Utility of high-order scheme for unsteady flow simulations: Comparison with second-order tool

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 are conducted from two perspectives: (i) the ability of different numerical schemes to accurately simulate turbulence problems using 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, is employed for comparison. This study considers the canonical cases of the two-dimensional Taylor-Green vortex (2D 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 on different meshing types. 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.