Simulation of three-dimensional compressible decaying isotropic turbulence using a redesigned discrete unified gas kinetic scheme

In this paper, a new mesoscopic approach with both the adjustable Prandtl number and the ratio of bulk to shear viscosity has been developed to simulate three-dimensional compressible decaying homogeneous isotropic turbulence under the framework of discrete unified gas kinetic scheme (DUGKS). In the new approach, two reduced model Boltzmann equations with newly designed source terms are solved. In the continuum limit, the Navier-Stokes-Fourier system can be recovered by applying the Chapman-Enskog analysis. A three-dimensional DUGKS code has been developed, incorporating the fifth-order weighted essentially non-oscillatory scheme to better reconstruct the particle distribution functions at the cell interfaces. In addition, a new lattice velocity model with 77 discrete particle velocities is applied to ensure that the accuracy of the Gauss-Hermite quadrature is up to the ninth-order, and as such, the heat flux can be accurately evaluated. To validate our code, we simulate two cases with different initial turbulent Mach numbers and Taylor microscale Reynolds numbers. The simulation results converge with the increase in resolution and agree well with the results from the literature. As a direct application of our DUGKS, we briefly study the influence of bulk viscosity on turbulence statistics and flow structures. Our results show that the DUGKS is a reliable tool for simulating compressible decaying isotropic turbulence at low and moderate turbulent Mach numbers. More parametric studies are needed in the future to further explore the full capabilities of this specific mesoscopic method.