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

In: An Introduction to Scientific Computing

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ionut Danaila & Pascal Joly & Sidi Mahmoud Kaber & Marie Postel, 2023. "Gas Dynamics: The Riemann Problem and Discontinuous Solutions: Application to the Shock Tube Problem," Springer Books, in: An Introduction to Scientific Computing, edition 2, chapter 0, pages 269-291, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-35032-0_12
    DOI: 10.1007/978-3-031-35032-0_12
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