Abstract
In this chapter we study the shock reflection in unsteady flow, i.e. the reflection of a moving shock by obstacle. In Chap. 1 we have discussed the simplest case, when a moving planar shock is reflected by a planar obstacle. In this flat case we solve the problem and give required results only by using algebraic computations. However, when the moving shock is not a planar shock, or the surface of the obstacle is not a plane, then the algebraic computations are not enough. In this case people must employ the theory of partial differential equations to describe the variation of the parameters of the flow field. Generally, to simplify the initial state we often assume that the incident shock is a planar shock with constant speed and assume the surface of the obstacle is curved.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
G-Q.Chen and M.Feldman, Mathematics of Shock Reflection-Diffraction and von Neumann’s Conjectures, Princeton University Press, Princeton and Oxford, 2018
S.X. Chen, On reflection of multidimensional shock front. Jour. Diff. Eqs. 80, 199–236 (1989)
S.X. Chen, Mach configuration in pseudo-stationary compressible flow. Jour. Amer. Math. Soc. 21, 63–100 (2008)
S.X.Chen, Smoothness of shock front solutions for system of conservation laws, Lecture Notes in Math., 1306(1990),38-60, Springer-Verlag, New York/Berlin
S. Canic, B.L. Keyfitz, E.H. Kim, A free boundary problem for a quasilinear degenerate elliptic equation: Regular reflection of weak shocks. Comm. Pure Appl. Math. 55, 71–92 (2002)
S.X. Chen, Linear approximation of shock reflection at a large angle. Comm. Partial Diff. Eqs. 21, 1103–1114 (1996)
D.Serre, Ecoulements de fluides parfaits en deux variables independentes de type espace. Reflexion d’un choc plan un diedre compressif, Arch. Rational Mech. Anal, 132(1995),15-36
Y. Zheng, Two-dimensional regular shock reflection for the pressure gradient system of conservation laws. Acta Math. Appl. Sin. Engl. Ser. 22, 177–210 (2006)
G-Q.Chen and M.Feldman, Global solution to shock reflection by large-angle wedges for potential flow, Ann. Math.,171(2010),1067-1182
D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Orders (Springer-Verlag, New York, Second Edition, 1983)
M. Bae, G.-Q. Chen, M. Feldman, Regularity of solutions to regular shock reflection for potential flow. Invent. Math. 175, 505–543 (2009)
V. Elling, Regular reflection in self-similar potential flow and the sonic criterion. Comm. Math. Anal. 8, 22–69 (2010)
V.M. Teshukov, Stability of regular shock wave reflection. J. Appl. Mech. Tech. Phys. 30(2), 189–196 (1989)
G. Ben-Dor, Shock Waves Reflection Phenomena, 2nd edn. (Springer-Verlag, Berlin, Heiderberg, New York, 2007)
S.X.Chen, Stability of E-H Mach configuration in pseudo-steady compressible flow, Frontier in differential geometry, partial differential equations and mathematical physics, World Sci. Publ. (2014),35-47
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Shanghai Scientific and Technical Publishers
About this chapter
Cite this chapter
Chen, S. (2020). Shock Reflection in Unsteady Flow. In: Mathematical Analysis of Shock Wave Reflection. Series in Contemporary Mathematics, vol 4. Springer, Singapore. https://doi.org/10.1007/978-981-15-7752-9_5
Download citation
DOI: https://doi.org/10.1007/978-981-15-7752-9_5
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-7751-2
Online ISBN: 978-981-15-7752-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)