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NJIT Applied Mathematics Colloquium

Friday, February 18th 2011, 11:30am
Cullimore Lecture Hall II
New Jersey Institute of Technology

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Mathematical Models and Adaptive Numerical Methods for High-Speed Reactive Flow

Don Schwendeman

RPI


Abstract

The aim of the talk is to present results of recent studies of mathematical models of high-speed reactive flow. The main focus of these studies has been the macro-scale behavior of detonation waves (initiation, propagation, failure) in heterogeneous explosives. Modeling the behavior of heterogeneous explosives is difficult due to their complex morphology, thermo-mechanical response, and combustion chemistry. Typically the micro-scale is averaged (either explicitly or implicitly) leading to continuum models that are suitable for studies of macro-scale behavior. Results for two particular models will be discussed. The governing equations for both models are systems of hyperbolic partial differential equations (representing balances of mass, momentum, energy, species, etc) which may or may not be capable of a conservation form. A numerical method is needed to obtain solutions of the equations and a high-resolution shock-capturing approach will be described. The method is carried out in parallel on overlapping grids and employs adaptive mesh refinement to locally increase the grid resolution near shocks and detonations. A brief discussion of some background material will be presented along with numerical simulations of detonation initiation and propagation in various configurations in order to illustate strengths and weaknesses of the two mathematical models.




Last Modified: Jan 2011
Linda Cummings
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