Error response surfaces in large-eddy simulation of a spatially-evolving mixing layer

A response surface based methodology is used to quantify the error in Large-Eddy Simulation (LES) of a spatially-evolving mixing layer flow and its sensitivity to different simulation parameters, viz. the grid stretching and the subgrid scale model constant. An algebraic error Cost Function (eCF) is evaluated with respect to the results of a highly resolved LES (HRLES), for a few quantities of interest, namely the mean streamwise velocity, the momentum thickness and the shear stress. Starting from a database of coarser LES simulations, error response surfaces are then built in the parameter space through two different approaches: generalized Polynomial Chaos and Kriging. A typical feature of the considered spatially-evolving flow is the progressive transition from a laminar regime, highly dependent on the inlet condition, to a fully-developed turbulent one. Therefore the computational domain is divided in two different zones (inlet dependent and fully turbulent) and the error analysis is carried out for these two zones separately. The comparison between the different response surfaces generated by gPC or Kriging shows an excellent agreement of the resulting pdfs for each physical quantity analyzed. The same agreement is recovered when comparing the stochastic mean value or the variance of the error cost function. Conversely extreme events (i.e. the maximum and minimum error recovered ) exhibit a remarkable sensitivity to the model used to build up the response surface.