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Gas Flow in One Dimension

  • A. J. Chorin
  • J. E. Marsden
Part of the Texts in Applied Mathematics book series (TAM, volume 4)

Abstract

In this chapter we discuss compressible flow in one dimension. In the first section we develop the geometry of characteristics and in the second we introduce the notion of a weak solution and the entropy condition for shocks. In the third section we discuss the Riemann problem, i.e., a flow problem with particular discontinuous initial data. A general construction, due to Glimm, which uses the solution of Riemann problems to produce solutions of arbitrary problems, is then presented. This construction is the basis of both some existence proofs and some methods of numerical computation in gas dynamics. In the final section we generalize the discussion to the flow of a gas that allows chemical energy release.

Keywords

Weak Solution Riemann Problem Constant State Combustion Wave Slip Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Reference

  1. R. DiPerna, Comm. Pure Appl. Math. 9 [1973]26.MathSciNetGoogle Scholar
  2. T.P. Liu, J. Diff. Equations, 18 [1975]218.zbMATHCrossRefGoogle Scholar
  3. Chorin, J. Compo Phys. 22 [1976]517.MathSciNetzbMATHCrossRefGoogle Scholar
  4. A.J. Chorlo, J. Compo Phys. 25 [1977]253.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • A. J. Chorin
    • 1
  • J. E. Marsden
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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