Local variational multi-scale method for turbulence simulation
Collis, S. Scott
Doctor of Philosophy
Accurate and efficient turbulence simulation in complex geometries is a formidable challenge. Traditional methods are often limited by low accuracy and/or restrictions to simple geometries. We explore the merger of Discontinuous Galerkin (DG) with Variational Multi-Scale (VMS), termed Local VMS (LVMS), to overcome these limitations. DG spatial discretizations support arbitrarily high-order accuracy on unstructured grids amenable for complex geometries. Furthermore, high-order hierarchical representation within DG provides a natural framework for a priori scale separation crucial for VMS implementation, a promising approach to LES. We study the efficacy of LVMS for turbulence simulation using a fully-developed turbulent channel flow. First, a detailed spatial resolution study is undertaken to record the effects of the DG discretization on turbulence statistics. Here, the local hp-refinement capabilities of DG are exploited to obtain reliable low-order statistics efficiently. Then, we explore the effects of enforcing Dirichlet boundary conditions through numerical fluxes in DG that allows solution jumps (slip) at the channel walls. This feature of DG is effective in mitigating the high near-wall resolution requirements in the wall-normal direction that enables reasonable drag predictions even with moderate resolutions. However, using coarse resolutions leads to significant slip at the channel walls that affect drag predictions. Here, modifying the numerical viscous flux to regulate this slip through a penalty is found to improve drag predictions. Thus, demonstrating the potential of the numerical viscous flux to act as a rudimentary wall-model. Next, for reduced-order modeling, we evaluate the merits of Spectral Filtering (SF) and Polynomial Dealiasing (PD) for improving non-linear stability. While both approaches are successful, PD is found to be better suited for Sub-Grid Scales (SGS) modeling. Finally, a VMS model is implemented to account for SGS effects. Results in good agreement with reference are obtained demonstrating the effectiveness of LVMS for wall-bounded turbulence. The locality of DG provides the flexibility to specify model parameters individually on each element. This unique feature of LVMS can be exploited for surgical modeling in a wide range of turbulent flows.