Discrete unified gas kinetic scheme on unstructured meshes

•A discrete unified gas kinetic scheme for the Boltzmann model equation on arbitrary unstructured meshes is presented.•The asymptotic preserving property of the method at the Navier–Stokes limit has been numerically demonstrated.•Multiscale flow problems in a wide range of Knudsen numbers demonstrated the effectiveness of the proposed method.

The recently proposed discrete unified gas kinetic scheme (DUGKS) is a finite volume method for multiscale flow computations with asymptotic preserving property. The solution of the Boltzmann model equation is directly used for the construction of numerical flux and makes the scheme applicable in all flow regimes. In previous applications of the DUGKS, structured meshes have been mostly employed, which may have difficulties for problems with complex geometries. In this paper we will extend the DUGKS to unstructured meshes, with the implementation of computational fluid dynamics techniques to the DUGKS. Several test cases, i.e., the cavity flow ranging from continuum to free molecular regimes, a multiscale flow problem between two connected cavities with large pressure and density variations, high speed flows past multiple cylinders in slip and transitional regimes, and an impulsive start problem are performed. The results are compared with the well-defined Direct Simulation Monte Carlo (DSMC) or Navier–Stokes (NS) solutions in their applicable regimes. The numerical results demonstrate the effectiveness of the proposed DUGKS for the study of multiscale flow problems.