High-order Gas Kinetic Schemes for Large Eddy Simulation

The gas-kinetic scheme (GKS) is a finite volume method based on the Bhatnagar--Gross--Krook (BGK) model. In recent years, equipped with two-stage fourth-order (S2O4) temporal discretization and weighted essentially non-oscillatory (WENO) reconstruction, high-order GKS (HGKS) has been developed with high temporal and spatial resolutions and applied in direct numerical simulation (DNS) for turbulent flows with parallel computation. In this thesis, we will apply the HGKS in explicit large eddy simulation (hereafter referred to simply as “eLES”) and implicit large eddy simulation (iLES). At the same time, the properties of the methods will be evaluated for turbulent flow simulation. The compact GKS has been developed in recent years and exhibited superiority compared with the non-compact schemes for compressible flow simulation. In this thesis, we will test the HGKS with compact reconstruction for turbulence simulation and study its feasibility and superiority in iLES.

Firstly, the quantitative comparisons between iLES and eLES are conducted by HGKS. ILES and eLES will be used in unbounded turbulence, in which the compressible Taylor-Green vortex problem will be studied. With the reference of DNS, iLES performs better than eLES on the same coarse grids. Based on the turbulent kinetic energy, the dissipation in iLES and eLES are evaluated. It seems that the numerical dissipation in iLES can be treated as the built-in SGS modeling dissipation, which accounts for the reasonable performance from iLES.

Secondly, we employ eLES and iLES in HGKS for wall-bounded turbulence, and study turbulent channel flows. The main objective is to further compare the performance of iLES and eLES. From the simulation results, iLES is generally superior to eLES in predicting several important flow properties, including the mean velocity profiles, Reynolds stress, and Q-criterion iso-surfaces. This superior performance of iLES indicates that the numerical dissipation of the high-order scheme is enough to replace the sub-grid dissipation needed in large eddy simulation. If the explicit LES model is adopted, the overall dissipation will be in excess of the required one. The overall satisfactory results show that the high-order GKS can provide appropriate numerical dissipation and is suitable for iLES.

Finally, the HGKS with higher-order non-compact reconstruction and compact reconstruction are developed for turbulence simulation. This work aims to show the performance of higher-order non-compact reconstruction and compact reconstruction for iLES. We apply the schemes to three-dimensional Taylor-Green vortex problem and turbulent channel flows. The turbulent statistics show that both higher-order non-compact reconstruction and compact reconstruction indeed improve the numerical accuracy of iLES. The compact reconstruction has compact stencils. Considering the multi-scale characteristics of turbulent flows, the compact reconstruction has a consistent physical and numerical domains of dependence without employing additional information from cells which have no any physical connection with the targeted cell in the non-compact reconstruction. The compact GKS has a reliable physical basis for turbulence simulation in resolving the multi-scale structure effectively.

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