THESIS
2022
1 online resource (xvii, 91 pages) : illustrations (some color)
Abstract
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 sc...[
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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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