Gas Dynamics: The Riemann Problem and Discontinuous Solutions: Application to the Shock Tube Problem

Ionut Danaila (), Pascal Joly, Sidi Mahmoud Kaber and Marie Postel
Additional contact information
Ionut Danaila: Université de Rouen Normandie, CNRS, Laboratoire de mathématiques Raphaël Salem
Pascal Joly: Laboratoire Jacques-Louis Lions
Sidi Mahmoud Kaber: Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions
Marie Postel: Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions

Chapter Chapter 12 in An Introduction to Scientific Computing, 2023, pp 269-291 from Springer

Abstract: Abstract This chapter gives a comprehensive study of the shock tube problem. This universal test case is first used to introduce some basic notions (conservation laws, characteristics, and Riemann invariants) about nonlinear hyperbolic systems of partial differential equations (PDEs). The exact solution is derived and compared with numerical solutions obtained using first- and second-order schemes (Lax-Wendroff and MacCormack). Upwind schemes (Godunov, Roe) specifically designed for hyperbolic equations are also presented.

Date: 2023
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-35032-0_12

Ordering information: This item can be ordered from
http://www.springer.com/9783031350320

DOI: 10.1007/978-3-031-35032-0_12

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().