Bridging Large Eddy Simulation and Reduced-Order Modeling of Convection-Dominated Flows through Spatial Filtering: Review and Perspectives

Numerical simulation of turbulent flows is one of the great challenges in Computational Fluid Dynamics (CFD). In general, Direct Numerical Simulation (DNS) is not feasible due to limited computer resources (performance and memory), and the use of a turbulence model becomes necessary. The paper will discuss several aspects of two approaches of turbulent modeling—Large Eddy Simulation (LES) and Variational Multiscale (VMS) models. Topics which will be addressed are the detailed derivation of these models, the analysis of commutation errors in LES models as well as other results from mathematical analysis.

of thesis entitled Large-Eddy Simulation of Wind Flow and Air Pollutant Transport inside Urban Street Canyons of Different Aspect Ratios submitted by Li, Xianxiang for the degree of Doctor of Philosophy at the University of Hong Kong in June 2008 The characteristics of the wind flow and air pollutant transport inside urban street canyons are of fundamental importance to the air quality monitoring and improvement. An investigation of these characteristics was performed in this study using both experimental and numerical techniques. The focus is on the mechanisms of pollutant transport and removal inside urban street canyons of high aspect ratios (AR, ratio of the building height to the street width). A physical model in water channel was first developed to study the wind flow in street canyons of different ARs of 0.5, 1.0, and 2.0. The velocity and turbulent fluctuation were measured by a Laser-Doppler Anemometer (LDA). The measured velocity and turbulent fluctuation at various locations were validated with several experimental datasets available in literature. The measured results in most locations were also in good agreement with previous numerical results. The comprehensive measurement data can provide a validation database for the numerical model development. To take into account the detailed transient turbulent processes, a large-eddy simulation (LES) model was developed based on a one-equation subgrid-scale (SGS) model and finite element method (FEM). This model was validated and fine-tuned by applying to an open channel flow at Reτ = 180. By comparing the calculated velocity and fluctuations with those obtained from experiment and direct numerical simulation (DNS), a set of model constants was determined for the LES model. A 1/7th wall model was further incorporated into this LES model to mitigate the strict near-wall resolution requirement. To validate the newly developed LES model for street canyons, the LES results for the street canyons of AR 1 and 2 were compared extensively with the waterchannel experimental data and previous LES results. The good agreement showed that the newly developed LES model was capable of predicting the complicated flow patterns and pollutant dispersion in street canyons. The validated LES model was then employed to simulate the street canyons of AR 3, 5, and 10. Three, five, and eight vertically aligned primary recirculations were found for the three cases, respectively, which showed decreasing strength with decreasing height. The very small ground-level wind speeds made the ground-level pollutants extremely difficult to disperse. Local maxima of the turbulence intensities were found at the interfaces between the primary recirculations and the free surface layer. The pollutant followed the trajectories of the primary recirculations. High pollutant concentration and variance were found near the buildings where wind flowed upward. Large gradients of pollutant concentration and variance were also observed at the interfaces between the primary recirculations and the free surface layer. Detailed analyses of concentration budget terms showed that the advection terms were responsible for pollutant redistribution within primary recirculations, while the turbulent transport terms were responsible for pollutant penetration between primary recirculations and pollutant removal from the street canyon. Based on the LES results, several quantities were introduced to compare the pollutant removal capability of different street canyon configurations. It was found that these quantities were all non-linear functions of the street canyon AR. Large-Eddy Simulation of Wind Flow and Air Pollutant Transport inside Urban Street Canyons of Different Aspect Ratios

Backflow stabilization by deconvolution-based large eddy simulation modeling

Shear improved Smagorinsky model for large eddy simulation of flow in a stirred tank with a Rushton disk turbine

The objective of the present work is to validate the compressible Large-Eddy Simulation (LES) models implemented in the in house parallel unstructured CFD code TermoFluids. Our research team has implemented and tested several LES models over the past years for the incompressible regimen. In order to be able to solve complex turbulent compressible flows, the models are revisited and modified if necessary. In addition, the performance of the implemented hybrid advection scheme is an issue of interest for the numerical simulation of turbulent compressible flows. The models are tested in the well known turbulent channel flow problem at different compressible regimens.

Spatial filtering has been central in the development of large eddy simulation reduced order models (LES-ROMs) (Wang et al. in Comput. Meth. Appl. Mech. Eng. 237–240:10–26, 2012, [9], Xie et al. in Data-driven filtered reduced order modeling of fluid flows, 2018, [11], Xie et al. in Comput. Methods Appl. Mech. Eng. 313:512–534, 2017, [12]) and regularized reduced order models (Reg-ROMs) (Iliescu et al. in Int. J. Numer. Anal. Mod. 2017, [4], Sabetghadam and Jafarpour in Appl. Math. Comput. 218:6012–6026, 2012, [7], Wells et al. in Int. J. Numer. Meth. Fluids 84:598–615, 2017, [10]) for efficient and relatively accurate numerical simulation of convection-dominated fluid flows. In this paper, we perform a numerical investigation of spatial filtering. To this end, we consider one of the simplest Reg-ROMs, the Leray ROM (L-ROM) (Iliescu et al. in Int. J. Numer. Anal. Mod. 2017, [4], Sabetghadam and Jafarpour in Appl. Math. Comput. 218:6012–6026, 2012, [7], Wells et al. in Int. J. Numer. Meth. Fluids 84:598–615, 2017, [10]), which uses ROM spatial filtering to smooth the flow variables and decrease the amount of energy aliased to the lower index ROM basis functions. We also propose a new form of ROM differential filter (Sabetghadam and Jafarpour in Appl. Math. Comput. 218:6012–6026, 2012, [7], Wells et al. in Int. J. Numer. Meth. Fluids 84:598–615, 2017, [10]) and use it as a spatial filter for the L-ROM. We investigate the performance of this new form of ROM differential filter in the numerical simulation of a flow past a circular cylinder at a Reynolds number \(Re=760\).

Numerical stabilization is often used to eliminate (alleviate) the spurious oscillations generally produced by full order models (FOMs) in under‐resolved or marginally‐resolved simulations of convection‐dominated flows. In this article, we investigate the role of numerical stabilization in reduced order models (ROMs) of marginally‐resolved, convection‐dominated incompressible flows. Specifically, we investigate the FOM–ROM consistency, that is, whether the numerical stabilization is beneficial both at the FOM and the ROM level. As a numerical stabilization strategy, we focus on the evolve‐filter‐relax (EFR) regularization algorithm, which centers around spatial filtering. To investigate the FOM‐ROM consistency, we consider two ROM strategies: (i) the EFR‐noEFR, in which the EFR stabilization is used at the FOM level, but not at the ROM level; and (ii) the EFR‐EFR, in which the EFR stabilization is used both at the FOM and at the ROM level. We compare the EFR‐noEFR with the EFR‐EFR in the numerical simulation of a 2D incompressible flow past a circular cylinder in the convection‐dominated, marginally‐resolved regime. We also perform model reduction with respect to both time and Reynolds number. Our numerical investigation shows that the EFR‐EFR is more accurate than the EFR‐noEFR, which suggests that FOM‐ROM consistency is beneficial in convection‐dominated, marginally‐resolved flows.

The dynamic two-parameter mixed model (DMM2) has been recently introduced into the large eddy simulation (LES) by Salvetti and Banerjee [“a priori Tests of A New Dynamic Subgrid-Scale Model for Finite-Difference Large-Eddy Simulations”, Phys. Fluids, 7 (1995) pp. 2831–2847], Horiuti [“A New Dynamic Two-Parameter Mixed Model for Large-Eddy Simulation”, Phys. Fluids, 9 (1997) pp. 3443–3464], Meneveau and Katz [“Dynamic Testing of Subgrid Models in Large Eddy Simulation Based on the Cermano Identity”, Phys. Fluids, 11 (1999) pp. 245–247], Sarghini et al. [“Scale-Similar Models for Large-eddy Simulations”, Phys. Fluids, 11 (1999) pp. 1596–1607], and Morinishi and Vasilyev [“A Recommended Modification to the Dynamic Two-Parameter Mixed Subgrid Scale Model for Large Eddy Simulation of Wall Bounded Turbulent Flow”, Phys. Fluids, 13 (2001) pp. 3400–3410]. However, current approaches in the literature are mathematically inconsistent. In this paper, the DMM2 has been optimized using the functional variational method. The mathematical inconsistency has been removed and a governing system of two integral equations for the model coefficients of the DMM2 has been obtained. Numerical simulation of turbulent Couette flow is used to validate the new optimal DMM2. The numerical results agree with the direct numerical simulation (DNS) data, the classical wall law and experimental correlations that are available in the literature.

A reduced order model for turbulent flows in the urban environment using machine learning

The LES model's role in jet noise

Standard Computational Fluid Dynamic (CFD) techniques are widely used in the design of hydraulic valves for optimising the valve performance and reducing the production effort. They calculate the turbulent flow and predict cavitation. Unfortunately, the currently used models are often inadequate and out of date to catch the complexity of these phenomena such as the transient interaction between cavitation and turbulence. Advanced computational methods have been developed and applied to other engineering branches. Despite this fact, they face many difficulties to be employed in hydraulics. In this paper, a first step is taken towards the usage of these cutting edge CFD methods for hydraulic valves. At first, the different challenges for a CFD code to simulate valve flows are highlighted. A novel computational approach is then presented. It combines a Large Eddy Simulation (LES) model for the turbulence modelling as well as a Full Cavitation Model (FCM). The LES technique explicitly resolves the large turbulence scales while the smaller ones are modelled. The FCM not only predicts vapour but also gas cavitation, which plays a vital role in hydraulic fluids. This method is tested to simulate the flow in a pilot stage of a jet-pipe servo-valve. The test case is presented and the different boundary conditions used for the simulations are given. The results of the simulation are compared with experimental results showing a good agreement. A comparison between the LES model and the standard two-equation turbulence model shows the advantages of the LES approach. Finally, the transient features of the flow are highlighted in terms of velocity oscillation.

This chapter presents important issues that one needs to consider in order to perform direct numerical simulation (DNS) and large eddy simulation (LES) of turbulent flows. We also present important similarities and differences between DNS and LES. We show that DNS though potentially a powerful tool cannot be used as a design tool for engineering applications and show LES has a good potential as a design tool. We present different subgrid scale models that can be used to perform LES with the advantages and disadvantages of each one. We present challenges in performing LES and DNS especially in the presence of wall and in applications dealing with convective heat transfer. Different ways of treating a solid wall by using suitable models in LES are also presented in this chapter.

Based on a pseudo-spectral large eddy simulation (LES) model, an LES model with an anisotropy turbulent kinetic energy (TKE) closure model and an explicit multi-stage third-order Runge-Kutta scheme is established. The modeling and analysis show that the LES model can simulate the planetary boundary layer (PBL) with a uniform underlying surface under various stratifications very well. Then, similar to the description of a forest canopy, the drag term on momentum and the production term of TKE by subgrid city buildings are introduced into the LES equations to account for the area-averaged effect of the subgrid urban canopy elements and to simulate the meteorological fields of the urban boundary layer (UBL). Numerical experiments and comparison analysis show that: (1) the result from the LES of the UBL with a proposed formula for the drag coefficient is consistent and comparable with that from wind tunnel experiments and an urban subdomain scale model; (2) due to the effect of urban buildings, the wind velocity near the canopy is decreased, turbulence is intensified, TKE, variance, and momentum flux are increased, the momentum and heat flux at the top of the PBL are increased, and the development of the PBL is quickened; (3) the height of the roughness sublayer (RS) of the actual city buildings is the maximum building height (1.5–3 times the mean building height), and a constant flux layer (CFL) exists in the lower part of the UBL.

There are two main strategies for improving the projection-based reduced order model (ROM) accuracy—(i) improving the ROM, that is, adding new terms to the standard ROM; and (ii) improving the ROM basis, that is, constructing ROM bases that yield more accurate ROMs. In this paper, we use the latter. We propose two new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct two new Lagrangian ROMs, which we denote α-ROM and λ-ROM. We show that both Lagrangian ROMs are more accurate than the standard Eulerian ROMs, that is, ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). In particular, the α-ROM can be orders of magnitude more accurate than the standard Eulerian ROMs. We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs’ accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis.

Present-day demands on combustion equipment are increasing the need for improved understanding and prediction of turbulent combustion. Large eddy simulation (LES), in which the large-scale flow is resolved on the grid, leaving only the small-scale flow to be modeled, provides a natural framework for combustion simulations, as the transient nature of the flow is resolved. In most situations, however, the flame is thinner than the LES grid, and subgrid modeling is required to also handle the turbulence-chemistry interactions. Here, we examine the predictive capabilities of the flamelet LES models, such as the Flamelet Progress Variable LES (LES-FPV) models, and the finite rate chemistry LES models, such as the LES-Thickened Flame Model (LES-TFM), the partially stirred reactor model (LES-PaSR) and the Eddy Dissipation Concept (LES-EDC) model. These different combustion LES models are used here to study the reacting flow in an axisymmetric dump combustor at a Reynolds number of 55,800, the Damköhler number of 167 and a Karlowitz number of 0.15, placing the flame in the corrugated flame regime. The computational results are compared to experimental data of velocity and temperature to examine predictive capabilities of the different models.