This article is cited in 2 scientific papers (total in 2 papers)
Continuous compression waves in the two-dimensional Riemann problem
A. A. Charakhch'yan
Dorodnicyn Computing Center, Russian Academy of Sciences,
ul. Vavilova 40, Moscow, 119333, Russia
The interaction between a plane shock wave in a plate and a wedge is considered within the framework of the nondissipative compressible fluid dynamic equations. The wedge is filled with a material that may differ from that of the plate. Based on the numerical solution of the original equations, self-similar solutions are obtained for several versions of the problem with an iron plate and a wedge filled with aluminum and for the interaction of a shock wave in air with a rigid wedge. The behavior of the solids at high pressures is approximately described by a two-term equation of state. In all the problems, a two-dimensional continuous compression wave develops as a wave reflected from the wedge or as a wave adjacent to the reflected shock. In contrast to a gradient catastrophe typical of one-dimensional continuous compression waves, the spatial gradient of
a two-dimensional compression wave decreases over time due to the self-similarity of the solution. It is conjectured that a phenomenon opposite to the gradient catastrophe can occur in an actual flow with dissipative processes like viscosity and heat conduction. Specifically, an initial shock wave is transformed over time into a continuous compression wave of the same amplitude.
shock waves, compression waves, shock wave reflection, Riemann problem, self-similar solution, gasdynamic equations.
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Computational Mathematics and Mathematical Physics, 2009, 49:10, 1774–1780
A. A. Charakhch'yan, “Continuous compression waves in the two-dimensional Riemann problem”, Zh. Vychisl. Mat. Mat. Fiz., 49:10 (2009), 1853–1859; Comput. Math. Math. Phys., 49:10 (2009), 1774–1780
Citation in format AMSBIB
\paper Continuous compression waves in the two-dimensional Riemann problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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V. V. Milyavskii, V. E. Fortov, A. A. Frolova, K. V. Khishchenko, A. A. Charakhch'yan, L. V. Shurshalov, “On the mechanism of pressure increase with increasing porosity of the media compressed in conical and cylindrical targets”, Comput. Math. Math. Phys., 50:12 (2010), 2082–2094
Charakhch'yan A.A., Khishchenko K.V., Fortov V.E., Frolova A.A., Milyavskiy V.V., Shurshalov L.V., “Shock compression of some porous media in conical targets: numerical study”, Shock Waves, 21:1 (2011), 35–42
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