Improving the discrete unified gas kinetic scheme for efficient simulation of three-dimensional compressible turbulence

The discrete unified gas-kinetic scheme (DUGKS) is a relatively new, finite-volume formulation of the Boltzmann equation. It has two major advantages over the lattice Boltzmann method (LBM) in that it can simulate compressible (and even non-continuum) flows, and can naturally incorporate a non-uniform mesh. Recently, we have successfully simulated three-dimensional (3D), incompressible turbulent flows including homogeneous isotropic turbulence (Phys. Rev. E., 94, 043304, 2016) and turbulent channel flow (Computers & Fluids, 2017, doi: 10.1016/j.compfluid.2017.03.007). In this talk, we report results on using DUGKS to simulate compressible isotropic homogeneous turbulence. The relevant issues in simulating 3D compressible flows using DUGKS include the choice of the set of discrete velocities, efficient and accurate numerical integration method, numerical limiter to treat local discontinuity, and parallel implementation. We use the standard Maxwellian equilibrium but adjust the heat flux to achieve variable Prandtl numbers. We also introduce a method (L. Mieussems, J. Comp. Phys. 162, 429-466) to restore the physically correct entropy balance. A series of test simulations will be reported for both decaying and forced compressible turbulences.