Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Efficient numerical stability analysis of detonation waves in ZND

Authors: Jeffrey Humpherys and Kevin Zumbrun
Journal: Quart. Appl. Math. 70 (2012), 685-703
MSC (2000): Primary 76E99; Secondary 76L05
DOI: https://doi.org/10.1090/S0033-569X-2012-01276-X
Published electronically: June 20, 2012
MathSciNet review: 3052085
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Abstract: As described in the classic works of Lee-Stewart and Short-Stewart, the numerical evaluation of linear stability of planar detonation waves is a computationally intensive problem of considerable interest in applications. Reexamining this problem from a modern numerical Evans function point of view, we derive a new algorithm for their stability analysis, related to a much older method of Erpenbeck, that, while equally simple and easy to implement as the standard method introduced by Lee-Stewart, appears to be potentially faster and more stable.

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Additional Information

Jeffrey Humpherys
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: jeffh@math.byu.edu

Kevin Zumbrun
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47402
Email: kzumbrun@indiana.edu

DOI: https://doi.org/10.1090/S0033-569X-2012-01276-X
Received by editor(s): November 6, 2010
Published electronically: June 20, 2012
Additional Notes: This work was supported in part by the National Science Foundation award numbers DMS-0607721 and DMS-0300487, and National Science Fountation CAREER award DMS-0847074. Thanks to Mark Williams for stimulating discussions regarding the numerical literature on stability of ZND detonations.
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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