33 research outputs found
On the inadmissibility of non-evolutionary shocks
In recent years, numerical solutions of the equations of compressible magnetohydrodynamic (MHD) flows have been found to contain intermediate shocks for certain kinds of problems. Since these results would seem to be in conflict with the classical theory of MHD shocks, they have stimulated attempts to reexamine various aspects of this theory, in particular the role of dissipation. In this paper, we study the general relationship between the evolutionary conditions for discontinuous solutions of the dissipation-free system and the existence and uniqueness of steady dissipative shock structures for systems of quasilinear conservation laws with a concave entropy function. Our results confirm the classical theory. We also show that the appearance of intermediate shocks in numerical simulations can be understood in terms of the properties of the equations of planar MHD, for which some of these shocks turn out to be evolutionary. Finally, we discuss ways in which numerical schemes can be modified in order to avoid the appearance of intermediate shocks in simulations with such symmetry
One-dimensional nonlinear stability of pathological detonations
In this paper we perform high-resolution one-dimensional time-dependent numerical simulations of detonations for which the underlying steady planar waves are of the pathological type. Pathological detonations are possible when there are endothermic or dissipative effects in the system. We consider a system with two consecutive irreversible reactions A[rightward arrow]B[rightward arrow]C, with an Arrhenius form of the reaction rates and the second reaction endothermic. The self-sustaining steady planar detonation then travels at the minimum speed, which is faster than the Chapman–Jouguet speed, and has an internal frozen sonic point at which the thermicity vanishes.
The flow downstream of this sonic point is supersonic if the detonation is unsupported or subsonic if the detonation is supported, the two cases having very different detonation wave structures. We compare and contrast the long-time nonlinear behaviour of the unsupported and supported pathological detonations. We show that the stability of the supported and unsupported steady waves can be quite different, even near the stability boundary. Indeed, the unsupported detonation can easily fail while the supported wave propagates as a pulsating detonation. We also consider overdriven detonations for the system. We show that, in agreement with a linear stability analysis, the stability of the steady wave is very sensitive to the degree of overdrive near the pathological detonation speed, and that increasing the overdrive can destabilize the wave, in contrast to systems where the self-sustaining wave is the Chapman–Jouguet detonation
The Fanno model for turbulent compressible flow
The paper considers the derivation and properties of the Fanno model for nearly unidirectional turbulent flow of gas in a tube. The model is relevant to many industrial processes. Approximate solutions are derived and numerically validated for evolving flows of initially small amplitude, and these solutions reveal the prevalence of localized large-time behaviour, which is in contrast to inviscid acoustic theory. The properties of large-amplitude travelling waves are summarized, which are also surprising when compared to those of inviscid theory
Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state
Unsteady flow in collapsible tubes has been widely studied for a number of different physiological applications; the principal motivation for the work of this paper is the study of blood flow in the jugular vein of an upright, long-necked subject (a giraffe). The one-dimensional equations governing gravity- or pressure-driven flow in collapsible tubes have been solved in the past using finite-difference (MacCormack) methods. Such schemes, however, produce numerical artifacts near discontinuities such as elastic jumps. This paper describes a numerical scheme developed to solve the one-dimensional equations using a more accurate upwind finite volume (Godunov) scheme that has been used successfully in gas dynamics and shallow water wave problems. The adapatation of the Godunov method to the present application is non-trivial due to the highly nonlinear nature of the pressure–area relation for collapsible tubes.
The code is tested by comparing both unsteady and converged solutions with analytical solutions where available. Further tests include comparison with solutions obtained from MacCormack methods which illustrate the accuracy of the present method.
Finally the possibility of roll waves occurring in collapsible tubes is also considered, both as a test case for the scheme and as an interesting phenomenon in its own right, arising out of the similarity of the collapsible tube equations to those governing shallow water flow
Dark cloud chemistry in initially H-rich regions
The chemistry in dark regions of dense cores is explored as a function of the initial abundance ratio of H to H 2, on the assumption that some cores form on a timescale and are younger than the time required for the H :H 2 ratio to attain its equilibrium value. Observational diagnostics of non-equilibrium values of the initial H :H 2 ratio are identified. In initially H-rich material, the abundances of OH, NH 3, CN, and HNC are for some time higher than they are in initially H-poor material. In initially H-poor regions, the abundances of CO, species containing multiple carbon atoms in each molecule, and CS are larger for an (observationally significant) period than in initially H-rich material
The modifcation by diffuse radiation of "cometary tail" formation behind globules
We study the evolution of a globule of neutral material immersed in the more tenuous hotter plasma of an H II region surrounding newly born OB stars. The neutral globule is illuminated by the direct ionizing radiation of OB stars, and by diffuse radiation emitted by recombination in the surrounding ionized gas. We perform 2D, time dependent axisymmetric hydrodynamic simulations, and find that, for values of the diffuse field of the order of 10% of the direct field, the evolution of the globule is completely different to its evolution when the diffuse field is neglected
Thermal instability in ionized plasma
We study magnetothermal instability in the ionized plasmas including the
effects of Ohmic, ambipolar and Hall diffusion. Magnetic field in the single
fluid approximation does not allow transverse thermal condensations, however,
non-ideal effects highly diminish the stabilizing role of the magnetic field in
thermally unstable plasmas. Therefore, enhanced growth rate of thermal
condensation modes in the presence of the diffusion mechanisms speed up the
rate of structure formation.Comment: Accepted for publication in Astrophysics & Space Scienc
Symbiotic starburst-black hole AGN -- I. Isothermal hydrodynamics of the mass-loaded ISM
Compelling evidence associates the nuclei of active galaxies and massive
starbursts. The symbiosis between a compact nuclear starburst stellar cluster
and a massive black hole can self-consistently explain the properties of active
nuclei. The young stellar cluster has a profound effect on the most important
observable properties of active galaxies through its gravity, and by mass
injection through stellar winds, supernovae and stellar collisions. Mass
injection generates a nuclear ISM which flows under gravitational and radiative
forces until it leaves the nucleus or is accreted onto the black hole or
accretion disc.
The radiative force exerted by the black hole--accretion disc radiation field
is not spherically symmetric. This results in complex flows in which regions of
inflow can coexist with high Mach number outflowing winds and hydrodynamic
jets. We present two-dimensional hydrodynamic models of such nISM flows, which
are highly complex and time variable. Shocked shells, jets and explosive
bubbles are produced, with bipolar winds driving out from the nucleus. Our
results graphically illustrate why broad emission line studies have
consistently failed to identify any simple, global flow geometry. The real
structure of the flows is _inevitably_ yet more complex.Comment: 51 pages, 85 postscript figures, Latex, using MNRAS macros, to be
published in MNRAS. Postscript will full resolution pictures and mpeg
simulations available via http://ast.leeds.ac.uk/~rjrw/agn.htm
Dynamic Evolution Model of Isothermal Voids and Shocks
We explore self-similar hydrodynamic evolution of central voids embedded in
an isothermal gas of spherical symmetry under the self-gravity. More
specifically, we study voids expanding at constant radial speeds in an
isothermal gas and construct all types of possible void solutions without or
with shocks in surrounding envelopes. We examine properties of void boundaries
and outer envelopes. Voids without shocks are all bounded by overdense shells
and either inflows or outflows in the outer envelope may occur. These
solutions, referred to as type void solutions, are further
divided into subtypes and
according to their characteristic behaviours across the sonic critical line
(SCL). Void solutions with shocks in envelopes are referred to as type
voids and can have both dense and quasi-smooth edges.
Asymptotically, outflows, breezes, inflows, accretions and static outer
envelopes may all surround such type voids. Both cases of
constant and varying temperatures across isothermal shock fronts are analyzed;
they are referred to as types and
void shock solutions. We apply the `phase net matching procedure' to construct
various self-similar void solutions. We also present analysis on void
generation mechanisms and describe several astrophysical applications. By
including self-gravity, gas pressure and shocks, our isothermal self-similar
void (ISSV) model is adaptable to various astrophysical systems such as
planetary nebulae, hot bubbles and superbubbles in the interstellar medium as
well as supernova remnants.Comment: 24 pages, 13 figuers, accepted by ApS