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.
Date of this Version
Chigullapalli, S; Venkattraman, A; and Alexeenko, Alina A., "Modeling of Viscous Shock Tube Using ES-BGK Model Kinetic Equations" (2009). School of Aeronautics and Astronautics Faculty Publications. Paper 32.