Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a-priori analysis of direct numerical simulations of isotropic turbulence
M. Buzzicotti, M. Linkmann, H. Aluie, L. Biferale, J. Brasseur, C. Meneveau
The effects of different filtering strategies on the statistical properties of the resolved-to-sub-filter scale (SFS) energy transfer are analyzed in forced homogeneous and isotropic turbulence. We carry out a priori analyses of statistical characteristics of SFS energy transfer by filtering data obtained from direct numerical simulations (DNS) with up to $2048^3$ grid points as a function of the filter cutoff scale. In order to quantify the dependence of extreme events and anomalous scaling on the filter, we compare a sharp Fourier Galerkin projector, a Gaussian filter and a novel class of Galerkin projectors with non-sharp spectral filter profiles. Of interest is the importance of Galilean invariance and we confirm that local SFS energy transfer displays intermittency scaling in both skewness and flatness as a function of the cutoff scale. Furthermore, we quantify the robustness of scaling as a function of the filtering type.
By analyzing the Karman-Howarth equation for filtered velocity fields in turbulent flows, we show that the two-point correlation between filtered strain-rate and subfilter stress tensors plays a central role in the evolution of filtered-velocity correlation functions. Two-point correlations-based {\it statistical priori tests} thus enable rigorous and physically meaningful studies of turbulence models. Using data from direct numerical simulations of isotropic and channel flow turbulence we show that local eddy viscosity models fail to exhibit the long tails observed in the real subfilter stres…
We propose a new model of turbulence for use in large-eddy simulations (LES). The turbulent force, represented here by the turbulent Lamb vector, is divided in two contributions. The contribution including only subfilter fields is deterministically modeled through a classical eddy-viscosity. The other contribution including both filtered and subfilter scales is dynamically computed as solution of a generalized (stochastic) Langevin equation. This equation is derived using Rapid Distortion Theory (RDT) applied to the subfilter scales. The general friction operator therefore includes both advect…
Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH（于利希研究中心于利希超级计算中心）；RWTH Aachen University（亚琛工业大学）
Models for finite-rate-chemistry in underresolved flows still pose one of the main challenges for predictive simulations of complex configurations. The problem gets even more challenging if turbulence is involved. This work advances the recently developed PIESRGAN modeling approach to turbulent premixed combustion. For that, the physical information processed by the network and considered in the loss function are adjusted, the training process is smoothed, and especially effects from density changes are considered. The resulting model provides good results for a priori and a posteriori tests o…
A previously developed modeling procedure for large eddy simulations (LESs) is extended to allow physical space implementations for inhomogeneous flows. The method is inspired by the well-established theoretical analyses and numerical investigations of homogeneous, isotropic turbulence. A general procedure that focuses on recovering the full subgrid scale (SGS) dissipation from resolved fields is formulated, combining the advantages of both the structural and the functional strategy of modeling. The interscale energy transfer is obtained from the test-filtered velocity field, corresponding sub…
In the study by Sadeghi & Oberlack [JFM 899, A10 (2020)] it is claimed that new scaling laws are derived for the case of passive scalar dynamics under the influence of a constant mean gradient in decaying homogeneous isotropic turbulence. However, these scaling laws are not new and have already been derived and discussed in Bahri (2016). No novel analytical achievements are made by Sadeghi & Oberlack, as the title of their study misleadingly wants to suggest. In fact, the already established self-similar scaling laws obtained by Bahri through simple dimensional analysis are already more genera…
A Lagrangian particle cloud model is proposed that accounts for the effects of Reynolds-averaged particle and turbulent stresses and the averaged carrier-phase velocity of the sub-particle-cloud scale on the averaged motion and velocity of the cloud. The SPARSE (Subgrid Particle Average Reynolds Stress Equivalent) model is based on a combination of a truncated Taylor expansion of a drag correction function and Reynolds averaging. It reduces the required number of computational parcels to trace a cloud of particles in Eulerian-Lagrangian methods for the simulation of particle-laden flow. Closur…
In Large-Eddy simulation of particle-laden flow, the effect of the unresolved scales on the particles needs to be modelled. In this work we analyse three very promising models, namely the approximate deconvolution method (ADM) which was proposed for particle-laden flow independently by Kuerten (Phys. Fluids 18, 2006) and Shotorban and Mashayek (Phys. Fluids 17, 2005) and two stochastic models, proposed by Shotorban and Mashayek (J. Turbul. 7, 2006) and Simonin et al. (Appl. Sci. Res. 51, 1993). We present results from a priori and a posteriori analysis of these models in isotropic turbulence a…
Dynamic mixed turbulence modeling using a super-resolution generative adversarial approach
RWTH Aachen University（亚琛工业大学）；University of Cambridge（剑桥大学）；University of Southampton（南安普顿大学）；University of Notre Dame（圣母大学）；University of Edinburgh（爱丁堡大学）
In isotropic helical turbulence, a new single helical model is suggested for large eddy simulation. Based on the Kolmogrov's hypotheses, the helical model is proposed according to the balance of helicity dissipation and the average of helicity flux across the inertial range, and the helical model is a kind of eddy viscosity model. The coefficient of the helical model is constant and can be also determined dynamically. Numerical simulations of forced and decaying isotropic helical turbulence demonstrate that the helical model predicts the energy and helicity evolution well. The statistical char…
The statistics of the velocity gradient tensor in turbulent flows are of both theoretical and practical importance. The Lagrangian view provides a privileged perspective for studying the dynamics of turbulence in general, and of the velocity gradient tensor in particular. Stochastic models for the Lagrangian evolution of velocity gradients in isotropic turbulence, with closure models for the pressure Hesssian and viscous Laplacian, have been shown to reproduce important features such as non-Gaussian probability distributions, skewness and vorticity strain-rate alignments. The Recent Fluid Defo…
For helical isotropic turbulence, an improved two-term helical subgrid-scale (SGS) model is proposed and four types of dynamic methods are given to do large-eddy simulation (LES), which include the standard dynamic procedure, the least quatratic sum dynamic procedure, the dynamic procedure with single con- straint of helicity dissipation and the dynamic one with dual constraints of energy and helicity dissipation. Tested a priori and a posteriori in both steady and decaying helical isotropic turbulence, the four types of dynamic helical models and the dynamic Smogorinsky model are compared wit…
A dynamic procedure for the Lagrangian Averaged Navier-Stokes-$α$ (LANS-$α$) equations is developed where the variation in the parameter $α$ in the direction of anisotropy is determined in a self-consistent way from data contained in the simulation itself. The dynamic model is initially tested in forced and decaying isotropic turbulent flows where $α$ is constant in space but it is allowed to vary in time. It is observed that by using the dynamic LANS-$α$ procedure a more accurate simulation of the isotropic homogeneous turbulence is achieved. The energy spectra and the total kinetic energy de…
The dynamic model for large-eddy simulation (LES) of turbulent flows requires test filtering the resolved velocity fields in order to determine model coefficients. However, test filtering is costly to perform in large-eddy simulation of complex geometry flows, especially on unstructured grids. The objective of this work is to develop and test an approximate but less costly dynamic procedure which does not require test filtering. The proposed method is based on Taylor series expansions of the resolved velocity fields. Accuracy is governed by the derivative schemes used in the calculation and th…
Even though compressible plasma turbulence is encountered in many astrophysical phenomena, its effect is often not well understood. Furthermore, direct numerical simulations are typically not able to reach the extreme parameters of these processes. For this reason, large-eddy simulations (LES), which only simulate large and intermediate scales directly, are employed. The smallest, unresolved scales and the interactions between small and large scales are introduced by means of a subgrid-scale (SGS) model. We propose and verify a new set of nonlinear SGS closures for future application as an SGS…
With the continuing progress in large eddy simulations (LES), and ever increasing computational resources, it is currently possible to numerically solve the time-dependent and anisotropic large scales of turbulence in a large variety of flows. For some applications this large-scale resolution is satisfactory. However, a wide range of engineering problems involve flows at very large Reynolds numbers where the subgrid scale dynamics of a practical LES are critically important to design and yet are out of reach given the computational demands of solving the Navier Stokes equations; this difficult…
Most of the turbulent flows appearing in nature (e.g. geophysical and astrophysical flows) are subjected to strong rotation and stratification. These effects break the symmetries of classical, homogenous isotropic turbulence. In doing so, they introduce a natural decomposition of phase space in terms of wave modes and potential vorticity modes. The appearance of a new time scale associated to the propagation of waves, in addition to the eddy turnover time, increases the complexity of the energy transfers between the various scales; nonlinearly interacting waves may dominate at some scales whil…
We developed a novel autonomously dynamic nonlocal turbulence model for the large and very large eddy simulation (LES, VLES) of the homogeneous isotropic turbulent flows (HIT). The model is based on a generalized (integer-to-noninteger) order Laplacian of the filtered velocity field, and a novel dynamic model has been formulated to avoid the need for tuning the model constant. Three data-driven approaches were introduced for the determination of the fractional-order to have a model which is totally free of any tuning parameter. Our analysis includes both the $\textit{a priori}$ and the $\texti…
Approximate deconvolution forms a mathematical framework for the structural modeling of turbulence. The sub-filter scale flow quantities are typically recovered by using the Van Cittert iterative procedure. In this paper, however, we put forth a generalized approach for the iterative deconvolution process of sub-filter scale recovery of turbulent flows by introducing Krylov space iterative methods. Their accuracy and efficiency are demonstrated through a systematic a-priori analysis of solving the Kraichnan and Kolmogorov homogeneous isotropic turbulence problems in two- and three-dimensional …
Physics-Constrained Neural Closure for Lattice Boltzmann Large-Eddy Simulation
University of Rome “Tor Vergata”（罗马托尔维加塔大学）；Italian Institute of Technology（意大利理工学院）；Harvard University（哈佛大学）；Chalmers University of Technology（查尔姆斯理工大学）
Compressible magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical phenomena ranging from the intergalactic to the stellar scales. In studying them, numerical simulations are nearly inescapable, due to the large degree of nonlinearity involved. However the dynamical ranges of these phenomena are much larger than what is computationally accessible. In large eddy simulations (LES), the resulting limited resolution effects are addressed explicitly by introducing to the equations of motion additional terms associated with the unresolved, subgrid-scale (SGS) dynamics. This renders the…
University of Stuttgart（斯图加特大学）；Hewlett Packard Enterprise（慧与公司）
Over the last years, supervised learning (SL) has established itself as the state-of-the-art for data-driven turbulence modeling. In the SL paradigm, models are trained based on a dataset, which is typically computed a priori from a high-fidelity solution by applying the respective filter function, which separates the resolved and the unresolved flow scales. For implicitly filtered large eddy simulation (LES), this approach is infeasible, since here, the employed discretization itself acts as an implicit filter function. As a consequence, the exact filter form is generally not known and thus, …
