Direct numerical simulation of homogeneous shear turbulence subject to a shear periodic boundary with the lattice Boltzmann method

Homogeneous shear turbulence subject to a shear periodic boundary condition is the simplest form of sustainable turbulent flows widely investigated to enhance the understanding of turbulence. Although the lattice Boltzmann method (LBM) has been successfully used to simulate many turbulent flows, direct numerical simulation of homogeneous shear turbulence has yet to be reported. This work proposes a scheme that constructs proper distribution functions on ghost layers to enforce the shear periodic boundary. The validation tests confirm that this scheme preserves the second-order accuracy of LBM. The proposed scheme is then employed to conduct the direct numerical simulation of homogeneous shear turbulence. The results of turbulence statistics show reasonable agreement with the benchmark results, demonstrating the capability of LBM as a tool for turbulent flow studies.