The viscous effects on unsteady shock wave propagation are investigated by numerical solution of the Boltzmann model kinetic equations. The kinetic equations are solved for two unsteady non-equilibrium flow problems, namely, the one-dimensional Riemann problem and a two-dimensional viscous shock-tube. The numerical method comprises the discrete velocity method in the velocity space and the finite volume discretization in physical space using various flux schemes. The discrete version of H-theorem is applied for analysis of accuracy of the numerical solution as well as of the onset of non-equilibrium. Simulations show that the maximum entropy generation rate in viscous shock tube occurs in the boundary layer / shock wave interaction region. The entropy generation rate is used to determine the time-variation of the speed of propagation of shock, contact discontinuity and rarefaction waves.


This is the published version of S. Chigullapalli*, V. Ayyaswamy, and A. Alexeenko. 2009. “Modeling of Viscous Shock Tube Using ES-BGK Model Kinetic Equations”. First published as an 47th AIAAAerospace Sciences Meeting and Aerospace Exposition Paper and is available online at: http://arc.aiaa.org/doi/pdf/10.2514/6.2009-1317.

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