Gravitational Collapse and Fragmentation in Molecular Clouds with Adaptive Mesh Refinement

We describe a powerful methodology for numerical solution of 3-D self-gravitational hydrodynamics problems with extremely high resolution. Our method utilizes the technique of local adaptive mesh refinement (AMR), employing multiple grids at multiple levels of resolution. These grids are automatically and dynamically added and removed as necessary to maintain adequate resolution. This technology allows for the solution of problems in a manner that is both more efficient and more versatile than other fixed and variable resolution methods. The application of AMR to simulate the collapse and fragmentation of a molecular cloud, a key step in star formation, is discussed. Such simulations involve many orders of magnitude of variation in length scale as fragments form. In this paper we briefly describe the methodology and present an illustrative application for nonisothermal cloud collapse. We describe the numerical Jeans condition, a criterion for stability of self-gravitational hydrodynamics problems. We show the first well-resolved nonisothermal evolutionary sequence beginning with a perturbed dense molecular cloud core that leads to the formation of a binary system consisting of protostellar cores surrounded by distinct protostellar disks. The scale of the disks, of order 100 AU, is consistent with observations of gaseous disks surrounding single T-Tauri stars and debris disks surrounding systems such as $\beta$ Pictoris.Comment: 10 pages, 6 figures (color postscript). To appear in the proceedings of Numerical Astrophysics 1998, Tokyo, March 10-13, 199

On the Nonlinearity of Modern Shock-Capturing Schemes

The development is reviewed of shock capturing methods, paying special attention to the increasing nonlinearity in the design of numerical schemes. The nature is studies of this nonlinearity and its relation to upwind differencing is examined. This nonlinearity of the modern shock capturing methods is essential, in the sense that linear analysis is not justified and may lead to wrong conclusions. Examples to demonstrate this point are given

Reflected near-field blast pressure measurements using high speed video

Background: The design and analysis of protective systems requires a detailed understanding of, and the ability to accurately predict, the distribution of pressure loads acting on an obstacle following an explosive detonation. In particular, there is a pressing need for accurate characterisation of blast loads in the region very close to a detonation, where even small improvised devices can produce serious structural or material damage. Objective: Accurate experimental measurement of these near-field blast events, using intrusive methods, is demanding owing to the high magnitudes (> 100 MPa) and short durations (< 1 ms) of loading. The objective of this article is to develop a non-intrusive method for measuring reflected blast pressure distributions using image analysis. Methods: This article presents results from high speed video analysis of near-field spherical PE4 explosive blasts. The Canny edge detection algorithm is used to track the outer surface of the explosive fireball, with the results used to derive a velocity-radius relationship. Reflected pressure distributions are calculated using this velocity-radius relationship in conjunction with the Rankine-Hugoniot jump conditions. Results: The indirectly measured pressure distributions from high speed video are compared with directly measured pressure distributions and are shown to be in good qualitative agreement with respect to distribution of reflected pressures, and in good quantitative agreement with peak reflected pressures (within 10% of the maximum recorded value). Conclusions: The results indicate that it is possible to accurately measure blast loads in the order of 100s MPa using techniques which do not require sensitive recording equipment to be located close to the source of the explosion

Experimental measurement of specific impulse distribution and transient deformation of plates subjected to near-field explosive blasts

The shock wave generated from a high explosive detonation can cause significant damage to any objects that it encounters, particularly those objects located close to the source of the explosion. Understanding blast wave development and accurately quantifying its effect on structural systems remains a considerable challenge to the scientific community. This paper presents a comprehensive experimental study into the loading acting on, and subsequent deformation of, targets subjected to near-field explosive detonations. Two experimental test series were conducted at the University of Sheffield (UoS), UK, and the University of Cape Town (UCT), South Africa, where blast load distributions using Hopkinson pressure bars and dynamic target deflections using digital image correlation were measured respectively. It is shown through conservation of momentum and Hopkinson-Cranz scaling that initial plate velocity profiles are directly proportional to the imparted impulse distribution, and that spatial variations in loading as a result of surface instabilities in the expanding detonation product cloud are significant enough to influence the transient displacement profile of a blast loaded plate