No abstract

From the aspect of the multiscale nature of the rarefied flow, a simple hybrid strategy is proposed in this paper in the process of flux reconstruction to couple the improved discrete velocity method (IDVM) and the G13-based gas kinetic flux solver (G13-GKFS). The flow field is divided into the IDVM area and G13 area according to the kinetic nature of the Knudsen layer and the criteria of the local Knudsen number. By eliminating the storage of the distribution functions and evolution of the microscopic equation, the reduction of the computational effort and memory storage can be achieved without sacrificing the accuracy in the whole flow field. Four different non-equilibrium cases from the micro-flow to the supersonic flow are tested by the present hybrid method. The results show good performance and better efficiency. Furthermore, under the framework of the present hybrid method, different non-equilibrium distribution functions with higher-order moments could be employed and coupled easily.

In this work, the explicit formulations of the Grad's distribution function for 13 moments (G13)-based gas kinetic flux solver (GKFS) for simulation of flows from the continuum regime to the rarefied regime are presented. The present solver retains the framework of GKFS, and it combines some good features of the discrete velocity method (DVM) and moment method. In the G13-GKFS, the macroscopic governing equations are first discretized by the finite volume method, and the numerical fluxes are evaluated by the local solution of the Boltzmann equation. To reconstruct the local solution of the Boltzmann equation, the initial distribution function is reconstructed by the Grad's distribution function for 13 moments, which enables the G13-GKFS to simulate flows in the rarefied regime. Thanks to this reconstruction, the evolution of distribution function is avoided, and the numerical fluxes can be expressed by explicit formulations. Therefore, the computational efficiency of G13-GKFS is much higher than that of DVM. The accuracy and computational efficiency of the present solver in explicit form are examined by several numerical examples. Numerical results show that the present solver can predict accurate results for flows in the continuum regime and reasonable results for flows in the rarefied regime. More importantly, the central processing unit time of the present solver is about 1% of that of DVM for two-dimensional (2D) microflow problems, and it is about twice of the conventional Navier–Stokes solver for 2D continuum flows.

No abstract

No abstract