Abstract
The early-time, linearized impulsive piston problem is solved analytically for a gas obeying the energy-conserving Bhatnagar-Gross-Krook equation. The piston is adiabatic by reflecting particles specularly. Exact solutions for the density, mean velocity, and temperature are obtained as simple quadratures which are evaluated numerically. Flow features are related to the properties of certain “γ figures.” Density near the piston is found to rise and then fall as the early, near free-molecular flow converts to a transient thermal boundary layer and emerging viscous-acoustic front. A temperature maximum is observed traveling first at the isothermal sound speed and then slowing to half the adiabatic sound speed as the post-front profile flattens. Comparisons are made with a previous isothermal BGK study and with Moran and Shen's results for the linearized Navier-Stokes equations. Agreement with the latter results down to transition times proves the value of retaining high frequency components in a Navier-Stokes description of the flow.
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