This NATO Advanced Research Workshop was devoted to the pre sentation, evaluation, and critical discussion of numerical methods in nonrelativistic and relativistic hydrodynamics, radia tive transfer, and radiation-coupled hydrodynamics. The unifying theme of the lectures was the successful application of these methods to challenging problems in astrophysics. The workshop was subdivided into 3 somewhat independent topics, each with their own subtheme. Under the heading radiation hydrodynamics were brought together context, theory, methodology, and application of radia tive transfer and radiation hydrodynamics in astrophysics. The intimate coupling between astronomy and radiation physics was underscored by examples from past and present research. Frame-dependence of both the equation of transfer (plus moments) and the underlying radiation quantities was discussed and clarified. Limiting regimes in radiation-coupled flow were identified and described; the dynamic diffusion regime received special emphasis. Numerical methods for continuum and line transfer equations in a given background were presented. Two examples of methods for computing dynamically coupled radia tion/matter fields were given. In l-d and assuming LTE the complete equations of radiation hydrodynamics can be solved with current computers. Such is not the case in 2- or 3-d, which were identified as target areas for research. The use of flux-limiters was vigorously discussed in this connection, and enlivened the meeting.

Graduate-level text examines propagation of thermal radiation through a fluid and its effects on the hydrodynamics of fluid motion. Topics include approximate formulations of radiative transfer and relativistic effects of fluid motion; microscopic physics associated with the equation of transfer; inverse Compton scattering; and hydrodynamic description of fluid. 1973 edition.

The discipline of radiation hydrodynamics is the branch of hydrodynamics in which the moving fluid absorbs and emits electromagnetic radiation, and in so doing modifies its dynamical behavior. That is, the net gain or loss of energy by parcels of the fluid material through absorption or emission of radiation are sufficient to change the pressure of the material, and therefore change its motion; alternatively, the net momentum exchange between radiation and matter may alter the motion of the matter directly. Ignoring the radiation contributions to energy and momentum will give a wrong prediction of the hydrodynamic motion when the correct description is radiation hydrodynamics. Of course, there are circumstances when a large quantity of radiation is present, yet can be ignored without causing the model to be in error. This happens when radiation from an exterior source streams through the problem, but the latter is so transparent that the energy and momentum coupling is negligible. Everything we say about radiation hydrodynamics applies equally well to neutrinos and photons (apart from the Einstein relations, specific to bosons), but in almost every area of astrophysics neutrino hydrodynamics is ignored, simply because the systems are exceedingly transparent to neutrinos, even though the energy flux in neutrinos may be substantial. Another place where we can do ''radiation hydrodynamics'' without using any sophisticated theory is deep within stars or other bodies, where the material is so opaque to the radiation that the mean free path of photons is entirely negligible compared with the size of the system, the distance over which any fluid quantity varies, and so on. In this case we can suppose that the radiation is in equilibrium with the matter locally, and its energy, pressure and momentum can be lumped in with those of the rest of the fluid. That is, it is no more necessary to distinguish photons from atoms, nuclei and electrons, than it is to distinguish hydrogen atoms from helium atoms, for instance. There are all just components of a mixed fluid in this case. So why do we have a special subject called ''radiation hydrodynamics'', when photons are just one of the many kinds of particles that comprise our fluid? The reason is that photons couple rather weakly to the atoms, ions and electrons, much more weakly than those particles couple with each other. Nor is the matter-radiation coupling negligible in many problems, since the star or nebula may be millions of mean free paths in extent. Radiation hydrodynamics exists as a discipline to treat those problems for which the energy and momentum coupling terms between matter and radiation are important, and for which, since the photon mean free path is neither extremely large nor extremely small compared with the size of the system, the radiation field is not very easy to calculate. In the theoretical development of this subject, many of the relations are presented in a form that is described as approximate, and perhaps accurate only to order of {nu}/c. This makes the discussion cumbersome. Why are we required to do this? It is because we are using Newtonian mechanics to treat our fluid, yet its photon component is intrinsically relativistic; the particles travel at the speed of light. There is a perfectly consistent relativistic kinetic theory, and a corresponding relativistic theory of fluid mechanics, which is perfectly suited to describing the photon gas. But it is cumbersome to use this for the fluid in general, and we prefer to avoid it for cases in which the flow velocity satisfies {nu} “c. The price we pay is to spend extra effort making sure that the source-sink terms relating to our relativistic gas component are included in the equations of motion in a form that preserves overall conservation of energy and momentum, something that would be automatic if the relativistic equations were used throughout.

This course was intended to provide the participant with an introduction to the theory of radiative transfer, and an understanding of the coupling of radiative processes to the equations describing compressible flow. At moderate temperatures (thousands of degrees), the role of the radiation is primarily one of transporting energy by radiative processes. At higher temperatures (millions of degrees), the energy and momentum densities of the radiation field may become comparable to or even dominate the corresponding fluid quantities. In this case, the radiation field significantly affects the dynamics of the fluid, and it is the description of this regime which is generally the charter of radiation hydrodynamics. The course provided a discussion of the relevant physics and a derivation of the corresponding equations, as well as an examination of several simplified models.

This book leads directly to the most modern numerical techniques for compressible fluid flow, with special consideration given to astrophysical applications. Emphasis is put on high-resolution shock-capturing finite-volume schemes based on Riemann solvers. The applications of such schemes, in particular the PPM method, are given and include large-scale simulations of supernova explosions by core collapse and thermonuclear burning and astrophysical jets. Parts two and three treat radiation hydrodynamics. The power of adaptive (moving) grids is demonstrated with a number of stellar-physical simulations showing very crispy shock-front structures.