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Further Results on Guderley Mach Reflection and the Triple Point Paradox

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Abstract

Recent numerical solutions and shock tube experiments have shown the existence of a complex reflection pattern, known as Guderley Mach reflection, which provides a resolution of the von Neumann paradox of weak shock reflection. In this pattern, there is a sequence of tiny supersonic patches, reflected shocks and expansion waves behind the triple point, with a discontinuous transition from supersonic to subsonic flow across a shock at the rear of each supersonic patch. In some experiments, however, and in some numerical computations, a distinctly different structure which has been termed Guderley reflection has been found. In this structure, there appears to be a single expansion fan at the triple point, a single supersonic patch, and a smooth transition from supersonic to subsonic flow at the rear of the patch. In this work, we present numerical solutions of the compressible Euler equations written in self-similar coordinates at a set of parameter values that were used in previous computations which found the simple single patch structure described above. Our solutions are more finely resolved than these previous solutions, and they show that Guderley Mach reflection occurs at this set of parameter values. These solutions lead one to conjecture that the two patterns are not distinct: rather, Guderley reflection is actually underresolved Guderley Mach reflection.

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Authors and Affiliations

  1. Department of Mathematics, College of Staten Island, City University of New York, Staten Island, NY, USA

    Allen M. Tesdall

  2. Department of Mathematics, University of Houston, Houston, TX, USA

    Richard Sanders

  3. Department of Mathematics and Informatics, University of Sofia, Sofia, Bulgaria

    Nedyu Popivanov

Authors
  1. Allen M. Tesdall
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  2. Richard Sanders
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  3. Nedyu Popivanov
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Corresponding author

Correspondence to Allen M. Tesdall.

Additional information

Allen M. Tesdall’s research was supported by CUNY Research Foundation PSC-CUNY Grant #66237-00 44. Nedyu Popivanov’s research was partially supported by the Bulgarian NSF under Grant DCVP 02/1/2009, “Centre of Excellence on Supercomputer Applications,” and by Sofia University Grant 94/2014.

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Tesdall, A.M., Sanders, R. & Popivanov, N. Further Results on Guderley Mach Reflection and the Triple Point Paradox. J Sci Comput 64, 721–744 (2015). https://doi.org/10.1007/s10915-015-0028-1

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  • DOI: https://doi.org/10.1007/s10915-015-0028-1

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