A discrete unified gas kinetic scheme on unstructured grids for viscid compressible flows and its parallel algorithm

In this paper, we present a discrete unified gas kinetic scheme (DUGKS) on unstructured grids for high-speed viscid compressible flows on the basis of double distribution function (the density and the total energy distribution functions) Boltzmann-BGK equations. In the DUGKS, the discrete equilibrium distribution functions are constructed based on a D2Q17 circular function. In order to accelerate the simulation, we also illustrate a corresponding parallel algorithm. The DUGKS is validated by two benchmark problems, i.e., flows around the NACA0012 airfoil and flows past a circular cylinder with the Mach numbers range from 0.5 to 2.5. Good agreements with the referenced results are observed from the numerical results. The results of parallel test indicate that the DUGKS is highly parallel scalable, in which the parallel efficiency achieves $93.88\mathrm{\%}$ on a supercomputer using up to $4800$ processors. The proposed method can be utilized for high-resolution numerical simulation of complex and high Mach number flows.