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arXiv · 1208.5183

Stability of Transonic Characteristic Discontinuities in Two-Dimensional Steady Compressible Euler Flows

Gui-Qiang G. Chen·Vaibhav Kukreja·Hairong Yuan
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Abstract

For a two-dimensional steady supersonic Euler flow past a convex cornered wall with right angle, a characteristic discontinuity (vortex sheet and/or entropy wave) is generated, which separates the supersonic flow from the gas at rest (hence subsonic). We proved that such a transonic characteristic discontinuity is structurally stable under small perturbations of the upstream supersonic flow in $BV$. The existence of a weak entropy solution and Lipschitz continuous free boundary (i.e. characteristic discontinuity) is established. To achieve this, the problem is formulated as a free boundary problem for a nonstrictly hyperbolic system of conservation laws; and the free boundary problem is then solved by analyzing nonlinear wave interactions and employing the front tracking method.

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Gui-Qiang G. Chen, Vaibhav Kukreja, Hairong Yuan. 2012-08-26. Stability of Transonic Characteristic Discontinuities in Two-Dimensional Steady Compressible Euler Flows. https://doi.org/10.1063/1.4790887

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