An efficient discrete unified gas-kinetic scheme for compressible turbulence

Abstract

In this paper, we develop an efficient Boltzmann-equation-based mesoscopic approach to simulate three-dimensional (3D) compressible turbulence, using reduced Gauss-Hermite quadrature (GHQ) orders by redefining the second distribution in terms of the total energy in the double distribution function approach. This allows the use of two sets of 3D off-lattice discrete particle velocity models, namely, a 27 discrete velocity model of the seventh-order GHQ accuracy (D3V27A7) combined with a 13 discrete velocity model of the fifth-order GHQ accuracy (D3V13A5), to achieve full consistency with the Navier-Stokes-Fourier system. The source terms in the Boltzmann-Bhatnagar-Gross-Krook system are designed to adjust both the Prandtl number and bulk-to-shear viscosity ratio. Compressible decaying homogeneous isotropic turbulence (DHIT) is simulated at low and moderate turbulent Mach numbers to validate our code. It is observed that the simulation results are in good agreement with those in the existing literatures. Furthermore, the terms in the transport equation of turbulent kinetic energy are analyzed in detail, to illustrate four different transient stages from the initial random flow field to the developed DHIT. It is shown that the transient pressure-dilatation transfer happens rapidly, while the small-scale vortical structures take a longer time to establish physically. Compared to the existing literatures, our approach represents the most efficient mesoscopic scheme for compressible turbulence under the double distribution function formulation.

Effect of thermal fluctuations on spectra and predictability in compressible decaying isotropic turbulence

“…In § 5, we employed the USP method to simulate 3-D compressible decaying isotropic turbulence (CDIT) with an initial solenoidal velocity field, focusing on the influence of molecular thermal fluctuations. In recent years, other researchers have examined this case using alternative numerical approaches, with a specific emphasis on the pressure-dilatation behaviours (Cao et al 2019;Qi et al 2022). For instance, Qi et al (2022) employed the discrete unified gas-kinetic scheme to simulate CDIT at low and moderate M t0 .…”

“…In recent years, other researchers have examined this case using alternative numerical approaches, with a specific emphasis on the pressure-dilatation behaviours (Cao et al 2019;Qi et al 2022). For instance, Qi et al (2022) employed the discrete unified gas-kinetic scheme to simulate CDIT at low and moderate M t0 . Based on the time evolution of solenoidal dissipation and pressure-dilatation terms in the TKE equation, they divided the turbulent decaying process into four stages.…”

“…For instance, Qi et al. (2022) employed the discrete unified gas-kinetic scheme to simulate CDIT at low and moderate . Based on the time evolution of solenoidal dissipation and pressure-dilatation terms in the TKE equation, they divided the turbulent decaying process into four stages.…”

Numerical modeling of two‐phase flows in the presence of dynamic and thermal interactions

“…Reynolds simulations were demonstrated to give more accurate predictions of the diffusion flow fields compared to simulations using one‐ and two‐equation turbulence models. Qi et al 14 developed a mesoscopic approach based on Boltzmann equations in modeling 3D compressible turbulence using the Gauss–Ermitt quadratic formula. It allowed using two sets of 3D out‐of‐lattice discrete particle velocity models to achieve consistency with the Navier–Stokes–Fourier system.…”