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A Shock-Fitting Primer
Paperback
Series: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science
Technology & EngineeringGeneral MathematicsPhysics
ISBN13: 9781138116634
Publisher: CRC Press
Published: Jun 14 2017
Pages: 416
Weight: 1.28
Height: 0.85 Width: 6.14 Depth: 9.21
Language: English
A defining feature of nonlinear hyperbolic equations is the occurrence of shock waves. While the popular shock-capturing methods are easy to implement, shock-fitting techniques provide the most accurate results. A Shock-Fitting Primer presents the proper numerical treatment of shock waves and other discontinuities.
The book begins by recounting the events that lead to our understanding of the theory of shock waves and the early developments related to their computation. After presenting the main shock-fitting ideas in the context of a simple scalar equation, the author applies Colombeau's theory of generalized functions to the Euler equations to demonstrate how the theory recovers well-known results and to provide an in-depth understanding of the nature of jump conditions. He then extends the shock-fitting concepts previously discussed to the one-dimensional and quasi-one-dimensional Euler equations as well as two-dimensional flows. The final chapter explores existing and future developments in shock-fitting methods within the framework of unstructured grid methods.
Throughout the text, the techniques developed are illustrated with numerous examples of varying complexity. On the accompanying downloadable resources, MATLAB(R) codes serve as concrete examples of how to implement the ideas discussed in the book.
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