High-order gas-kinetic schemes with non-compact and compact reconstruction for implicit large eddy simulation. (30th April 2023) - Zhao, Wenjin
Abstract: 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. Highlights: The HGKS with non-compact and compact reconstruction are developed for ILES. Compact reconstruction shows consistent physical and numerical domains of dependence. The results with compact reconstruction outweigh those of non-compact reconstruction. In the same order, compact reconstruction resolves much smaller turbulent structures. The HGKS with compact reconstruction shows great strength in multi-scale turbulence.