Chuandong Lin, Aiguo Xu, Guangcai Zhang, Yingjun Li, Sauro Succi
We present a Polar Coordinate Lattice Boltzmann(PCLB) model for compressible flows. A method to evaluate the continuum distribution function from the discrete distribution function is indicated. Within the model, the temporal and spatial evolutions are treated with via the operator-splitting scheme. The temporal evolution is calculated analytically and the convection term is solved via a Modified Warming-Beam (MWB) scheme. Within the MWB scheme a suitable switch function is introduced. The new PCLB model works not only for subsonic flows but also for supersonic flows. It is validated and verified via the following four well-known benchmark tests. As an original application, we studied the non-equilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed and consequently the RM instability occurs. It is found that, the effects of deviating from thermodynamic equilibrium at the material interface differ significantly from those at the mechanical interfaces. The coupling effect of molecular motions in different degrees of freedom is much more pronounced at the material interface. The initial perturbation at the material interface enhances this coupling effect. The amplitude of deviations from equilibrium at the shock wave is much higher than those at the rarefaction wave and material interface. Our LB results confirm that the temperature increase first initiates the increase of internal kinetic energy in the degree of freedom corresponding to the direction of temperature gradient, then increases those in other degrees of freedom. By comparing each component of the high-order moments and its value in equilibrium, we can draw qualitative information on the actual distribution function.
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http://arxiv.org/abs/1302.7104
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