Lattice Boltzmann accelerated direct simulation Monte Carlo for dilute gas flow simulations

Hybrid particle–continuum computational frameworks permit the simulation of gas flows by locally adjusting the resolution to the degree of non-equilibrium displayed by the flow in different regions of space and time. In this work, we present a new scheme that couples the direct simulation Monte Carlo (DSMC) with the lattice Boltzmann (LB) method in the limit of isothermal flows. The former handles strong non-equilibrium effects, as they typically occur in the vicinity of solid boundaries, whereas the latter is in charge of the bulk flow, where non-equilibrium can be dealt with perturbatively, i.e. according to Navier–Stokes hydrodynamics. The proposed concurrent multiscale method is applied to the dilute gas Couette flow, showing major computational gains when compared with the full DSMC scenarios. In addition, it is shown that the coupling with LB in the bulk flow can speed up the DSMC treatment of the Knudsen layer with respect to the full DSMC case. In other words, LB acts as a DSMC accelerator.\u3cbr/\u3e\u3cbr/\u3eThis article is part of the themed issue ‘Multiscale modelling at the physics–chemistry–biology interface’\u3cbr/\u3

DSMC-LBM mapping scheme for rarefied and non-rarefied gas flows

We present the formulation of a kinetic mapping scheme between the Direct Simulation Monte Carlo (DSMC) and the Lattice Boltzmann Method (LBM) which is at the basis of the hybrid model used to couple the two methods in view of efficiently and accurately simulate isothermal flows characterized by variable rarefaction effects. Owing to the kinetic nature of the LBM, the procedure we propose ensures to accurately couple DSMC and LBM at a larger Kn number than usually done in traditional hybrid DSMC—Navier–Stokes equation models. We show the main steps of the mapping algorithm and illustrate details of the implementation. Good agreement is found between the moments of the single particle distribution function as obtained from the mapping scheme and from independent LBM or DSMC simulations at the grid nodes where the coupling is imposed. We also show results on the application of the hybrid scheme based on a simpler mapping scheme for plane Poiseuille flow at finite Kn number. Potential gains in the computational efficiency assured by the application of the coupling scheme are estimated for the same flow

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

\u3cp\u3eWe 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.\u3c/p\u3