Turbulence simulation and multiple scale subgrid models

The problem of modelling turbulence in CFD is due to the wide range of length scales present in a turbulent flow. The physics of these scales is examined, and the need for models of the small scale motions is made clear. A review is given of methods of turbulence modelling. These methods can be divided into two classes: Reynolds averaged Navier-Stokes (RANS) models, and large eddy simulation (LES). The Reproducing Kernel Particle method (RKPM) is then presented and proposed as a class of filters for LES of inhomogeneous turbulent flows. Important properties of the method are discussed, including the effectiveness of the RKPM reproduction as a low-pass filter. The commutation of the filtering operation with differentiation is demonstrated, showing that the commutation error can be made arbitrarily small. A one-dimensional non-linear example problem is solved using a Galerkin method in which a bi-scale constitutive model is used for the subgrid scale terms. The extension of the method to the three-dimensional equations of fluid dynamics is then outlined, where the method is used as a filter in a dynamic subgrid stress model. Emphasis is placed on the multi-scale properties of RKPM, which allow the reproduction of different scales of the solution using the same set of nodal parameters.