- Conference date: 9–13 July 2012
- Location: Zaragoza, Spain
Resonant gas oscillation in a closed tube bounded by an oscillating plate and a vapor-liquid interface is theoretically analyzed by applying the asymptotic theory to the ES-BGK Boltzmann equation for the case of M P ∼ Kn ≪ 1 and a small evaporation coefficient , where M P and Kn are the Mach number of the plate and the Knudsen number, respectively. As a result, we derive a nonlinear integro-differential equation for determining the wave profile with the evaporation and condensation including α. We numerically solve the integro-differential equation with the method of Fourier series, and obtain a parameter plane for shock formation conditions and also the prediction of critical condition for shock formation.
- Integrodifferential equations
- Number theory
- Tube theories
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