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Transonic shock and rarefaction wave interactions of two-dimensional Riemann problems for the self-similar nonlinear wave system

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Abstract

This paper addresses the self-similar transonic irrotational flow in gas dynamics in two space dimensions.We consider a configuration that the incident shock becomes a transonic shock as it enters the sonic circle, interacts with the rarefaction wave downstream, and then becomes sonic. The rarefaction wave further downstream becomes sonic (degenerate) creating an unknown boundary for the governing system. We present the Riemann data for this configuration, provide the characteristic decomposition of the system, and formulate the boundary value problem for this configuration. The numerical results are presented, and a method to establish the existence result is briefly discussed.

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Authors and Affiliations

  1. California State University, Long Beach, CA, 90840-1001, USA

    Eun Heui Kim

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  1. Eun Heui Kim
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Correspondence to Eun Heui Kim.

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Research supported by the National Science Foundation under grant DMS-1109202.

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Kim, E.H. Transonic shock and rarefaction wave interactions of two-dimensional Riemann problems for the self-similar nonlinear wave system. Bull Braz Math Soc, New Series 47, 431–444 (2016). https://doi.org/10.1007/s00574-016-0160-z

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  • DOI: https://doi.org/10.1007/s00574-016-0160-z

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