta(dot)B = 0 constraint of the A4HD equations is only an initial condition constraint. One does not need the Delta(dot)B condition to close the MHD system. We formulate our new low dissipative high order scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the Delta(dot)B condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.

Yee, H. C.↗