High-order gas-kinetic schemes with non-compact and compact reconstruction for implicit large eddy simulation

High-order gas-kinetic scheme (HGKS) with 5th-order non-compact reconstruction has been well implemented for implicit large eddy simulation (ILES) in nearly incompressible turbulent channel flows. In this study, the HGKS with higher-order non-compact reconstruction and compact reconstruction will be validated in turbulence simulation. For higher-order non-compact reconstruction, 7th-order reconstruction in both normal and tangential directions are implemented. On the other hand, the compact HGKS with 5th-order compact reconstruction in normal direction is developed. Current work aims to show the benefits of high-order non-compact reconstruction and compact reconstruction for ILES. The accuracy of HGKS is verified by numerical simulation of three-dimensional advection of density perturbation. For the non-compact 7th-order scheme, 16 Gaussian points are required on the cell-interface to preserve the order of accuracy. Then, HGKS with non-compact and compact reconstruction is used in the three-dimensional Taylor-Green vortex (TGV) problem and turbulent channel flows. Accurate ILES solutions have been obtained from HGKS. In terms of the physical modeling underlying the numerical algorithms, the compact reconstruction has the consistent physical and numerical domains of dependence without employing additional information from cells which have no any direct physical connection with the targeted cell. The compact GKS shows a favorable performance for turbulence simulation in resolving the multi-scale structures.

Automated summary

This study validates the effectiveness of high-order non-compact and compact reconstruction in turbulence simulation using the high-order gas-kinetic scheme (HGKS). The accuracy of HGKS is confirmed through numerical simulations of three-dimensional density perturbation advection. Both non-compact 7th-order and compact 5th-order reconstruction schemes are shown to provide accurate solutions for turbulent flows.