A Numerical Study of a Converging Cylindrical Shock (Classic Reprint)

Gary A. Sod

ISBN 10: 1332170617 / ISBN 13: 9781332170616

Published by Forgotten Books, 2022

About this Item

Print on Demand. This book presents a numerical procedure to solve the one-dimensional equations of gas dynamics for a cylindrically or spherically symmetric flow. The method involves combining Glimm's method and operator splitting, eliminating the singular nature near the axis and the inability to put the momentum equation in conservation form, which are major problems in solving such systems. The author applies the method to the problem of a converging cylindrical shock, demonstrating the increase in shock strength as it converges toward the axis. The book provides insights into the behavior of shock waves and contact discontinuities in converging cylindrical flows, offering valuable knowledge for researchers in gas dynamics and related fields. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Seller Inventory # 9781332170616_0

Bibliographic Details

• Title: A Numerical Study of a Converging Cylindrical Shock (Classic Reprint)
• Publisher: Forgotten Books
• Publication Date: 2022
• Language: English
• ISBN 10: 1332170617
• ISBN 13: 9781332170616
• Binding: Paperback
• Condition: New
• Book Type: print-on-demand item
• Seller catalogs:
  • Physics

About this title

Synopsis

Numerical study of a converging cylindrical shock shows how a careful scheme can capture sharp shock fronts.

The report explains a practical approach to solving the one‑dimensional gas dynamics equations in Cartesian coordinates, while using operator splitting and Glimm’s method to keep shocks and contact discontinuities perfectly sharp.

Readers will see how random sampling and Riemann problems are used to advance the solution, how boundary conditions at the axis are handled, and how the converging shock strengthens and reflects as it approaches the axis. The work also discusses the accompanying ordinary differential equations solved with a simple Euler step and reports on computational requirements and visualization of results.

• How Glimm’s scheme solves Riemann problems exactly and efficiently for shock-dominated flows
• How axis boundary conditions are applied in a cylindrical setting
• What happens to pressure, velocity, density, and energy as a converging shock evolves and reflects
• What the figures and numerical details reveal about the method’s accuracy and behavior

Ideal for readers of computational fluid dynamics and numerical methods who want a concrete example of shock tracking in a converging geometry.