Filtering Techniques for Turbulent Flow Simulation

the long version

This monograph presents a theoretical analysis of filtering techniques for turbulent flow simulation. Both space and space-time filtering approaches are considered. The basic characteristics of these techniques are described and contrasted with conventional approaches of turbulence modeling. The mathematical nature of the approximation of the nonlinear terms in the filtered equations of motion is investigated, and it is shown that those approximations possess an asymptotic nature. The filtering effect in Fourier space is investigated, and a three-scale filtering approach is also presented. Both the space-time and three-scale filtering approaches are numerously tested in the context of random Burgers' flow. Some familiarity with fluid dynamics, turbulence, numerical methods for the solution of partial differential equations, asymptotic expansions and Fourier transforms is expected from the reader. The monograph is intended for researchers and graduate students interested in turbulent flow simulation, and it will be primarily used as a reference.