Utility of High-Order Scheme for Unsteady Flow Simulations: Comparison with Second-Order Tool

TL;DR

This study demonstrates that high-order numerical schemes significantly improve accuracy, stability, and physical fidelity in unsteady turbulent flow simulations compared to traditional second-order methods, across various mesh types.

Contribution

The paper provides a comprehensive comparison showing high-order schemes outperform second-order methods in accuracy, stability, and physical detail for unsteady turbulence simulations.

Findings

High-order scheme reduces numerical dissipation by nearly 90% compared to second-order.

High-order scheme accurately captures vortex structures and flow instabilities across mesh types.

Results show better agreement with reference data and less grid dependence for high-order methods.

Abstract

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.