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High-speed compressible flow and other advection-dominated problems of fluid dynamics

Finite element methods are described for modeling high speed compressible flows with strong advection, problems important to aerodynamics. The situations are characterized by high pressure and temperature gradients, transients and the appearance of discontinuities, factors which require mesh refinement during computations. Techniques are developed for temporal and spatial discretization of a model problem. Several observations are made regarding the explicit and implicit features of the calculations, the use of the Lax-Wendroff scheme to produce a mass-matrix for obtaining accurate results for transients, methods of performing stability analyses, and simplification techniques. Examples are provided of solving the nonlinear shallow-water equations and describing compressible flows, particularly transonic flows. Domain splitting is defined for improving the calculations at each time step and in different parts of the flow regime while simultaneously advancing the calculations towards a solution.

Zienkiewicz, O. C.↗

Characteristics-based methods applied to infinite Prandtl number thermal convection in the hard turbulent regime

Characteristics-based methods for the advection-diffusion equation are presented and directly applied to study thermal convection with extremely large Rayleigh number (Ra). It is shown that the operator-splitting method for advection-diffusion problems is very accurate for determining the advected field at extremely high Peclet number (Pe). The technique presented is considered to have great potential for solving advection-dominated problems, while the Langrangian method is more accurate for lower Pe. It is noted that the accuracy of these characteristics-based methods strongly depends on the quality of interpolation. The computational time for the operator-splitting method grows with the number of time steps employed. The Langrangian method was used for simulations of convection at very high Ra, up to 3 x 10 to the 9th, and time-dependent, thermal convection solutions were obtained for infinite Prandtl number.

Malevsky, A. V.↗

Self-Consistent Models of Accretion Disks

The investigations of advection-dominated accretion flows (ADAFs), with emphasis on applications to X-ray binaries containing black holes and neutron stars is presented. This work is now being recognized as the standard paradigm for understanding the various spectral states of black hole X-ray Binaries (BHXBs). Topics discussed include: (1) Problem in BHXBS, namely that several of these binaries have unusually large concentrations of lithium in their companion stars; (2) A novel test to show that black holes have event horizons; (3) Application of the ADAF model to the puzzling X-ray delay in the recent outburst of the BHXB, GRO J1655-40; (4) Description of the various spectral states in BHXBS; (5) Application of the ADAF model to the famous supermassive black hole at the center of our Galaxy, Sgr A(*); (6) Writing down and solving equations describing steady-state, optically thin, advection-dominated accretion onto a Kerr black hole; (7) The effect of "photon bubble" instability on radiation dominated accretion disks; and (8) Dwarf nova disks in quiescence that have rather low magnetic Reynolds number, of order 10(exp 3).

Narayan, Ramesh↗

Variability Analysis and the Structure of Active Galactic Nuclei

This five-year Long-Term Space Astrophysics grant provided the support for several major steps in advancing our knowledge of the internal structure of active galactic nuclei. The single largest portion of this program had to do with the development and application of techniques for "reverberation mapping", the use of spectral monitoring of several different bands related by radiation reprocessing to infer the internal geometry of sources. Major steps were taken in this regard, particularly in establishing the distribution in radius of emission line material, and in relating the apparent reprocessing of continuum bands to the underlying structure of the accretion disk. Another major effort built directly upon these results. Once the case for continuum reprocessing was made by the monitoring, it next behooved us to understand the spectral output of AGN as a result of this reprocessing. As a result, our view of continuum production in AGN is now much better focussed on the key problems. A third focus of effort had to do with the nature of X-ray variability in AGN, and what it can tell us about the dynamics of extremely hot material in the immediate outskirts of the supermassive black holes that form the central engines of active galactic nuclei. In addition to these primary efforts, this grant also supported many other, smaller projects. Several of these were demonstrations of how the material spewed out of AGN in relativistic.ets generate the radiation by which we observe them. J Finally, the portion of this study that had to do with continuum production by accretion disks in AGN led naturally to several papers in which new developments were presented having to do with "advection-dominated accretion disks", those disks in which accretion appears to proceed at a substantial rate, but in which radiation processes are weak.

Krolik, Julian H.↗

Variability Analysis and the Structure of Active Galactic Nuclei

This five-year Long-Term Space Astrophysics grant provided the support for several major steps in advancing our knowledge of the internal structure of active galactic nuclei. The single largest portion of this program had to do with the development and application of techniques for 'reverberation mapping, the use of spectral monitoring of several different bands related by radiation reprocessing to infer the internal geometry of sources. Major steps were taken in d-ds regard, particularly in establishing the distribution in radius of emission line material, and in relating the apparent reprocessing of continuum bands to the underlying structure of the accretion disk. Another major effort built directly upon these results. Once the case for continuum reprocessing was made by the monitoring, it next behooved us to understand the spectral output of AGN as a result of this reprocessing. As a result, our view of continuum production in AGN is now much better focussed on the key problems. A third focus of effort had to do with the nature of X-ray variability in AGN, and what it can tell us about the dynamics of extremely hot material in the immediate outskirts of the supermassive black holes that form the central engines of active galactic nuclei. In addition to these primary efforts, this grant also supported many other, smaller projects. Several of these were demonstrations of how the material spewed out of AGN in relativistic jets generate the radiation by which we observe them. Finally, the portion of this study that had to do with continuum production by accretion disks in AGN led naturally to several papers in which new developments were presented having to do with 'advection-dominated accretion disks', those disks in which accretion appears to proceed at a substantial rate, but in which radiation processes are weak.

Krolik, Julian H.↗