High-order Gas-kinetic Schemes with Non-compact and Compact Reconstruction for Implicit Large Eddy Simulation

TL;DR

This paper evaluates high-order gas-kinetic schemes with non-compact and compact reconstructions for improved implicit large eddy simulation of turbulence, demonstrating their accuracy and efficiency in complex flow problems.

Contribution

It introduces higher-order non-compact and compact reconstructions in HGKS and validates their effectiveness for turbulence simulation, enhancing previous 5th-order implementations.

Findings

7th-order non-compact scheme requires 16 Gaussian points for accuracy

Both schemes accurately simulate turbulence in TGV and channel flows

Compact reconstruction preserves physical domain of dependence without extra cell info

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 normal reconstruction and tangential reconstruction are implemented. In terms of compact reconstruction, 5th-order normal reconstruction is adopted. 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.