FLOW: Spectral-element simulations of turbulent separation

Fluid flows are complicated and nonlinear, which calls for accurate numerical treatment. Traditionally, this has been has been achieved by spectral methods. Apart from accuracy, these methods provide little geometrical flexibility which severely limits their practical use. Spectral-element methods (SEM), on the other hand, are able to combine the high accuracy of traditional spectral methods with the geometrical flexibility of finite element methods (FEM). In this project, the spectral-element method is employed in conjunction with turbulence simulations, a combination which has not yet been fully exploited.

The first step focused on the numerical properties of the SEM. In particular, the previously known numerical instabilities arising in turbulence simulations were analysed. It was concluded that by employing proper stabilization tools, SEM is well-suited for simulations of turbulence, due to its combination of accuracy, flexibility and not least due to its excellent scaling properties. As a proof of concept, a highly resolved simulation was performed of a turbulent and fully three-dimensional diffuser flow at Re = 10000 (see figure below). Up to 32 768 parallel processors were used to compute the complex and chaotic turbulent flow experiencing separation, which has given a far more detailed picture than previous computations and experiments have been able to deliver. The mean flow properties were shown to compare very well to experimental data. Currently, time resolved data from this simulation is under investigation. Typical structures and dominant frequencies involved in the separation process are identified. This involves spectral analysis of time signal probes and decomposition of the flow into orthogonal eigenfunctions known as Proper Orthogonal Decomposition (POD). In a side project, POD has been compared to another decomposition called Koopman mode analysis. For this purpose, a so-called minimal flow unit has been studied, which enables the study of real turbulence in a simplified way, thereby enhancing the understanding of wall-bounded turbulence.

DNS data.