Turbulence simulation and multiple scale subgrid models

Abstract

The problem of modelling turbulence in CFD is due to the wide range of length scales present in a turbulent¯ow. 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 ®lters for LES of inhomogeneous turbulent ows. Important properties of the method are discussed, including the effectiveness of the RKPM reproduction as a low-pass ®lter. The commutation of the ®ltering operation with differentiation is demonstrated, showing that the commutation error can be made arbitrarily small. A onedimensional 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¯uid dynamics is then outlined, where the method is used as a ®lter 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.

Adaptive Finite Element Methods for Incompressible Fluid Flow

“…The quantity N(u) may represent the mean value over [0,T) of the drag or lift on a body with boundary r l immersed in a flow, depending on the choice of'l/J with for example 'l/JI = ' l/J2 = 0, ' l/J3 = 1 to give the lift if the X3 is oriented vertically (and U3~0). Instead of directly using (29), we may use the following alternative expression with the idea of increasing the precision, see [7],…”

“…For an overvi ew of finite element methods for the incompressible Navier-Stokes equations including references , we refer to [25]. For a survey of turbulence mod eling we refer to [6], [29] and [8] and references th erein.…”

High-Resolution Finite Volume Methods on Unstructured Grids for Turbulence and Aeroacoustics

“…In particular, the development of commutative filters for this kind of grids is specially complex. The use of MLS has been proposed [114], and also other approaches based on LeastSquares [115], or in discrete triangular filters with weights assigned to each vertex [116].…”

Large eddy simulation of a 3-D spatially developing turbulent round jet

“…It is therefore more accurate and reliable than the Reynolds-averaged Navier-Stokes (RANS) simulation and its cost is less than DNS, especially for flows at high Reynolds numbers [4][5][6][7][8][9].…”