The Effects of Numerical Scheme Resolvability for Large-Eddy Simulations

The dissertation addresses the formulation of Large-Eddy Simulations (LES) with direct consideration of a base finite difference scheme, and with the intent of reducing numerical error influences on the closure model and ultimately the solution. As such, spectral characteristics of the explicitly-defined LES filter are considered with respect to the discretization method’s spectral accuracy (i.e., resolvability). Analysis and development of discrete filtering stencils is undertaken, placing emphasis on the ability to specify desired scale-separation (e.g., cut-off wavenumber and scale-discriminant attenuation) relative to the computational grid. Assessment of the LES procedure is preceded by the establishment of a suitable base scheme, comprised of high-order discretizations and the addition of stabilization presented in a filter-based artificial dissipation form. Subsequent robustness and preservation of the overall solution accuracy is achieved by tuning the dissipation according to the dispersion characteristics of the underlying numerical method and seeking to deliberately remove the effects of discretization error. Extension to LES is then established by properly defining the explicit filter in relation to these numerical characteristics. Effectiveness of the procedure is evaluated by means of a priori and a posteriori inspection of turbulence calculations for the Burgers and Navier-Stokes equations, wherein the impacts of discretization and filter cut-off are assessed in light of scale-similarity and “perfect” modeling (i.e., a DNS-based closure). Results demonstrate the benefits of employing mutually tuned high-order discretizations and filters in the limit of the idealized “perfect” model, yet highlight the likely possibility of modeling error overshadowing such gains when actual closures, such as scale-similarity models, are used. In an attempt to enhance the scale-similarity models considered herein, the filter-based artificial dissipation is employed in order to enforce the prescribed LES field, and is shown to reduce overall model error. Meanwhile, its use is shown to be beneficial even in the presence of “perfect” modeling, wherein the dissipation can be tuned to specifically target discretization errors