KINETIC MODELS WITH ROTATIONAL DEGREES OF FREEDOM FOR HYBRID METHODS

Flow fields where localised rarefaction phenomena are relevant, occur in various engineering applications such as supersonic/hypersonic and micro-flows. The methods that are commonly employed to simulate rarefied flows, Direct Simulation Monte Carlo (DSMC) and discrete-velocity methods for kinetic Boltzmann equations, require higher computational cost than continuum methods. This has motivated the development of hybrid techniques which restrict the use of the expensive non-continuum approaches to regions where significant non-equilibrium effects occur. In the present work, a computational framework which includes methods for the kinetic Boltzmann equations, and has been successfully employed for different monoatomic cases [1], is improved and used to predict rarefied high speed flows. A novel aspect of the method is the parallelisation of the computational load. While in the literature, a split of either the physical space or the phase space among the processors is employed, the current framework allows both levels of parallelisation at the same time. For rarefied gas flows at high velocities it is necessary to take into account the excitation of the internal degrees of freedom; these flows are characterised by large non-equilibrium regions with multiple temperatures (translational, rotational and vibrational temperature). For this reason, the framework has been recently developed with the addition of kinetic models for diatomic gases, presented in [2, 3], which are based on the assumption that the fraction of collisions involving the excitation of the rotational degrees of freedom is a given constant or is a function of the flow temperatures. As a first stage the rotational degrees of freedom has been taken into account for the cases of normal shocks, and a flat plate. Furthermore, kinetic models for diatomic gases are not yet established in the context of the hybrid approaches and the coupling between a diatomic kinetic model and a Navier-Stokes solver still presents a number of challenging tasks. Among them, the evaluation of a different way of coupling in order to increase the efficency of the hybrid approach is also objective of the present work. Indeed, to reduce the computational cost of hybrid simulations by reducing the region where the expensive method is needed, a Gas-Kinetic Scheme based on the Rykov model is proposed.