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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 which allows chemical energy release.

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© 1979 Springer-Verlag New York Inc.

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Chorin, A.J., Marsden, J.E. (1979). Gas Flow in One Dimension. In: A Mathematical Introduction to Fluid Mechanics. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0082-3_3

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  • DOI: https://doi.org/10.1007/978-1-4684-0082-3_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90406-1

  • Online ISBN: 978-1-4684-0082-3

  • eBook Packages: Springer Book Archive

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