We present a review of the application of numerical methods to solve the problem of the stellar/solar wind with the local interstellar medium. Most of approaches described are developed by the authors. They include both purely gas dynamic and magnetohydrodynamic methods. Some attention is given to the influence of the neutral component of the interstellar medium on the flow structure. Far-field boundary conditions are formulated which are usually required in astrophyscal application owing to the extremely large length scale of these problems. Results are presented of the stationary and nonstationary, axisymmetric and geniunly three-dimensional calculations. Newly developed high-resolution numerical methods are discussed which can be applied to a large variety of astrophysical problems. The bibliography includes 113 references. The review will be published in ``CFD Review 97'' by John Wiley. From: Nikolai V. Pogorelov <pogo@jet.planet.kobe-u.ac.jp> Jul 1998 (see also Periodic stellar wind / interstellar medium interaction. 1995A&A...297..835P)

The influence of electron thermal conduction on the 2D gas dynamics of colliding stellar winds is investigated. It is shown that, as a result of the non-linear dependence of the electron thermal flux on the temperature, the pre-heating zones (in which the hot gas in the interaction region heats the cool winds in front of the shocks) have finite sizes. The dependence of the problem of the structure of the flow in the interaction region on the dimensionless parameters is studied, and a simple expression is derived for the size of the pre-heating zones at the axis of symmetry. It is shown that small values of the thermal conductivity do not suppress the Kelvin-Helmholtz instability if the adiabatic flow is subject to it. Further studies, both numerical and analytical, in this direction will be of great interest. The influence of thermal conduction on the XRAY emission from the interaction region is also estimated. 1998MNRAS.300..686M

The properties of radiative steady-state colliding stellar winds in binary systems are studied. It is shown that the presence of a singularity at the stagnation point has a major influence on the structure of these flows. This problem is of great importance if their stability properties are considered. None of the existing models treats this mathematical problem properly, and special efforts must be undertaken in the future in order to come to a firm conclusion about the physical nature of possible instabilities. At the moment, neither numerical nor analytical models can be considered to be of acceptable accuracy in the case of highly radiative steady-state colliding stellar winds. 1998MNRAS.298..1021M

We present an analytic model for the thin-shell, radiative interaction between a hypersonic, plane-parallel wind and a rigid, spherical obstacle. This problem has clear applications, e.g., to the interaction of winds from young stars and dense cloudlets, and to the interaction of the wind from a binary partner with the photosphere of the second star. We also present a comparison of the analytic model with a full, axisymmetric numerical simulation. We find only a partial agreement between the numerical simulation and the analytic model, apparently as a result of the very strong `thin-shell' instabilities of the post-bow shock flow. Our analytic model predicts the surface density, flow velocity and the energy radiated per unit area, as well as the total luminosity of the bow shock. The model can therefore be used directly for carrying out comparisons with observations of different astrophysical objects. 1998MNRAS.297..383C

Following the proposal by Damineli that the central object of Eta Carinae may be an early-type binary, we perform numerical simulations of the XRAY emission from colliding stellar winds. A synthetic light curve has been generated which qualitatively agrees with the recent XRAY variability, and provides further support for the binary model. In particular, the model predicts a rise in the observed XRAY emission towards periastron, followed by a sharp drop and subsequent recovery. This is indeed what is seen in the RXTE light curve, although some problems concerning the XRAY spectrum at periastron still need to be explained. The simulations suggest that the width of the periastron dip will provide strong constraints on the binary and stellar wind properties of the components of Eta Car. 1998MNRAS.299L...5P

We have performed 3D numerical simulations of an over-pressurized Herbig-Haro-type jet which propagates into a sidestreaming environment. The interaction between the jet and the sidewind results in a perpendicular acceleration of the jet material, and a consequent curvature of the jet as it moves into the anisotropic medium. We find that an approximately steady configuration is achieved both for a sidewind that is perpendicular to the jet and for a sidewind inclined at 45 deg towards the jet source. The curvature obtained in both these models is consistent with analytic models of the jet/sidewind problem. We have also calculated Halpha maps, which show an emitting sheath around the upwind (with respect to the sidewind) side of the jet beam. This emitting sheath may explain part of the observed emission from curved stellar jets. 1998MNRAS.298..871L

Full Refereed Scanned Article

In this paper we explore the physics of time-dependent hydrodynamic collimation of jets from young stellar objects (YSOs). Using parameters appropriate to YSOs, we have carried out high-resolution hydrodynamic simulations modeling the interaction of a central wind with an environment characterized by a toroidal density distribution which has a moderate opening angle of theta rho ~ 90 deg. The results show that for all but low values of the equator-to-pole density contrast the wind/environment interaction produces strongly collimated supersonic jets. The jet is composed of shocked wind gas. Using analytical models of wind-blown bubble evolution, we show that the scenario studied here should be applicable to YSOs and can, in principle, initiate collimation on the correct scales (R <~ 100 AU). Comparison of our simulations with analytical models demonstrates that the evolution seen in the simulations is a mix of wind-blown bubble and jet dynamics. The simulations reveal a number of time-dependent nonlinear features not anticipated in previous analytical studies. These include: a prolate wind shock; a chimney of cold swept-up ambient material dragged into the bubble cavity; a plug of dense material between the jet and bow shocks. We find that the collimation of the jet occurs through both de Laval nozzles and focusing of the wind via the prolate wind shock. Using an analytical model for shock focusing we demonstrate that a prolate wind shock can, by itself, produce highly collimated supersonic jets. Animations from these simulations are available over the internet at http://www.msi.umn.edu/Projects/twj/jetcol.html. The scanned article is available at: 1996ApJ...472..684F

see also U of MN Computational Astrophysics page

We present 3D numerical hydrodynamical simulations of precessing supersonic heavy jets to explore their evolution, how they differ from straight jets, and how well they serve as a model for generating molecular outflows from young stellar objects (YSOs). The dynamics are studied with a number of high-resolution simulations on a Cartesian grid (128x128x128 zones) using a high-order finite difference method. A range of cone angles and precession rates are included in the study. Two higher resolution runs (256x256x256 zones) were made for comparison in order to confirm numerical convergence of global flow characteristics. Morphological, kinematical and dynamical characteristics of precessing jets are described, and compared to important properties of straight jets and also to observations of YSOs. In order to examine the robustness of precessing jets as a means of producing molecular outflows around YSOs, `synthetic observations' of the momentum distributions of the simulated precessing jets are compared to observations of molecular outflows. It is found that precessing jets match better the morphology, highly forward-driven momentum and momentum distributions along the long axis of molecular outflows than do wind-driven or straight jet-driven flow models.1996MNRAS.282.1114C

We perform two-dimensional gasdynamical simulations to model the growth of a stellar wind bubble araound a Wolf-Rayet (W-R) star, taking into account the prior main-sequence red supergiant phases. Following the three wind model we have proposed, we take the main-sequence, red supergiant, and W-R winds each to be constant in time.1995ApJ...455..160G

see also part I: Wolf-Rayet Bubbles I: Analytic solutions

This paper reports the results of the numerical study of the formation of aspherical planetary nebulae through the generalized interacting winds model, taking into account the effects caused by the evolving central star and fast wind. The results show for the first time that aspherical nebulae do form within the required time-scale. Consideration of the development of the nebula shows that in the early stages it is the ionization of the aspherical AGB wind that contributes considerably to the shaping of the nebula. Furthermore, the passing through of the ionization front may modify the density distribution in the slow wind, leading to the formation of a surrounding envelope, and sometimes a different morphology for the nebula from that to be expected from the initial conditions. I consider how the different phases of ionization fronts and wind swept bubbles can be observationally distinguished. 1995MNRAS.277..173M

The emergence of these nebulae is accomplished with the 'Roe-solver' characteristic-based modeling technique extended by Eulderink (1990). The technique treats the Riemann problem with a numerical approximation that linearizes the problem. The correct velocity is thereby found if the initial discontinuity is a pure contact discontinuity or a pure shock. The aspherical planetary nebulae can be modeled in terms of aspherical bubbles by utilizing a density contrast in the remnants of the AGB wind. The analytical results of Icke (1988) are generally confirmed including the division of the shocks into spherical and 'protruding' parts. A cusp is described that forms the transition between these two parts and relates to a high degree of collimation in the high-density flow. A wide range of morphologies can be formed in the nebulae if it is assumed that intermediate-mass stars lose mass in two successive hydrodynamical stages. 1991A&A...252..718M

• I - Numerical methods and their application to the investigation of outer shell instabilities
• II - Variable mass-loss rates and the possibility of outer-shell fragmentation in relation to the origin of interstellar bullets.
• III - Self-confining flows in media with strong density gradients.
• IV - Properties of bow shocks around dense clumps in free wind regions.

I - This paper is the first of a series on the evolution and stability of stellar wind bubbles. Interactions between winds and the interstellar medium are dealt with, but processes leading to wind generation and acceleration are not studied. In the present paper a second order two-dimensional hydrodynamical code is developed and shown to have clear advantages over widely used first-order schemes. Its application range is discussed and research perspectives are outlined. The code is tested on existing analytical solutions for the internal structure of wind bubbles. Models of spherically symmetric adiabatic bubbles are shown to be quantitatively correct. A good qualitative agreement with one-dimensional numerical models is also achieved when radiative energy losses are taken into account. Outer shells of radiative models are tested for stability against density and velocity perturbations. It is shown that contrary to common belief they cannot fragment as soon as they cool. The instability of the shell is not a pure thermal one and its growth time is much longer than the cooling time.1985A&A...143...59R,

II,III,IV: The formation and evolution of stellar-wind bubbles (SWBs) are investigated by means of numerical simulations using the code of part I. The observational evidence for variable winds, self-confining flows, and the possibility of bow shocks in Herbig-Haro objects (HHs) is reviewed, and the simulation results are presented graphically and discussed. High-density models are found to produce more rapidly propagating disruptions in the SWBs, with fragments similar to the interstellar bullets proposed to explain the origin of HHs. In T-Tau-like models with compact circumstellar disks, SWBs break out to form secondary SWBs and/or hollow cylinders. Models constructed to explore the shocked-cloudlet hypothesis for HH formation (with winds in excess of Mach 50) are found to become sensitive to cooling efficiency when cooling is taken into account, and to yield predictions which are also consistent with the interstellar-bullet hypothesis. , 1985A&A...147..209R

The results of 2 - D axisymmetric calculations of a supernova remnant (SNR) crossing a large scale density discontinuity are presented. The X-ray and H-alpha appearance of the remnants at selected evolutionary times and viewing angles is calculated and presented in form of isophote maps. The numerical results are discussed in light and current optical, X-ray and radio observations of SNRs in general and the Cygnus loop in particular. The large scale structure and asymmetries of the Cygnus loop can be explained by a supernova remnant breaking out of a dense molecular cloud. 1985A&A...148...52T