Design and Application of Discrete Explicit Filters

In the context of Large Eddy Simulation (LES) of turbulent flows, there is a current need to compare and evaluate different proposed subfilter-scale models in order to assess their suitability for various applications. In order to carefully compare subfilter-scale models and compare LES predictions to Direct Numerical Simulation (DNS) results (the latter would be helpful in the comparison and validation of models), there is a real need for a "grid-independent" LES capability and explicit filtering methods offer one means by which this may be achieved. Advantages of explicit filtering are that it provides a means for eliminating aliasing errors, allows for the direct control of commutation errors, and most importantly allows a decoupling between the mesh spacing and the filter width which is the primary reason why there are difficulties in comparing LES solutions obtained on different grids. This book considers the design and assessment of discrete explicit filters and their application to isotropic turbulence prediction. This book was submitted for the degree of Masters of Applied Science at the Graduate Department of Aerospace Engineering at the University of Toronto.