Modeling of multispecies gases in non-equilibrium

Since the computational complexity of the DSMC method increases significantly for smaller Knudsen numbers (i.e. in the transition and continuum regions), various particle continuum methods have been introduced in recent years that are able to treat flows in these regions more efficiently. The main advantage of these methods compared to classical CFD methods is the simple coupling with DSMC, since these methods also use particles to describe the flow field. The Bhatnagar-Gross-Krook (BGK) method and the Fokker-Planck (FP) solution algorithm are two prominent examples, both implemented in the open-source code PICLas.

The basic idea of the BGK method is that the Boltzmann collision term is approximated by particle relaxations. The particle distribution function is relaxed with a certain relaxation frequency, which depends on the transport coefficients of the flow, in the direction of a target distribution function. Based on the robust Ellipsoidal Statistical BGK model (ESBGK), our code implements the capabilities to handle gas mixture flows as well as molecules with internal degrees of freedom. For the latter, the rotational and quantized vibrational energies are additionally relaxed. For the implementation, this means that each particle has three different probabilities to relax in the translational, rotational and vibrational degrees of freedom. For gas mixtures, the transport coefficients of the mixture, i.e. the viscosity and the thermal conductivity, must be calculated correctly. This is done either with the help of Wilke's mixing rules or the collision integrals.

The currently implemented models were validated in detail with various supersonic Couette flows and hypersonic flows around a truncated 70° cone. This showed an overall very good agreement with the DSMC method while at the same time significantly reducing the computing time.