High-order methods for steady, unsteady and transitional flow over a cylinder

Abstract

In this thesis, the flow around a cylinder is chosen as a test case for higher-order numerical reconstruction techniques. No direct comparison of these higher-order methods has been carried out for this particular test case. Especially for low Mach number, incompressible flows with Implicit Large Eddy Simulation method. The cylinder test case is both a proven test case in literature, as well as a test case that can be scaled up in terms of flow speed with other parameters remaining unchanged. The scaling of flow speed around the cylinder allows ease of flow regime change. Thus the flow was modelled in this thesis from laminar flow to turbulent flow, going through a transitional regime in between. The simulations were set up such that numerical reconstruction methods could be directly compared to one another at the range of flow speeds, and subsequently in both two-dimensional and three-dimensional flows. The numerical reconstruction methods for the ILES cases ranged from first order reconstruction through to higher-order methods as high as ninth-order (in the weighted essentially non-oscillatory scheme). With the speed of computation for the twodimensional simulations, it was possible to test all of these schemes directly with one another. However, three-dimensional simulations require a significantly greater CPU run-time. Therefore, based on the results of the two-dimensional simulations, a group of the higher-order methods were chosen for continuing analysis in the three-dimensional simulations. In the laminar flow regime, all the numerical schemes agreed very well with literature data. As the flow speed increased, discrepancies started to appear in the results, to varying degrees based on the flow speed, the numerical scheme used, and the dimensionality of the flow. An analysis of the results showed that two-dimensional simulations were suitable up to Reynolds 300. From this flow speed onwards, three-dimensional simulations are deemed necessary. At lower Reynolds number flows the two-dimensional simulations provided good predictions of the flow. At the higher Reynolds numbers, the 3D simulations outperformed the 2D simulations. Specific numerical reconstruction schemes were found to perform better at certain aspects of the flow. For example, the coefficients around the cylinder or the velocities in the wake varied based solely on the numerical scheme used. Finally, during the course of the post-processing of the simulations, a spectral analysis was carried out. The flow field was analysed at specific points in the wake (ranging from near, medium and far wake). The spectral analysis proved suitable for examining the fluctuations in the wake of the cylinder, showing the redistribution of energy in the wake towards higher frequencies. In addition, the wake showed increased power densities for the fluctuations as the flow moved away from the cylinder, before then decreasing again as dissipation into the surrounding flow occurred.