Abstract
In this paper, we introduce the discrete Maxwellian equilibrium distribution function for incompressible flow and force term into the two-stage third-order Discrete Unified Gas-Kinetic Scheme (DUGKS) for simulating low-speed turbulent flows. The Wall-Adapting Local Eddy-viscosity (WALE) and Vreman sub-grid models for Large-Eddy Simulations (LES) of turbulent flows are coupled within the present framework. Meanwhile, the implicit LES are also presented to verify the effect of LES models. A parallel implementation strategy for the present framework is developed, and three canonical wall-bounded turbulent flow cases are investigated, including the fully developed turbulent channel flow at a friction Reynolds number (Re) about 180, the turbulent plane Couette flow at a friction Re number about 93 and lid-driven cubical cavity flow at a Re number of 12000. The turbulence statistics, including mean velocity, the r.m.s. fluctuations velocity, Reynolds stress, etc. are computed by the present approach. Their predictions match precisely with each other, and they are both in reasonable agreement with the benchmark data of DNS. Especially, the predicted flow physics of three-dimensional lid-driven cavity flow are consistent with the description from abundant literature. The present numerical results verify that the present two-stage third-order DUGKS-based LES method is capable for simulating inhomogeneous wall-bounded turbulent flows and getting reliable results with relatively coarse grids.
Highlights
Turbulent flow is one of the most common and complicated problems in fluid dynamics
4 Summary In the present work, both the incompressible discrete Maxwellian equilibrium distribution function and the external force are introduced into the two-stage third-order Discrete Unified GasKinetic Scheme (DUGKS) for simulating low-speed turbulent flows
The turbulence statistics, including mean velocity, the r.m.s. fluctuations velocity, Reynolds stress, et al, are compared with the results of direct numerical simulation (DNS) and largeeddy simulation (LES) given in the previous literature
Summary
Turbulent flow is one of the most common and complicated problems in fluid dynamics. In the study of turbulent flows, they are usually formulated in terms of the Navier-Stokes (NS) equations for the macroscopic variables that are functions of position and time. The RANS method solves the time-averaged NS equations and the effect of the unsteady turbulent motions on the mean flow-field is approximated by turbulence models. Another alternative method, namely, the largeeddy simulation (LES) method [5,6,7] has attracted a vast amount of attention of the engineering and scientific communities. The fully developed turbulent channel flow with a friction Reynolds number Reτ = 180, the turbulent plane Couette flow with a friction Reynolds number Reτ = 93 and the three-dimensional lid-driven cubical cavity flow with Reynolds number Re = 12000 are investigated to validate the capability and accuracy of the present high-order DUGKS (with D3Q19) for turbulent simulations.
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