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Unsplit Schemes for Hyperbolic Conservation Laws with Source Terms in One Space Dimension

Papalexandris, Miltiadis V. and Leonard, Anthony and Dimotakis, Paul E. (1997) Unsplit Schemes for Hyperbolic Conservation Laws with Source Terms in One Space Dimension. Journal of Computational Physics, 134 (1). pp. 31-61. ISSN 0021-9991. https://resolver.caltech.edu/CaltechAUTHORS:20160602-181443806

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Abstract

The present work is concerned with an application of the theory of characteristics to conservation laws with source terms in one space dimension, such as the Euler equations for reacting flows. Space-time paths are introduced on which the flow/chemistry equations decouple to a characteristic set of ODE's for the corresponding homogeneous laws, thus allowing the introduction of functions analogous to the Riemann invariants in classical theory. The geometry of these paths depends on the spatial gradients of the solution. This particular decomposition can be used in the design of efficient unsplit algorithms for the numerical integration of the equations. As a first step, these ideas are implemented for the case of a scalar conservation law with a nonlinear source term. The resulting algorithm belongs to the class of MUSCL-type, shock-capturing schemes. Its accuracy and robustness are checked through a series of tests. The stiffness of the source term is also studied. Then, the algorithm is generalized for a system of hyperbolic equations, namely the Euler equations for reacting flows. A numerical study of unstable detonations is performed.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1006/jcph.1997.5692DOIArticle
http://www.sciencedirect.com/science/article/pii/S0021999197956928PublisherArticle
Additional Information:© 1997 Academic Press. Received February 12, 1996; revised February 17, 1997. Article No. CP975692. The authors thank Dr. Tasso Lappas and Professor Joseph Shepherd for many stimulating discussions and the anonymous referees of this paper for their comments and insightful suggestions. This work is part of a larger effort to understand mixing and combustion, sponsored by the Air Force Office of Scientific Research Grants F49620-94-1-0353 and F49626-93-1-00338, whose support is gratefully acknowledged.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)F49620-94-1-0353
Air Force Office of Scientific Research (AFOSR)F49626-93-1-00338
Issue or Number:1
Record Number:CaltechAUTHORS:20160602-181443806
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160602-181443806
Official Citation:Miltiadis V. Papalexandris, Anthony Leonard, Paul E. Dimotakis, Unsplit Schemes for Hyperbolic Conservation Laws with Source Terms in One Space Dimension, Journal of Computational Physics, Volume 134, Issue 1, 1997, Pages 31-61, ISSN 0021-9991, http://dx.doi.org/10.1006/jcph.1997.5692. (http://www.sciencedirect.com/science/article/pii/S0021999197956928)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67626
Collection:CaltechAUTHORS
Deposited By: Paul Dimotakis
Deposited On:04 Jun 2016 17:58
Last Modified:03 Oct 2019 10:07

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