dugksFoam : An open source OpenFOAM solver for the Boltzmann model equation

A deterministic Boltzmann model equation solver called dugksFoam has been developed in the framework of the open source CFD toolbox OpenFOAM. The solver adopts the discrete unified gas kinetic scheme (Guo et al., 2015) with the Shakhov collision model. It has been validated by simulating several test cases covering different flow regimes including the one dimensional shock tube problem, a two dimensional thermal induced flow and the three dimensional lid-driven cavity flow. The solver features a parallel computing ability based on the velocity space decomposition, which is different from the physical space decomposition based approach provided by the OpenFOAM framework. The two decomposition approaches have been compared in both two and three dimensional cases. The parallel performance improves significantly using the newly implemented approach. A speed up by two orders of magnitudes has been observed using 256 cores on a small cluster. Program summary Program Title: dugksFoam Program Files doi:http://dx.doi.org/10.17632/zwn7t9cf5w.1 Licensing provisions: The MIT License Programming language: C++ External routines/libraries: OpenFOAM (http://www.openfoam.org) Nature of problem: Solving the Boltzmann equation with Shakhov model explicitly. Solution method: Discrete unified gas kinetic scheme (DUGKS) Restrictions: Symmetric boundary condition can only be applied at walls parallel to axis directions

Computable model on the collision integral of Boltzmann equation and application to rarefied aerodynamics

Due to its complexity in dealing with the collisional integral term of the Boltzmann equation and computational costs associated with multi-dimensional problems, deterministic methods are still restricted to simple flow such as one-dimensional linear flow. However, the recently emerged fast spectrum method has achieved breakthroughs in computational efficiency and accuracy, which can enable simulations for more realistic three-dimensional non-linear flows. In comparison with the dominant direct simulation Monte Carlo method, the deterministic method has advantages especially in simulating lowspeed flows where statistical variations prevail. Here, we review the development of fast spectrum method and discuss its applications for practical flow simulations. In particular, extended Boltzmann model is required for polyatomic and dense gases where the Boltzmann equation may not be valid. We present the applications of extended Boltzmann model for polyatomic gases in predicting spectra of both spontaneous and coherent Rayleigh-Brillouin Scattering, and in simulating space vehicle reentries with a broad range of Kn. Finally, we discuss the gas-kinetic unified algorithm (GKUA) of computable model Boltzmann equation and applications to the hypersonic aerodynamics of space reentry covering various flow regimes