DOI: 10.1615/TSFP5
NUMERICAL ANALYSIS OF THE MODELING AND NUMERICAL UNCERTAINTIES IN LARGE EDDY SIMULATION USING UPWIND-BIASED NUMERICAL SCHEMES
ABSTRACT
Accurate LES simulations can only be achieved if the numerical contamination of the smaller retained flow structures is taken into account as well as the subgrid parameterization (Geurts and Frohlich, 2002). The interaction of the numerical and the modeling error complicates quality assessment procedures or uncertainty estimators of LES even further. This topic has recently been discussed in the literature (Celik et al., 2005; Chow and Moin, 2003; Geurts and Frohlich, 2002; Klein, 2005; Kravchenko and Moin, 1997; Meyers et al.,
2003; Hoffman, 2004). Klein (2005) proposed to evaluate the
numerical as well as the modeling error using an approach
based on Richardson extrapolation, where it is assumed that
the modeling error scales like a power law.
Recently this method has been applied to several flow
cases, like channel and free-shear flows and so far very encouraging results have been obtained using 2nd order CDS
as discretization scheme. However, most commercial solvers
able to handle complex geometries are not strictly second
order accurate and often they are based on upwind biased
schemes. Therefore it is extremely important to assess the
applicability of the method to these schemes. The focus of
this work is to investigate the method using a more diffusive numerical scheme, e.g. QUICK (Quadratic Interpolation for Convective Kinematics). As the model equations presented by Klein (2005) allow to distinguish between modeling and numerical uncertainty, their interaction can be studied, also with respect to the error components obtained by the CDS calculations.
The next section will introduce the method, originally
proposed by Klein (2005) and recently extended by Freitag
and Klein (2006). Subsequently the scaling exponent will
be evaluated which is a necessary requirement to solve the
model equations. The method will be applied to a strongly
swirling, recirculating flow and to a channel flow.