Aec Computing and Applied Mathematics Center: Aec Research and Development Report (Classic Reprint) - Hardcover

Robert D. Richtmyer

9780656029327: Aec Computing and Applied Mathematics Center: Aec Research and Development Report (Classic Reprint)

Hardcover

ISBN 10: 0656029323 ISBN 13: 9780656029327

Publisher: Forgotten Books, 2018

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Stability insights for numerical fluid dynamics and shock problems that guide safe, reliable simulations.

In this report from the Aec Computing and Applied Mathematics Center, the authors present the Godunov–Ryabenkii stability criterion for linear difference schemes. It expands on the classic von Neumann approach by examining how boundary conditions affect growth of errors in numerical solutions, especially near shocks and interfaces.

The text explains how to analyze the spectrum of a family of operators and how local normal modes determine stability. It also compares the GR criterion with the von Neumann condition, showing when each provides a reliable guide for stability in the interior and near boundaries. The methods are illustrated with simple examples and extended to the case of a single space variable with boundaries at work.
What you’ll experience and learn:

The concept of the spectrum for a family of difference operators and how it relates to stability.
How boundary conditions can introduce new local normal modes that influence growth of errors.
A clear route to applying the GR criterion to practical difference schemes, including shock fitting.
How this framework compares to von Neumann analysis and when it gives stronger guidance near boundaries.

Ideal for readers of computational fluid dynamics and numerical analysis who want a practical, theory-grounded approach to ensuring stable simulations in the presence of shocks and boundaries.

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