Filtering techniques for complex geometry fluid flows

Abstract

SUMMARYWe develop a class of ®lters based upon the numerical solution of high-order elliptic problems in d which allow for independent determination of order and cut-o wave number and which default to classical Fourier-based ®lters in homogeneous domains. However, because they are based on the solution of a PDE, the present ®lters are not restricted to applications in tensor-product based geometries as is generally the case for Fourier-based ®lters. The discrete representation of the ®ltered output is constructed from a Krylov space generated in solving a well-conditioned system arising from a low-order PDE.

A posteriori analysis of low-pass spatial filters for approximate deconvolution large eddy simulations of homogeneous incompressible flows

“…Comparing the N = 2 plot with the N = 5 plot, the combination γ = 1.0 and N = 2 or N = 5 yields the best results. As expected, the No-AD performs the worst for both N = 2 and N = 5.Fig.22presents the third-order structure function defined in(47) for the AD-HDF-16 with N = 2 and N = 5 at t = 10. Results for the DNS and No-AD are also included for comparison purposes.…”

“…Fig. 12 presents the third-order structure function defined in (47) for the AD-TF, AD-SF and AD-7PF with N = 2 and N = 5 at t = 10. Results for the DNS and No-AD are also included for comparison purposes.…”

Consistency of the full and reduced order models for evolve‐filter‐relax regularization of convection‐dominated, marginally‐resolved flows

“…We recall that the filter radius is 𝛿 = 0.0032 and the relaxation parameter is 𝜒 = 1. We test the predictive capability of the model in the time interval [8,12]. In terms of relative velocity errors, EFR-EFR performs better than EFR-noROM, reaching values around 10 −2 and reducing the error by two order of magnitude, as illustrated in the left plot of Figure 17.…”

Nonintrusive Stabilization of Reduced Order Models for Uncertainty Quantification of Time-Dependent Convection-Dominated Flows

“…This effectively amounts to replacing the Laplacian ∆ in the standard DF (4.2) with an m-th order Laplacian ∆ m . The transfer function of the HODF (4.7) is significantly sharper than the transfer function of the HODF (4.6) (compare left and right panels of Figure 1 in [36] and also ). However, the authors in [36] emphasize that the condition number of S m r is extremely high.…”

“…The transfer function of the HODF (4.7) is significantly sharper than the transfer function of the HODF (4.6) (compare left and right panels of Figure 1 in [36] and also ). However, the authors in [36] emphasize that the condition number of S m r is extremely high. Thus, they propose to use a modified CG algorithm.…”