Continuous compression waves in the two-dimensional Riemann problem |
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Authors: | A A Charakhch’yan |
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Institution: | (1) Department of Mechanical Engineering, Saitama Institute of Technology, 1690 Fusaiji, Okabe-machi, Ohsato-gun, 369–0293 Saitama, Japan |
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Abstract: | 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. |
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Keywords: | |
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