Comparison of the LBE and DUGKS methods for DNS of decaying homogeneous isotropic turbulence

TL;DR

This paper compares the LBE and DUGKS methods for DNS of decaying homogeneous isotropic turbulence, highlighting their accuracy, efficiency, stability, and suitability for complex flow simulations.

Contribution

It provides a detailed comparison of LBE and DUGKS for turbulence DNS, emphasizing DUGKS's advantages in stability and nonuniform mesh adaptability.

Findings

LBE and DUGKS have similar accuracy for well-resolved flows.

LBE is less dissipative and slightly more efficient.

DUGKS offers better numerical stability and mesh flexibility.

Abstract

The main objective of this work is to perform a detailed comparison of the lattice Boltzmann equation (LBE) and the recently developed discrete unified gas-kinetic scheme (DUGKS) methods for direct numerical simulation (DNS) of the decaying homogeneous isotropic turbulence (DHIT) in a periodic box. The flow fields and key statistical quantities computed by both methods are compared with those from pseudo-spectral (PS) method. The results show that the LBE and DUGKS have almost the same accuracy when the flow field is well-resolved, and that the LBE is less dissipative and is slightly more efficient than the DUGKS, but the latter has a superior numerical stability, particularly for high Reynolds number flows. Therefore, the DUGKS method can be viewed as a viable tool for DNS of turbulent flows. It should be emphasized that the main advantage of the DUGKS when compared with the LBE method is its feasibility in adopting nonuniform meshes, which is critical for wall-bounded turbulent flows. The present work provides a basis for further applications of DUGKS in studying the physics of the turbulent flows.