Karl-Heinz A. Winkler

Adaptive-mesh radiation hydrodynamics—I. The radiation transport equation in a completely adaptive coordinate system

Abstract We formulate the radiation transport equation in a completely adaptive coordinate system, which we define as a system in which the mesh in spacetime, angles and frequency adapts automatically to the dynamical evolution of the radiation field and fluid flow.

Shocks, interfaces, and patterns in supersonic jets

Abstract Supersonic gaseous jets exhibit coherent nonlinear dynamic structures. We use a supercomputer to obtain solutions to the equations of two-dimensional inviscid hydrodynamics, representing both axisymmetric and planar jets boring their way through a uniform medium. We use color images to display these high resolution computations. Several basic morphologies of interfaces and shock structures arise which we discuss in simple terms. The global structure of the two-parameter solution space is analyzed. A number of the basic structures, which appear in the supercomputer simulations, seem to occur in both terrestrial and astrophysical supersonic jets.

Adaptive mesh techniques for fronts in star formation

Abstract We present an implicit, adaptive-grid, finite-difference technique specifically designed to locate and track arbitrary fronts, interfaces and structures in a radiation hydro flow. The adaptive mesh is constructed in such a way that the “average” change of the flow-variables per grid zone is the same throughout the entire grid. A local grid refinement of up to a factor of 10 6 compared to an equidistant mesh has been obtained on a machine with 14 decimal digits per word. Crucial to this type of approach is the use of a stiffness operator, which prevents tangling of the mesh. The elliptic equation for the grid motion is solved implicitly coupled with the equations for the flow variables. Per timestep very steep and narrow flow features can travel many times their own width in true space. However, with respect to the adaptive mesh the motion of such flow features is always less than one zone. Thus, the Courant-Friedrichs-Lewy [1] (CFL)-conditions accuracy limitation is always fulfilled although its stability criterion does not pose any timestep limitations for our implicit numerical method. In fact, the choice of timesteps is based purely on physical and accuracy considerations. Typical applications run on Courant numbers ranging from 0.1 to 10 12 . The performance of this numerical scheme is demonstrated on a planar 1-D shocktube and the formation of a one solar mass protostar in spherical symmetry.

Implicit Adaptive-Grid Radiation Hydrodynamics

Publisher Summary This chapter discusses implicit adaptive-grid radiation hydrodynamics. The term radiation hydrodynamics refers to flows in which radiation contributes significantly to, or totally dominates, the energy and momentum balance in the flow. In such flows, radiation plays at least three important roles: (1) it can drive the dynamics of the flow via direct energy and momentum input. These processes may be highly nonlocal because radiation produced at one region in the flow is absorbed at a remote location in a transparent medium in the vicinity of the source. (2) Radiation can drive the kinetics of the flow via radiation-induced changes in the internal state of the material. In the most general case, one may have to account for intricate chains of radiative and collisional processes that determine the occupation numbers in bound and free states of the material. (3) Finally, radiation provides the diagnostics from which an outside observer can infer the internal properties and the dynamic state of the fluid. From the macroscopic point of view, it is useful to consider the radiating fluid as a composite gas comprising material particles and photons.

Adaptive-grid methods with asymmetric time-filtering

We identify the three essential parts for a successful and robust adaptive grid distribution equation for systems of nonlinear partial differential equations: (1) the spatial function, which is composed of operators that control the shape and size of zones, and guarantees the stability and positivity of the corresponding metric, (2) the structure function, which provides an objective measure of the structure of the solution, and generates source terms that drive the grid distribution into any desired configuration, and (3) an asymmetric time filter, which ensures a smooth space-time evolution of the mesh globally, even when there are abrupt changes in the structure of the solution locally. The last part ensures that any catastrophic effects of grid redistribution due to the sudden appearance or disappearance of discontinuities in the solution caused by nonlinear interactions are avoided. Specifically, we describe and analyze an implicit, finite-difference, adaptive-grid technique for time dependent (as well as time independent) problems in one spatial dimension, which automatically detects, resolves and tracks all essential features in the solution. Our method is demonstrated on two examples in fluid dynamics: (1) the generation and propagation of a front in two-phase immiscible flow described by the Buckley-Leverett equation, and (2) the classical Riemann problem of ideal gas dynamics.

Adaptive-mesh radiation hydrodynamics—II. The radiation and fluid equations in relativistic flows

Abstract We derive the radiation and fluid equations for relativistic flows in conservative from in a completely adaptive coordinate system.

Propagation and Morphology of Pressure-Confined Supersonic Jets

The beautiful, high resolution radio maps of jets, lobes, and hot-spots coming off the VLA challenge theorists to explain these phenomena in terms of simple, well-understood physical laws. The difficulty is often not one of finding a reasonable set of physical laws, but of finding their solutions. Analytic solutions of jet structure are limited to steady, isentropic, 1-dimensional flow in channels of slowly-varying cross section; analytic studies of jet stability are limited to modes of small amplitude which, in this regime, assume equal importance as well as unimportance for the gross structure of the flow. Numerical simulation provides a means for investigating those time-dependent, multidimensional, nonlinear solutions that are beyond the reach of analytic tools — solutions that must be relevant to an understanding of astrophysical jets. In an age when computing hardware and software are advancing so rapidly compared to analytic techniques, it is natural to turn to the computer for answers, approximate though they may be.

Late stages of solar type protostars

A consistent hydrodynamical and radiative transfer calculation in spherical symmetry for a 1M⊙ protostar is presented. The calculation starts with Larsons initial conditions and continues until almost all the material has fallen onto a hydrostatic core with a large outer convection zone. The innermost percent of the mass is partially degenerate. Due to the numerical technique used, the radius of the hydrostatic core is determined with a high degree of accuracy.