The Local Variational Multiscale Method For Turbulence Simulation

Accurate and efficient turbulence simulation in complex geometries is a formidable chal-lenge. Traditional methods are often limited by low accuracy and/or restrictions to simplegeometries. We explore the merger of Discontinuous Galerkin (DG) spatial discretizationswith Variational Multi-Scale (VMS) modeling, termed Local VMS (LVMS), to overcomethese limitations. DG spatial discretizations support arbitrarily high-order accuracy on un-structured grids amenable for complex geometries. Furthermore, high-order, hierarchicalrepresentation within DG provides a natural framework fora prioriscale separation crucialfor VMS implementation. We show that the combined benefits of DG and VMS within theLVMS method leads to promising new approach to LES for use in complex geometries. The efficacy of LVMS for turbulence simulation is assessed by application to fully-developed turbulent channelflow. First, a detailed spatial resolution study is undertakento record the effects of the DG discretization on turbulence statistics. Here, the localhp refinement capabilites of DG are exploited to obtain reliable low-order statistics effi-ciently. Likewise, resolution guidelines for simulating wall-bounded turbulence using DGare established. We also explore the influence of enforcing Dirichlet boundary conditionsindirectly through numericalfluxes in DG which allows the solution to jump (slip) at thechannel walls. These jumps are effective in simulating the influence of the wall commen-surate with the local resolution and this feature of DG is effective in mitigating near-wallresolution requirements. In particular, we show that by locally modifying the numericalviscousflux used at the wall, we are able to regulate the near-wall slip through a penaltythat leads to improved shear-stress predictions. This work, demonstrates the potential ofthe numerical viscousflux to act as a numerically consistent wall-model and this successwarrents future research. As in any high-order numerical method some mechanism is required to control aliasingeffects due to nonlinear interactions and to ensure nonlinear stability of the method. Inthis context, we evaluate the merits of two approaches to de-aliasing -- spectralfilteringand polynomial dealiasing. While both approaches are successful, polynomial-dealiasingis found to be better suited for use in large-eddy simulation. Finally, results using LVMSare reported and show good agreement with reference direct numerical simulation therebydemonstrating the effectiveness of LVMS for wall-bounded turbulence. This success pavesthe way for future applications of LVMS to more complex turbulentflows. 3.