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Exact self-similar solutions for the magnetized Noh Z pinch problem

Physics of Plasmas

Velikovich, A.L.; Giuliani, J.L.; Zalesak, S.T.; Thornhill, J.W.; Gardiner, T.A.

A self-similar solution is derived for a radially imploding cylindrical plasma with an embedded, azimuthal magnetic field. The plasma stagnates through a strong, outward propagating shock wave of constant velocity. This analysis is an extension of the classic Noh gasdynamics problem to its ideal magnetohydrodynamics (MHD) counterpart. The present exact solution is especially suitable as a test for MHD codes designed to simulate linear Z pinches. To demonstrate the application of the new solution to code verification, simulation results from the cylindrical R - Z version of Mach2 and the 3D Cartesian code Athena are compared against the analytic solution. Alternative routines from the default ones in Athena lead to significant improvement of the results, thereby demonstrating the utility of the self-similar solution for verification. © 2012 American Institute of Physics.

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TYPE Journal Article YEAR 2012
ScopusOSTI

A Stochastic Programming Formulation for Disinfectant Booster Station Placement to Protect Large-Scale Water Distribution Systems

Computer Aided Chemical Engineering

Hackebeil, Gabriel A.; Mann, Angelica V.; Hart, William E.; Klise, Katherine A.; Laird, Carl D.

We present a methodology for optimally locating disinfectant booster stations for response to contamination events in water distribution systems. A stochastic programming problem considering uncertainty in both the location and time of the contamination event is formulated resulting in an extensive form that is equivalent to the weighted maximum coverage problem. Although the original full-space problem is intractably large, we show a series of reductions that reduce the size of the problem by five orders of magnitude and allow solutions of the optimal placement problem for realistically sized water network models. © 2012 Elsevier B.V.

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TYPE Conference YEAR 2012
ScopusOSTI
Results 65601–65700 of 99,299
Results 65601–65700 of 99,299