| Shock capturing schemes, which are commonly used in compressible flow simulations, introduce excessive amounts of numerical viscosity which smears out small scale flow features. A few low-dissipation methods have been proposed in the recent literature. They are more selective in the sense that they explicitly identify the portion of the numerical flux that is diffusive and damp its effect in 'smooth' regions of the flow. This work employs flux vector splitting methods; the dissipative portions of the Steger-Warming schemes are explicitly identified and various shock detection switches are explored.; For high Reynolds number flows, especially when the energetic scales are close to the Nyquist limits of the grids used, aliasing errors become noticeable. These high frequency oscillations that arise due to the nonlinear nature of the Navier-Stokes equations cause solutions to become unstable. When dissipative methods are used, these errors are suppressed; however when using low-dissipation schemes, they can be prominent and need to be addressed by some other means. In this thesis, we focus on methods that enhance stability by enforcing 'secondary conservation' - the fluxes are constrained in such a way that a conservation law for a secondary, positive quantity is also satisified. In particular, we focus on kinetic energy, and a fully discrete (in time and space) 'kinetic energy consistent' scheme is derived and tested.; Hybrid RAMS-LES methods such as Detached Eddy Simulations are necessary in order to make simulations of high speed flows with attached boundary layers affordable. A popular DES model is based on the Spalart-Allmaras RANS equation; a minor modification to the length scale makes the model behave in a hybrid manner. The S-A model itself was constructed using mostly empirical arguments by the authors. This model is analyzed and its connection to other turbulence models, in particular, the ksgs equation, is explored. A dynamic version of the model is proposed and tested on simulations of decaying isotropic turbulence. |
