LES-ADM accuracy assessment via an error-landscape approach

This paper investigates the accuracy and robustness of the approximate deconvolution method (ADM) in large eddy simulation (LES) using an error-landscape approach. Two canonical turbulence test cases—forced and decaying homogeneous isotropic turbulence (F-HIT / D-HIT)—are analyzed. We assess how user-defined parameters in ADM, including the filter type, its order (), and the number of deconvolution iterations (), affect the predictive performance of the model. Finite and compact difference filters are employed for deconvolution. Along with the box and Gaussian filters, these are also used as an LES filter. The resulting errors associated with the use of ADM are compared with LES errors arising from the Smagorinsky model with a model constant in the range (20 levels), and a no-model approach. The LES results are validated against direct numerical simulation (DNS) data. For the F-HIT case, we focus on the accuracy of the prediction of time-averaged kinetic energy and skewness of the velocity components and their derivatives. In the case of the Smagorinsky model, accurate results are obtained for, while for ADM and appear to be required. An exception is the prediction of the velocity-derivative skewness, which, in all cases, differs significantly from the DNS solution due to its strong reliance on small-scale flow features. The classical error-landscape approach is applied for the D-HIT configuration. By performing direct comparisons of key solution properties, this approach enables identifying the parameter range in which ADM attains optimal accuracy leading to results that are more accurate than can be obtained by applying the Smagorinsky model, as well as regions where ADM-based simulations may become unstable or exhibit accuracy levels inferior to the reference no-model case. The latter arises especially on coarse grids when, or when the LES filter does not sufficiently attenuate the solution at the grid cut-off frequency. From the perspective of simulation stability, the safer choice is to perform deconvolution with a high-order filter, preferably an implicit formulation, which also ensures considerable accuracy. The total analysis encompasses comparisons of over simulations. It provides valuable guidance for the effective use and future development of stable ADM-based modeling strategies. In this respect, an important finding is that increasing, rather than improving deconvolution accuracy, may lead to instability reflecting the ill-posedness of recovering scales that are poorly represented on the chosen simulation grid.

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