On the formation of weak plane shock waves by impulsive motion of a piston
1966 ◽
Vol 25
(4)
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pp. 705-718
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The piston problem for a viscous heat-conducting gas is studied under the assumption that the piston Mach number ε is small. The linearized Navier–Stokes equations are found to be valid up to times of the order of ε−2mean free times after the piston is set in motion, while at large times the solution is governed by Burgers's equation. Boundary conditions for the large-time solution are supplied by the matching principle of the method of inner and outer expansions, which is also used to construct a composite solution valid both for small and for large times.
2021 ◽
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2000 ◽
pp. 61-67
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