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arXiv · 2509.08212

Two-dimensional steady supersonic ramp flows of Bethe-Zel'dovich-Thompson fluids

Geng Lai
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Abstract

Two-dimensional (2D) steady supersonic ramp flows are important and well-studied flow patterns in aerodynamics. In the paper [41], Vimercati, Kluwick, and Guardone constructed various self-similar composite wave solutions consisting of centered simple waves and oblique shocks for the 2D steady supersonic flow of BZT fluids past compressible and rarefactive ramps. In the present paper, we study the stabilities of the self-similar fan-shock-fan and shock-fan-shock composite waves in 2D steady supersonic flows of BZT fluids. In contrast to ideal gases, the flow downstream (or upstream) of a shock of a BZT fluid may be sonic in the sense of the flow velocity relative to the shock front, and the formulation of boundary conditions for the shocks is usually unknown in advance. In order to study the stabilities of the composite waves, we establish some a priori estimates of different shock types by comparing the shock speed with the acoustic speed along the shocks and applying Liu's extended entropy condition, and to solve some post-sonic and pre-sonic shock free boundary problems. The sonic shocks are envelopes of one of the acoustic families of characteristics, and not characteristics. This results in a fact that the flow downstream (or upstream) of a sonic shock is not C1smooth up to the shock boundary. We use a weighted characteristic decomposition method and a hodograph transformation method to overcome the difficulty caused by the singularity on sonic shocks of 2D steady full Euler equations and potential flow equations, respectively. Some new iteration schemes are also proposed to solve the post-sonic and pre-sonic shock free boundary problems.

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Geng Lai. 2026-08-17. Two-dimensional steady supersonic ramp flows of Bethe-Zel'dovich-Thompson fluids. https://arxiv.org/abs/2509.08212

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