Philos Trans A Math Phys Eng Sci. 2015 Sep 13;373(2050). doi: 10.1098/rsta.2014.0276.

Free boundary problems in shock reflection/diffraction and related transonic flow problems.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

Gui-Qiang Chen, Mikhail Feldman

PMID: 26261363 PMCID: PMC4535264 DOI: 10.1098/rsta.2014.0276

Abstract

Shock waves are steep wavefronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how several long-standing shock reflection/diffraction problems can be formulated as free boundary problems, discuss some recent progress in developing mathematical ideas, approaches and techniques for solving these problems, and present some further open problems in this direction. In particular, these shock problems include von Neumann's problem for shock reflection-diffraction by two-dimensional wedges with concave corner, Lighthill's problem for shock diffraction by two-dimensional wedges with convex corner, and Prandtl-Meyer's problem for supersonic flow impinging onto solid wedges, which are also fundamental in the mathematical theory of multidimensional conservation laws.

© 2015 The Author(s) Published by the Royal Society. All rights reserved.

Keywords: Lighthill's problem; equation of mixed elliptic–hyperbolic type; global entropy solutions; shock wave; transonic flow; von Neumann's problem

Publication Types

• Journal Article
• Research Support, Non-U.S. Gov't
• Research Support, U.S. Gov't, Non-P.H.S.
• Review