Higher-Order Methods for Compressible Turbulent Flows Using Entropy Variables

A higher-order space-time discontinuous Galerkin method is presented for the simulation of compressible ows. The eect of the discrete formulation on the nonlinear stability of the scheme is assessed through numerical simulations. For marginally resolved turbulent simulations at moderate Reynolds number, polynomial dealiasing is shown to be necessary in order to maintain stability at high order. With increasing Reynolds number, the formulation using conservative variables is shown to be unstable at high order even when using polynomial dealiasing. Using an entropy variable formulation consistent with established entropy stability theory ensures nonlinear stability at high and innite Reynolds number. The eect of the numerical ux for underresolved turbulent simulations is investigated. A low-Mach modied ux term is presented to suppress the biased pressure-dilatation term seen with other upwind numerical uxes. Subgrid-scale modeling eects of dierent numerical ux functions on the kinetic energy spectrum are examined in the limit of innite Reynolds number.