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NUMERICAL ANALYSIS OF THE MODELING AND NUMERICAL UNCERTAINTIES IN LARGE EDDY SIMULATION USING UPWIND-BIASED NUMERICAL SCHEMES

Martin Freitag
Fachgebiet Energie- und Kraftwerkstechnik, Technische Universitt Darmstadt Petersenstr. 30, Darmstadt, D-64287, Germany

Markus Klein
Institute for Energy and Powerplant Technology (EKT), TU-Darmstadt, Petersenstr. 30, 64287, Darmstadt, Germany

Johannes Janicka
Institute of Energy and Power Plant Technology, TU Darmstadt, Jovanka-Bontschits-Strasse 2, 64287 Darmstadt, Germany; Darmstadt Graduate School of Excellence Energy Science and Engineering, TU Darmstadt, Jovanka-Bontschits-Strasse 2, 64287 Darmstadt, Germany

Resumo

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.