Hybrid lattice Boltzmann-direct simulation Monte Carlo approach for flows in three-dimensional geometries

We present the results of a comparative study performed with three numerical methods applied to a flow in a three-dimensional geometry characterized by weak compressibility and large rarefaction effects. The employed methods, all based on the kinetic theory of gases, are the Lattice Boltzmann Method (LBM) in a regularized formulation, the Direct Simulation Monte Carlo (DSMC) approach and a hybrid method coupling the LBM and the DSMC recently developed by Di Staso et al., in this contribution extended to the case of simulations involving many particles and three-dimensional geometries. Owing to the common kinetic nature shared by the employed methods and to their implementation in a single code infrastructure, a detailed comparison of the results can be performed on a quantitative ground. The numerical results permit to determine, for the studied flow problem, the range of applicability in terms of a geometry-based Knudsen number for the present LBM formulation. The need to employ the hybrid method is justified by the very large computational cost of the DSMC simulation. Limitations of the current hybrid method formulation in treating thermal and large compressibility effects are underlined and possible strategies to overcome them are delineated. Finally, good scalability properties of the parallel algorithms, as well as the large computational cost reduction guaranteed by the hybrid method, while providing an accurate solution, are demonstrated.