  The objective of this work is to investigate the utility and effectiveness of
the high-order scheme for simulating unsteady turbulent flows. To achieve it,
the studies were conducted from two perspectives: (i) the ability of different
numerical schemes for turbulence problems under the same set of meshes; and
(ii) the accuracy and stability of higher-order schemes for solving turbulence
statistics for different mesh types (hexahedral, tetrahedral, and polyhedral
cells). The simulations employ the third-order scheme for spatial
discretization of the governing equations, while a widely-used second-order
solver, namely pisoFoam, was employed for comparison. This study considers the
canonical cases of the Taylor-Green vortex (TGV) problem at Re=100, 1600 and
flow past a sphere at Re=10000 to address the aforementioned two key issues.
For the TGV case, the high-order model significantly improves the numerical
accuracy with convergence rates and reduces the numerical dissipation of nearly
1/10 of pisoFoam. In the latter case, the high-order scheme with large-eddy
simulation (LES) accurately predicts the vortex structures and the flow
instability, regardless of grid type. However, pisoFoam is found to be
sensitive to mesh types, which results in numerous non-physical structures in
the flow field due to numerical noise rather than flow physics, particularly
for tetrahedral cells. Furthermore, for the typical low- and high-order flow
statistics, the numerical results predicted by the present model show better
agreement with the reference data and have less dependence on the type of grids
compared with the conventional scheme. In addition, the obtained energy
spectrum by the high-order solver accurately captures the Kelvin-Helmholtz
(K-H) instability and the vortex shedding frequency, while these important
features are less pronounced by the traditional low-order model.
