DUGKS simulations of three-dimensional Taylor–Green vortex flow and turbulent channel flow

Abstract

The discrete unified gas-kinetic scheme (DUGKS) is a relatively new, finite-volume formulation of the Boltzmann equation. It has several advantages over the lattice Boltzmann method (LBM) in that it can naturally incorporate multiscale physical processes and non-uniform lattice mesh. With the goal of simulating a variety of turbulent flows, we investigate two aspects of DUGKS. First, we explore a parallel implementation strategy of DUGKS using domain decomposition and MPI (Message Passing Interface), and demonstrate the scalability of the parallel DUGKS code. We validate the resulting parallel code using the 3D Taylor-green vortex flow where small eddies are generated over time from large eddies. The DUGKS results are compared to short-time analytical solution as well as to those from LBM and pseudo-spectral method. The second-order accuracy of DUGKS is confirmed by using the highest-resulotion DUGKS flow as the benchmark. Second, we consider how to incorporate solid walls and non-uniform mesh in DUGKS for three-dimensional flows, by simulating a turbulent channel flow. The statistics of the simulated turbulent channel flow are compared to those based on LBM and spectral methods. It is found that the DUGKS results, even with a coarse non-uniform mesh, are overall better than the LBM results when compared to the spectral benchmark data.