Explicit and implicit LES closures for Burgers turbulence

Abstract

In this work, we perform an aposteriori error analysis on implicit and explicit large eddy simulation closure models for solving the Burgers turbulence problem. Our closure modeling efforts include both functional and structural models equipped with various low-pass filters. We introduce discrete binomial smoothing filters and an enhanced version of the Van Cittert algorithm to accelerate the convergence of approximate deconvolution processes including regularization and relaxation filtering approaches. Our implicit modeling efforts consist of various high-order schemes including compact and non-compact fifthorder upwind schemes as well as weighted essential non-oscillatory (WENO) and compact reconstructed WENO (CRWENO) schemes, and the resulting schemes are shown to effectively converge to the direct numerical simulation (DNS) for increasing resolutions. Comparing with DNS and underresolved DNS computations, our numerical assessments illustrate the ability of these methods to capture the energy content near grid cut-off scale.

Data-driven subgrid-scale modeling of forced Burgers turbulence using deep learning with generalization to higher Reynolds numbers via transfer learning

“…Furthermore, as shown in panel (d), LES with DDP outperforms LES with DSMAG in capturing the PDF's tails, which correspond to shocks. Note that the differences between the PDFs of DDP, FDNS, and DSMAG are not statistically significant (at 95% The curl up in KE around the maximum resolved k of LES is a common feature of spectral LES solvers applied to Burgers turbulence 38,39,46 . In (a)-(c), each curve is produced using 3 × 10 5 sequential samples that are 20∆t apart.…”

“…The domain is periodic with length L. Despite being one-dimensional, the presence of strongly nonlinear local regions in the form of shocks, often multiple shocks (Fig. 1(a)), makes Burgers turbulence a complex and challenging system, which has been used as the test-bed in various SGS and reduced-order modeling studies [34][35][36][37][38][39][40] . F(x,t) is defined as 34…”

“…(c) spectrum of KE. The curl up in KE around the maximum resolved k of LES is a common feature of spectral LES solvers applied to Burgers turbulence38,39,46 . In (a)-(c), each curve is produced using 3 × 10 5 sequential samples that are 20∆t apart.…”

A neural network approach for the blind deconvolution of turbulent flows

“…For the purpose of benchmarking we utilize a set of closures including the scale-similarity approach proposed by Bardina et al (1980) (denoted SS), the approximate deconvolution methodology given by Stolz & Adams (1999) with 3 iterative deconvolutions (which forms the conceptual analog of our proposed architecture and is denoted as AD 3 ) as well as the scale-similarity approach proposed by Layton & Lewandowski (2003) which may be interpreted to be an approximate deconvolution methodology which simply one iteration (and hence denoted AD 1 ). We clarify that while the decision to utilize three iterative deconvolutions for the approximate deconvolution approach (i.e., AD 3 ) is rather arbitrary, past studies (Maulik & San 2018) have shown that a choice of the number of iterations between 3 and 5 is usually sufficient for satisfactory subfilter recovery.…”

Time-series learning of latent-space dynamics for reduced-order model closure

“…The present study can be considered a nonintrusive counterpart of that investigation. Our test problems are given by the advection-dominated viscous Burgers equation [14] with a moving shock as well as a pseudo-turbulence test case denoted 'Burgulence' [30,31] showing the characteristic k −2 scaling in wavenumber (k) space.…”