A Shock-Fitting Primer

1. Auflage 2010
ISBN: 978-1-4398-0758-3
Verlag: CRC Press

Buch, Englisch, 416 Seiten, Format (B × H): 156 mm x 235 mm, Gewicht: 748 g

Reihe: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science

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® codes serve as concrete examples of how to implement the ideas discussed in the book.

Zielgruppe

Graduate students and researchers in applied mathematics, fluid mechanics, aeronautics, and mechanical engineering.

Autoren/Hrsg.

Salas, Manuel D.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik

Inhaltsverzeichnis

Introduction. Shock-Fitting Principles. Fundamental Concepts and Equations. Euler Equations: One-Dimensional Problems. Euler Equations: Two-Dimensional Problems. Floating Shock-Fitting with Unstructured Grids. References. Appendix. Index.

Über Autor(innen)

Manuel D. Salas is a distinguished research associate at NASA Langley Research Center in Hampton, Virginia, USA. During his tenure at NASA, Mr. Salas was head of the theoretical aerodynamics branch, chief scientist for fluid dynamics, director of high performance computing, and principal investigator for the hypersonic aerodynamic program. He was also director of the Institute for Computer Applications in Science and Engineering (ICASE) from 1996 to 2002.