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Shock Calculations and the Numerical Solution of Singular Perturbation Problems

Kreiss, H.-O. (1982) Shock Calculations and the Numerical Solution of Singular Perturbation Problems. In: Transonic, Shock, and Multidimensional Flows: Advances in Scientific Computing. Academic Press , New York, NY, pp. 289-311. ISBN 978-0-12-493280-7. http://resolver.caltech.edu/CaltechAUTHORS:20170718-084015866

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Abstract

This chapter presents shock calculations and discusses the numerical solution of singular perturbation problems. These methods can also be used for shock calculations. D. Brown has developed a much more sophisticated way to deal with shock calculations. He solves these problems using the Lax–Wendroff method on a fixed relatively coarse grid. Then the computer isolates those intervals where the gradient of the solution is large. A locally moving coordinate system is generated, and local singular perturbation problems are solved. In particular, a local mesh is constructed, which resolves the large gradients. D. Brown has also generalized the above technique to two space dimensions. The crudest way is to use the implicit Euler method in every direction.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/B978-0-12-493280-7.50017-6DOIArticle
http://www.sciencedirect.com/science/article/pii/B9780124932807500176PublisherArticle
Additional Information:© 1982 Academic Press, Inc.
Record Number:CaltechAUTHORS:20170718-084015866
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170718-084015866
Official Citation:H.-O. Kreiss, Shock Calculations and the Numerical Solution of Singular Perturbation Problems, In Transonic, Shock, and Multidimensional Flows, edited by Richard E. Meyer,, Academic Press, 1982, Pages 289-311, ISBN 9780124932807, https://doi.org/10.1016/B978-0-12-493280-7.50017-6. (http://www.sciencedirect.com/science/article/pii/B9780124932807500176)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79141
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Jul 2017 16:17
Last Modified:18 Jul 2017 16:17

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