Kinetic Models and Gas-Kinetic Schemes for Hybrid Simulation of Partially Rarefied Flows

Abstract

Approaches to predict flow fields that display rarefaction effects incur a cost in computational time and memory considerably higher than methods commonly employed for continuum flows. For this reason, to simulate flow fields where continuum and rarefied regimes coexist, hybrid techniques have been introduced. In the present work analytically defined Gas-Kinetic schemes based on the Shakhov and Rykov models, for monoatomic and diatomic gas flows, 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 rarefied gas flows at high velocities it is necessary to take into account the non-equilibrium among the internal degrees of freedom, the extension of the approach to employ diatomic gas models with rotational relaxation is a mandatory first step towards realistic simulations. Compared to previous works of Xu and co-workers the presented scheme is defined directly on the basis of kinetic models which involve a Prandtl number correction. Moreover, the methods are defined 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 flows. 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 rarefied flows.

Comparison of Discrete Velocity Method and Gas-Kinetic Method for Binary Gas Mixtures

“…The main aim was to obtain sufficient physical detail and accuracy, while achieving computational efficiency, enabling engineering simulations of realistic aerospace applications, including hypersonic, high-altitude flight of hypersonic cruise vehicles and spacecraft. This work builds on previous work by the authors in developing GKS methods for single-species diatomic gas flows [7] and forms a first stepping stone to a GKS method for (chemically-reacting) diatomic gas mixtures.…”

“…As originally introduced, GKS methods were Navier-Stokes solvers, and more recently the GKS approach has been extended by a number of authors, e.g. [7,10,11], with a capability to resolve thermal non-equilibrium and flow rarefaction effects. The strength of the gas-kinetic scheme lies in its capability to include the effect of collisions introducing a multi-scale effect which is missing in more commonly-used Navier-Stokes schemes.…”

“…The computational overhead of the UGKS is however similar to that of a DVM approach and therefore, despite the capabilities of the UGKS methodology, further work in the development of more computationally efficient methods is still an active line of research, e.g. [7,16,17].…”

A gas kinetic scheme for hybrid simulation of partially rarefied flows

“…As previously shown in [40,41], reconstructing the time-dependent distribution functions at the cell-faces, i. e., F 0 | i±1/2 and F 1 | i±1/2 , consistently on the basis of the CE solution of the Rykov model:…”

“…as discussed in [40,41]. Finally, similar to [20,21], since DF M (T ) and D 2 F M (T ) will be sensitive to numerical errors (especially, close to equilibrium regions where they tend to vanish, and to impose that the physical stress inside the shock layer should be larger than the stress in the NS equation), a limiter is needed.…”