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NASA NTRS1995

Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks

We investigate the asymptotic convergence of finite-difference schemes for the Euler equations when the limiting solution contains shocks. The Lax-Wendroff theorem guarantees that certain conservative schemes converge to correct, physically valid solutions. We focus on two one-dimensional operator-split schemes with explicit artificial-viscosity terms. One, an internal-energy scheme, does not satisfy the assumptions of Lax-Wendroff; the other, a conservative total-energy scheme, does. With viscous lengths chosen proportional to the grid size, we find that both schemes converge to their zero-grid-size limits at the theoretically expected rate, but only the conversative scheme converges toward correct solutions of the inviscid fluid equations. We show that the difference in their behaviors results directly from the presence of shocks in the limiting solution. Empirically, we find that when the viscous lenghts tend toward zero more slowly than the grid size, however the nonconservative scheme also converges toward correct solutions. We characterize the asymptotic behavior of the total-energy scheme in a particular problem in which a shock forms. As the grid is refined, a Cauchy error approaches the expected rate of change slowly. We show that the changes in the artificial viscosity alter the diffusion of small-amplitude waves. The differences associated with such waves make the dominant contribution to the Cauchy error. We formulate an analytic model to relate the rate of approach to the effect of varying diffusion in waves and find quantitative agreement with our numerical results.

Kimoto, Paul A.↗
NASA NTRS1987

The structure of the time-dependent interstellar shocks and grain destruction in the interstellar medium

A new theoretical analysis of the structure of interstellar shocks and the grain dynamics of these shocks is presented. The basic hydrodynamic equations for J-shocks in interstellar gas are given in which shock-driving pressure is allowed to be weakly time-dependent and the grains are treated as a separate two-dimensional fluid. Specific equations for the grain dynamics in the cooling postshock gas are derived. An analytic theory for the propagation of a shock driven into an interstellar cloud by the blast wave of a supernova remnant which sweeps over the cloud is developed. An improved calculation of the grain charge in postshock gas is described, giving a simple analytic approximation for the results. The consequences of including these processes in the numerical code of Seab and Shull (1983) are addressed, including the effect of realistic magnetic fields in low-density gas.

Mckee, Christopher F.↗
NASA NTRS1993

Initiating solar system formation through stellar shock waves

Isotopic anomalies in presolar grains and other meteoritical components require nucleosynthesis in stellar interiors, condensation into dust grains in stellar envelopes, transport of the grains through the interstellar medium by stellar outflows, and finally injection of the grains into the presolar nebula. The proximity of the presolar cloud to these energetic stellar events suggests that a shock wave from a stellar outflow might have initiated the collapse of an otherwise stable presolar cloud. We have begun to study the interactions of stellar shock waves with thermally supported, dense molecular cloud cores, using a three spatial dimension (3D) radiative hydrodynamics code. Supernova shock waves have been shown by others to destroy quiescent clouds, so we are trying to determine if the much smaller shock speeds found in, e.g., asymptotic giant branch (AGB) star winds, are strong enough to initiate collapse in an otherwise stable, rotating, solar-mass cloud core, without leading to destruction of the cloud.

Boss, A. P.↗
NASA NTRS2009

Simulation of Relativistic Shocks and Associated Radiation from Turbulent Magnetic Fields

Plasma instabilities (e.g., Buneman, Weibel and other two-stream instabilities) excited in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a new 3-D relativistic particle-in-cell code, we have investigated the particle acceleration and shock structure associated with an unmagnetized relativistic electron-positron jet propagating into an unmagnetized electron-positron plasma. The simulation has been performed using a long simulation system in order to study the nonlinear stages of the Weibel instability, the particle acceleration mechanism, and the shock structure. Cold jet electrons are thermalized and slowed while the ambient electrons are swept up to create a partially developed hydrodynamic (HD) like shock structure. In the leading shock, electron density increases by a factor of <_ 3.5 in the simulation frame. Strong electromagnetic fields are generated in the trailing shock and provide an emission site. We discuss the possible implication of our simulation results within the AGN and GRB context. We have calculated the time evolution of the spectrum from two electrons propagating in a uniform parallel magnetic field to verify the technique. The same technique will be used to calculate radiation from accelerated electrons (positrons) in turbulent magnetic fields generated by Weibel instability.

Nishikawa, K.↗
NASA NTRS1987

Shock structure in jets of arbitrary exit geometry

The shock structure and hydrodynamic stability of single and twin jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. Results are given for circular, elliptic and rectangular jets and the results compared with analysis and experiment. A finite difference technique is used to examine the effect of finite mixing layer thickness for a single jet. The hydrodynamic stability of twin circular jets is also considered. The variation of the stability characteristics are presented for the vortex sheet case for several separation distances. The formulation of the problem to account for finite thickness effects is also given.

Morris, P. J.↗
NASA NTRS2002

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great challenge to algorithm development. In addition, controlling the numerical error of the divergence free condition of the magnetic fields for high order methods has been a stumbling block. Lower order methods are not practical for the astrophysical problems in question. We propose to extend our hydrodynamics schemes to the MHD equations with several desired properties over commonly used MHD schemes.

Sjoegreen, Bjoern↗
NASA NTRS1977

A review of the thermonuclear runaway model of a nova outburst

Kraft's (1963) model for a nova outburst caused by a thermonuclear runaway in the hydrogen-rich matter accreted onto the white dwarf in a binary system is reviewed. Hydrostatic and hydrodynamic studies of this phenomenon are summarized, analyses of shock ejection based on hydrodynamic computer codes are discussed, and one specific hydrodynamic code is outlined. Results obtained with this code are presented and evaluated for an initial model containing a white dwarf with a hydrogen-rich envelope of 0.0001 to 0.001 solar mass in hydrostatic and thermal equilibrium. It is shown that an implicit hydrodynamic computer code is required in order to study the thermonuclear-runaway phenomenon. The early evolution of three models with different intrinsic luminosities is illustrated, and enhancement of CNO nuclei at the bottom of the hydrogen-rich envelope is investigated. It is suggested that the concentration of C-13, N-15, and O-17 should be greatly enhanced in nova ejecta.

Sparks, W. M.↗
NASA NTRS1989

Solution of the hydrodynamic device model using high-order non-oscillatory shock capturing algorithms

A micron n+ - n - n+ silicon diode is simulated via the hydrodynamic model for carrier transport. The numerical algorithms employed are for the non-steady case, and a limiting process is used to reach steady state. The simulation employs shock capturing algorithms, and indeed shocks, or very rapid transition regimes, are observed in the transient case for the coupled system, consisting of the potential equation and the conservation equations describing charge, momentum, and energy transfer for the electron carriers. These algorithms, termed essentially non-oscillatory, were successfully applied in other contexts to model the flow in gas dynamics, magnetohydrodynamics, and other physical situations involving the conservation laws in fluid mechanics. The method here is first order in time, but the use of small time steps allows for good accuracy. Runge-Kutta methods allow one to achieve higher accuracy in time if desired. The spatial accuracy is of high order in regions of smoothness.

Fatemi, Emad↗
NASA NTRS1991

Solution of the hydrodynamic device model using high-order non-oscillatory shock capturing algorithms

A micron n+ - n - n+ silicon diode is simulated via the hydrodynamic model for carrier transport. The numerical algorithms employed are for the non-steady case, and a limiting process is used to reach steady state. The simulation employs shock capturing algorithms, and indeed shocks, or very rapid transition regimes, are observed in the transient case for the coupled system, consisting of the potential equation and the conservation equations describing charge, momentum, and energy transfer for the electron carriers. These algorithms, termed essentially nonoscillatory, were successfully applied in other contexts to model the flow in gas dynamics, magnetohydrodynamics, and other physical situations involving the conservation laws in fluid mechanics. The method here is first order in time, but the use of small time steps allows for good accuracy. Runge-Kutta methods allow one to achieve higher accuracy in time if desired. The spatial accuracy is of high order in regions of smoothness.

Fatemi, Emad↗
NASA NTRS1985

Shock acceleration of diffuse ions at the earth's bow shock Acceleration efficiency and A/Z enhancement

Observations of particle spectra, intensity, and enhancement of alpha particles over protons at diffuse ion events at the quasi-parallel earth bow shock are compared to a Monte Carlo simulation of diffusive shock acceleration. The simulation includes the back reaction of accelerated particles on the shock structure, particle escape at an upstream free escape boundary, and a low energy per nucleon threshold for thermal leakage of downstream, shock-heated particles into the upstream region. The simulation assumes that the same scattering operator that gives rise to shock acceleration can also describe a viscous shock governed by hydrodynamic turbulence. This implies that accelerated ions can be drawn directly from the thermal solar wind with no separate superthermal seed population. Good agreement between the simulation and observations made during nearly radial magnetic field configurations lends support to thermal leakage of downstream, shock-heated ions as the mode of injection for diffusion ion events.

Ellison, D. C.↗
NASA NTRS1973

Proton scattering in the region near the earth's bow shock.

Lockheed spectrometer data from orbits 1 through 20 of Ogo 5 are used to study proton scattering near the bow shock. Correlative UCLA fluxgate magnetometer data from the satellite are used to complete motion studies of the bow shock when spectrometer data are missing. Thirty-eight analyzable sets of multiple shock crossings show 358 shock encounters ranging from 10 to 22 earth radii and spanning sun-earth-satellite angles from 30 to 90 deg. Gross features of the study show that the location and shape of the bow shock are in good agreement with the hydrodynamic model of the bow shock.

Ossakow, S. L.↗
NASA NTRS1976

Solution of a large hydrodynamic problem using the STAR-100 computer

A representative hydrodynamics problem, the shock initiated flow over a flat plate, was used for exploring data organizations and program structures needed to exploit the STAR-100 vector processing computer. A brief description of the problem is followed by a discussion of how each portion of the computational process was vectorized. Finally, timings of different portions of the program are compared with equivalent operations on serial machines. The speed up of the STAR-100 over the CDC 6600 program is shown to increase as the problem size increases. All computations were carried out on a CDC 6600 and a CDC STAR 100, with code written in FORTRAN for the 6600 and in STAR FORTRAN for the STAR 100.

Weilmuenster, K. J.↗
NASA NTRS1990

The shock process and light element production in supernovae envelopes

Detailed hydrodynamic modeling of the passage of supernova shocks through the hydrogen envelopes of blue and red progenitor stars was carried out to explore the sensitivity to model conditions of light element production (specifically Li-7 and B-11) which was noted by Dearborn, Schramm, Steigman and Truran (1989) (DSST). It is found that, for stellar models with M is less than or approximately 100 M solar mass, current state of the art supernova shocks do not produce significant light element yields by hydrodynamic processes alone. The dependence of this conclusion on stellar models and on shock strengths is explored. Preliminary implications for Galactic evolution of lithium are discussed, and it is suspected that intermediate mass red giant stars may be the most consistent production site for lithium.

Brown, Lawrence E.↗
NASA NTRS1991

The shock process and light-element production in supernova envelopes

Detailed hydrodynamic modeling of the passage of supernova shocks through the hydrogen enevlopes of blue and red progenitor stars was carried out to explore the sensitivity to model conditions of light element production (specifically Li7 and B-11) which was noted by Dearborn, Schramm, Steigman and Truran (1989) (DSST). It is found that, for stellar models with M is less than or approximately 100 M solar mass, current state of the art supernova shocks do not produce significant light element yields by hydrodynamic processes alone. The dependence of this conclusion on stellar models and on shock strengths is explored. Preliminary implications for Galactic evolution of lithium are discussed, and it is suspected that intermediate mass red giant stars may be the most consistent production site for lithium.

Brown, Lawrence E.↗
NASA NTRS2002

Shocks in Dense Clouds in the Vela Supernova Remnant: FUSE

We have obtained 8 LWRS FUSE spectra to study a recently identified interaction of the Vela supernova remnant with a dense cloud region along its western edge. The goal is to quantify the temperature, ionization, density, and abundance characteristics associated with this shock/dense cloud interface by means of UV absorption line studies. Our detection of high-velocity absorption line C I at +90 to +130 km/s with IUE toward a narrow region interior to the Vela SNR strongly suggests the Vela supernova remnant is interacting with a dense ISM or molecular cloud. The shock/dense cloud interface is suggested by (1) the rarity of detection of high-velocity C I seen in IUE spectra, (2) its very limited spatial distribution in the remnant, and (3) a marked decrease in X-ray emission in the region immediately west of the position of these stars where one also finds a 100 micron emission ridge in IRAS images. We have investigated the shock physics and general properties of this interaction region through a focussed UV absorption line study using FUSE spectra. We have FUSE data on OVI absorption lines observed toward 8 stars behind the Vela supernova remnant (SNR). We compare the OVI observations with IUE observations of CIV absorption toward the same stars. Most of the stars, which are all B stars, have complex continua making the extraction of absorption lines difficult. Three of the stars, HD 72088, HD 72089 and HD 72350, however, are rapid rotators (v sin i less than 100 km/s) making the derivation of absorption column densities much easier. We have measured OVI and CIV column densities for the "main component" (i.e. the low velocity component) for these stars. In addition, by removing the H2 line at 1032.35A (121.6 km/s relative to OVI), we find high velocity components of OVI at approximately 150 km/s that we attribute to the shock in the Vela SNR. The column density ratios and magnitudes are compared to both steady shock models and results of hydrodynamical SNR modeling. We find that the models require the shock to be relatively slow (approximately 100 - 170 km/s) to match the FUSE data. We discuss the implications of our results for models of the evolution of the Vela SNR.

Nichols, Joy↗
NASA NTRS1994

Postexplosion hydrodynamics of supernovae in red supergiants

Shock propagation, mixing, and clumping are studied in the explosion of red supergiants as Type II supernovae using a two-dimensional smooth particle hydrodynamic (SPH) code. We show that extensive Rayleigh-Talor instabilities develop in the ejecta in the wake of the reverse shock wave. In all cases, the shell structure of the progenitor is obliterated to leave a clumpy, well-mixed supernova remnant. However, the occurrence of mass loss during the lifetime of the progenitor can significantly reduce the amount of mixing. These results are independent of the Type II supernova explosion mechanism.

Herant, Marc↗