A gas kinetic scheme for hybrid simulation of partially rarefied flows

Abstract

Approaches to predict §ow ¦elds that display rarefaction e¨ects incur a cost in computational time and memory considerably higher than methods commonly employed for continuum §ows. For this reason, to simulate §ow ¦elds where continuum and rare¦ed regimes coexist, hybrid techniques have been introduced. In the present work, analytically de¦ned gas-kinetic schemes based on the Shakhov and Rykov models for monoatomic and diatomic gas §ows, respectively, are proposed and evaluated with the aim to be used in the context of hybrid simulations. This should reduce the region where more expensive methods are needed by extending the validity of the continuum formulation. Moreover, since for high-speed rare¦ed gas §ows it is necessary to take into account the nonequilibrium among the internal degrees of freedom, the extension of the approach to employ diatomic gas models including rotational relaxation process is a mandatory ¦rst step towards realistic simulations. Compared to previous works of Xu and coworkers, the presented scheme is de¦ned directly on the basis of kinetic models which involve a Prandtl number correction. Moreover, the methods are de¦ned fully analytically instead of making use of Taylor expansion for the evaluation of the required derivatives. The scheme has been tested for various test cases and Mach numbers proving to produce reliable predictions in agreement with other approaches for near-continuum §ows. Finally, the performance of the scheme, in terms of memory and computational time, compared to discrete velocity methods makes it a compelling alternative in place of more complex methods for hybrid simulations of weakly rare¦ed §ows.