Subgrid Viscosity Research Articles

Quantifying the impact of AGN feedback on the large-scale matter distribution using two- and three-point statistics

Abstract Feedback from active galactic nuclei (AGN) plays a critical role in shaping the matter distribution on scales comparable to and larger than individual galaxies. Upcoming surveys such as Euclid and LSST aim to precisely quantify the matter distribution on cosmological scales, making a detailed understanding of AGN feedback effects essential. Hydrodynamical simulations provide an informative framework for studying these effects, in particular by allowing us to vary the parameters that determine the strength of these feedback processes and, consequently, to predict their corresponding impact on the large-scale matter distribution. We use the EAGLE simulations to explore how changes in subgrid viscosity and AGN heating temperature affect the matter distribution, quantified via 2- and 3-point correlation functions, as well as higher order cumulants of the matter distribution. We find that varying viscosity has a small impact ($\approx 10~{{\%}}$) on scales larger than 1h−1 Mpc, while changes to the AGN heating temperature lead to substantial differences, with up to 70% variation in gas clustering on small scales (≲ 1h−1 Mpc). By examining the suppression of the power spectrum as a function of time, we identify the redshift range z = 1.5 − 1 as a key epoch where AGN feedback begins to dominate in these simulations. The 3-point function provides complementary insight to the more familiar 2-point statistics, and shows more pronounced variations between models on the scale of individual haloes. On the other hand, we find that effects on even larger scales are largely comparable.

Numerical Study of Supersonic Flow Past a Cylindrical Afterbody

The near wake of a cylindrical afterbody aligned with a uniform Mach 2.46 flow has been numerically investigated using Reynolds-Averaged Navier-Stokes equations (k-epsilon two equation model) and Large Eddy Simulation (dynamic sub-grid scale eddy viscosity model). Mean flow field properties obtained from numerical simulations, such as axial velocity, pressure on the base surface has been compared with the experimental results. It has been found that k-epsilon model fails to predict the flow properties in the recirculation region where better agreement has been observed between the data obtained from LES and measurements. Data obtained from LES has been further analyzed to investigate the turbulent flow field in the wake region. Parameters like turbulent kinetic energy and primary Reynolds stress have been calculated and compared with the results obtained from an experiment in order to achieve a better understanding of the role of turbulence in the flow field.

General relativistic simulations of collapsing binary neutron star mergers with Monte Carlo neutrino transport

Recent gravitational wave observations of neutron-star-neutron-star and neutron-star-black-hole binaries appear to indicate that massive neutron stars may not be too uncommon in merging systems. These discoveries have led to an increased interest in the simulation of merging compact binaries involving massive stars. In this paper, we present a first set of evolution of massive neutron star binaries using Monte Carlo radiation transport for the evolution of neutrinos. We study a range of systems, from nearly symmetric binaries that collapse to a black hole before forming a disk or ejecting material, to more asymmetric binaries in which tidal disruption of the lower mass star leads to the production of more interesting postmerger remnants. For the latter type of systems, we additionally study the impact of viscosity on the properties of the outflows, and compare our results to two recent simulations of identical binaries performed with the whiskythc code. We find agreement on the black hole properties, disk mass, and mass and velocity of the outflows within expected numerical uncertainties, and some minor but noticeable differences in the evolution of the electron fraction when using a subgrid viscosity model, with viscosity playing a more minor role in our simulations. The method used to account for r-process heating in the determination of the outflow properties appears to have a larger impact on our result than those differences between numerical codes. We also use the simulation with the most ejected material to verify that our newly implemented Lagrangian tracers provide a reasonable sampling of the matter outflows as they leave the computational grid. We note that, given the lack of production of hot outflows in these mergers, the main role of neutrinos in these systems is to set the composition of the postmerger remnant. One of the main potential uses of our simulations is, thus, as improved initial conditions for longer evolutions of such remnants.

Assessment of the shear stress transport dynamic ℓ2−ω delayed detached eddy simulation in Bachalo–Johnson flow with shock-induced separation

Driven by the need for simulating compressible flows, Germano identity-based [Z. Yin and P. A. Durbin, “An adaptive DES model that allows wall-resolved eddy simulation,” Int. J. Heat Fluid Flow 62, 499–509 (2016)] and Vreman operator-based [Bader et al., “A hybrid model for turbulence and transition, with a locally varying coefficient,” Flow, Turbul. Combust. 108, 935–954 (2022)] dynamic ℓ2−ω delayed detached eddy simulation (DDES) formulations are constructed on the k−ω shear stress transport (SST) model. The Bachalo–Johnson transonic axisymmetric bump is simulated to assess the models’ capability in handling the compressible boundary layers under pressure gradient and transonic shock–boundary layer interaction. The new dynamic ℓ2−ω DDES formulation based on k−ω SST overcomes the issues of freestream sensitivity and inaccurate compressible boundary layer profile observed in the original k−ω (88) based model. The new SST-based dynamic model using the Vreman operator to compute the model coefficient (Vreman-dynamic model) has superior performance against Germano identity-based model due to its capability of suppressing the subgrid viscosity during the initial development of a separating shear layer. The Vreman-dynamic model predicts a reattachment location similar to the zonal improved-DDES/direct numerical simulation approach by Spalart et al. [“Large-eddy and direct numerical simulations of the bachalo-johnson flow with shock-induced separation,” Flow, Turbul. Combust. 99, 865–885 (2017)] on a much coarser mesh demonstrating its potential for application in industrial flows.

A Method for Choosing the Spatial and Temporal Approximations for the LES Approach

Analysis and optimization of the hybrid upwind-central numerical methods for modern versions of large eddy simulations (LESs) are presented herein. Optimization was performed based on examination of the characteristics of the spatial and temporal finite-volume approximations of the convective terms of filtered Navier–Stokes equations. A method for selecting level of subgrid viscosity that corresponds to the chosen numerical scheme and makes it possible to obtain an extended inertial interval of the energy spectrum is proposed. A series of LESs of homogeneous isotropic turbulence decay were carried out, and the optimal values of the subgrid model constants included in the hybrid shear stress transport delay detached eddy simulation (SST-DDES) method were determined. A procedure for generating a consistent initial field of subgrid parameters for these simulations is described. The three-stage explicit Runge–Kutta method was demonstrated to be sufficient for stable time integration, while the popular explicit midpoint method was not. The slope of the energy spectrum was shown to be almost independent of the central-difference scheme order and of the mesh spacing when the correct numerical method was applied. Numerical viscosity was found to become much greater than subgrid viscosity when the upwind scheme contributed about 10% or more to the convective flux approximation.

Modeling and simulation of one- and two-row six-bladed ducted fans

The problem of simulation of efficient ducted fan type propulsors is considered. From experience of operation of twin blades in fantails of helicopters, it is known that this configuration creates less noise compared to a uniform arrangement of the blades around the circumference. However, the flow behind such fan is less uniform than that of a conventional ducted fan. For multicopter-type unmanned aircraft and air taxis, the key problem is flight in take-off and landing modes as well as acoustic and vortex fields created by propulsors in these modes. The decrease in the noise level in propellers with twin blades can potentially be accompanied by an increase in non-stationary vortex effects on the aircraft as well as a decrease in specific thrust. The objectives were to develop a method for simulation of ducted fan propellers in the takeoff and landing mode, to determine the optimal angle between the blades, and to compare a ducted fan with twin X-shaped blades to conventional blade position. Turbulent flows were calculated using transient Reynold-averaged Navier-Stokes equations, complemented by SST turbulence model, and large eddy simulation with WALE subgrid viscosity model. The calculations used the modification γ–Reθ Transition SST of the Langtry-Menter turbulence model, where there are relations for the intermittency criterion, which made it possible to consider the laminar-turbulent transition and the appearance of thin laminar separation bubbles that affect both the thrust of the propeller and the non-uniformity of the flow behind it. Testing was carried out on four-bladed propellers according to the known results of the TsAGI reference experiments. Testing of the γ–Reθ Transition SST Langtry-Menter turbulence model showed that it reproduces the dependence of the thrust coefficient and power factor on the blade angle better than the standard SST model. Calculations have shown that there is a clearly defined optimum angle between the paired blades. A comparison of three-bladed, six-bladed single and six-bladed propellers with twin blades showed that the latter option has slightly better thrust characteristics and creates a significantly lower noise level on the ground. The studied characteristics of ducted fans demonstrate the prospects for the use of propellers with twin blades in aircraft with vertical takeoff and landing. The developed numerical method can be directly used for industrial calculations of propellers and fans.

A numerical wave tank with large eddy simulation for wave breaking

A three-dimensional (3D) numerical wave tank (NWT) is developed based on OpenFOAM. The propagation and breaking of waves with a moderate wavelength that could be generated in the laboratory are studied. The wave periods range from 0.5 to 1.79 s and wave steepness goes up to 0.05. The volume of fluid method (VOF) is employed for interface capturing. The relaxation zone method is implemented for wave generation and absorption at the boundaries. Computationally significant factors like grid size, relaxation weight and time step are investigated to find the optimal parameters of the numerical models for various wave regimes. A relationship between grid size and time step, similar to the wave dispersion relation, is found. The accuracy and performance of the NWT are assessed through the reflecting coefficient, wave damping and phase distortion rates. Simulation conditions are monitored to achieve an error rate of less than 3%. To mitigate the effects of numerical errors on the calculation of the reflection coefficient, a modified version of Goda's approach is proposed. The coefficient of wave reflection at the outlet boundary calculated by the conventional Goda's method is as high as 4.3%. This value can be modified to be less than 2% after utilizing the revised Goda's method. Turbulent flows, especially for the breaking wave regime, are investigated by large eddy simulation. A one-equation sub-grid eddy viscosity model, with coefficients being derived from local flow properties, is employed for turbulence closure. A case study of wave breaking on a fixed bar is simulated. The validation of this NWT model is confirmed by comparing the numerical results with experimental data.

Application of immersed boundary based turbulence wall modeling to the Ahmed body aerodynamics

This paper applies a recently developed immersed boundary-turbulence wall modeling approach to turbulent flows over a generic car geometry, known as the Ahmed body, under massive flow separation within a lattice Boltzmann solver. Although the immersed boundary method combined with hierarchical Cartesian grid offers high flexibility in automatic grid generation around complex geometries, the near-wall solution is significantly deteriorated compared to the body-fitted simulation, especially when coupled to wall models for turbulent flows at high Reynolds number. Enhanced wall treatments have been proposed in the literature and validated for attached flow configurations. In this work, the Ahmed body with a slant surface of angle 35° is considered where the flow separates massively over the slant surface and the vertical base. The large eddy simulation is performed with a Reynolds stress constraint near-wall. The eddy viscosity is computed dynamically by taking into account the actually resolved Reynolds stresses. It approaches the mixing length eddy viscosity in attached boundary layers and returns to the subgrid eddy viscosity in detached boundary layers. An explicit equilibrium wall model has also been proposed to accelerate the calculation. Comparison with the no-slip boundary condition on the separated surfaces shows that the near-wall treatments with the equilibrium wall model operate reasonably well on both attached and detached boundary layers.

Meshless approach to the large-eddy simulation of the continuous casting process

The paper discusses the numerical solution of the large-eddy formulation for modelling the turbulent fluid flow with solidification in the continuous casting of steel. This industrially relevant problem is solved by a meshless method for the first time. The solid-liquid system is formulated within the continuum mixture formulation of the governing, mass momentum and energy equations. The Darcy porous media model describes the mushy region. The large-eddy formulation is based on the Smagorinsky model for sub-grid scale viscosity and the van Driest damping function. The synthetic turbulence is prescribed at the molten steel inlet. The generated turbulent fluctuations are isotopic and correlated in time through an asymmetric time filter. Explicit time discretisation, combined with meshless local radial basis function collocation method, is employed. Five-noded subdomains, non-uniform node arrangement and multiquadrics shape functions are used for solving a two-dimensional model. The sensitivity to different node arrangements, time steps, inlet temperature, and velocity boundary conditions is elaborated and successfully verified by comparison with our previously published meshless k − ε turbulence model of the same process.

개선된 PANS 난류 모델을 이용한 둥근 모서리가 있는 사각 실린더 주위 난류 유동에 대한 수치 모사

Computational simulations of turbulent flows around a square cylinder with rounded corners were performed to investigate turbulent characteristics at sub-critical and critical Reynolds numbers. A hybrid combination of unresolved turbulence viscosity in PANS and sub-grid scale turbulence viscosity in LES provided a good agreement of drag coefficient and vortex shedding frequency with previous results whereas k-ω SST model in RANS simulation failed to describe a transitional behavior of drag coefficient and vortex shedding frequency at sub-critical and critical Reynolds numbers.

Adaptive detached eddy simulation of transition under the influence of free-stream turbulence and pressure gradient

Abstract

A hybrid immersed boundary/wall-model approach for large-eddy simulation of high-Reynolds-number turbulent flows

We propose an improved hybrid immersed boundary (IB)/wall-model approach for high-Reynolds-number large-eddy simulations (LES). A preliminary test shows that the existing model that modifies sub-grid viscosity based on the mixing-length model leads to deviation of the wall shear stress when implemented at high Reynolds numbers. To correct the deviation of the wall shear stress at high Reynolds numbers, the sub-grid viscosity at the border of the IB force is reconstructed based on the near-wall balance of shear stress. A correct value for wall shear stress can thus feed back to the border of the IB force and LES solution. The proposed method is tested on several numerical examples, namely a turbulent pipe-flow with friction Reynolds numbers up to 1.0×105, turbulent flow over a circular cylinder with Reynolds numbers up to 1.4×105, turbulent flow over a sphere with Reynolds numbers up to 1.0×104, and turbulent flow over a pitching airfoil with a Reynolds number of 4.8×104. The results provide reasonable predictions compared with previous studies.

Defect-deferred correction method based on a subgrid artificial viscosity modeling

An alternative first step approximation based on subgrid artificial viscosity modeling (SAV) is proposed for defect-deferred correction method (DDC) for incompressible Navier-Stokes equation at high Reynolds number. This new approach not only preserves all qualifications of the conventional artificial viscosity (AV) based DDC, such as unconditional stability, high order of accuracy and so on, it has also shown its superiority over choosing AV approximation in the predictor step. Both theory and computational results presented in this paper illustrate that this alternative approach indeed increases the efficiency of the DDC method.

Defect-deferred correction method based on a subgrid artificial viscosity model for fluid-fluid interaction

A defect-deferred correction method, increasing both temporal and spatial accuracy, for fluid-fluid interaction problem with nonlinear interface condition is considered by geometric averaging of the previous two-time levels. In the defect step, an artificial viscosity is added only on the fluctuations in the velocity gradient by removing this effect on a coarse mesh. The dissipative influence of the artificial viscosity is further eliminated in the correction step while gaining additional temporal accuracy at the same time. The stability and accuracy analyses of the resulting algorithm are investigated both analytically and numerically.

개선된 PANS 난류 모델을 이용한 높은 레이놀즈 수를 갖는 실린더 주위 난류 유동에 대한 수치 모사

Computational simulations of turbulent flows around a circular cylinder were performed to investigate the drag coefficient and Strouhal number at sub-critical and critical Reynolds numbers. Unstructured grids with 3.1 million cells including prism layers were used in the present study. Both RANS and PANS simulations using k-ω SST model failed to predict a transitional behavior of drag coefficient and vortex shedding frequency at sub-critical and critical Reynolds numbers due to the absence of laminar separation bubble. But a hybrid combination of unresolved turbulence viscosity in PANS and sub-grid scale turbulence viscosity in LES provided a good agreement of drag coefficient and vortex shedding frequency with previous results.

Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height

In this work we present a Reduced Basis VMS-Smagorinsky Boussinesq model, applied to natural convection problems in a variable height cavity, in which the buoyancy forces are involved. We take into account in this problem both physical and geometrical parametrizations, considering the Rayleigh number as a parameter, so as the height of the cavity. We perform an Empirical Interpolation Method to approximate the sub-grid eddy viscosity term that lets us obtain an affine decomposition with respect to the parameters. We construct an a posteriori error estimator, based upon the Brezzi–Rappaz–Raviart theory, used in the greedy algorithm for the selection of the basis functions. Finally we present several numerical tests for different parameter configuration.

An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows

This report extends the mathematical support of a subgrid artificial viscosity (SAV) method to simulate the incompressible Navier-Stokes equations to better performing a linearly extrapolated BDF2 (BDF2LE) time discretization. The method considers the viscous term as a combination of the vorticity and the grad-div stabilization term. SAV method introduces global stabilization by adding a term, then anti-diffuses through the extra mixed variables. We present a detailed analysis of conservation laws, including both energy and helicity balance of the method. We also show that the approximate solutions of the method are unconditionally stable and optimally convergent. Several numerical tests are presented for validating the support of the derived theoretical results.

On the use of dynamic turbulence modelling in fire applications

In an attempt to make a step forward towards predictive fire modelling, the application of turbulence modelling approaches, calculating the sub-grid scale viscosity, kinetic energy, turbulent Prandtl and Schmidt numbers based on a dynamic procedure, has been tested on a wide range of pool fire scenarios (i.e., MaCFP workshop test cases). Through the use of Large Eddy Simulations, it is investigated whether the applied modelling approaches can accurately predict the pool fire dynamics on different grid sizes and result in improved predictions compared to models using constant parameters. Additionally, it is evaluated whether the theoretical constants related to turbulence modelling, derived from isotropic decaying turbulence scenarios, are justified in turbulent buoyant flows.

Large Eddy Simulations of cavitating tip vortex flows

In the current study, tip vortex flows are numerically studied by employing Large Eddy Simulation. Wet flow, cavitation inception, and cavitating tip vortex simulations are carried out on an elliptical foil. The mesh resolution requirements for tip vortex prediction are evaluated by employing different mesh resolutions. Two different LES models, Implicit LES and Localized Dynamic Kinematic Model, are utilized to model the sub-grid scale viscosity, and its impacts on the tip vortex prediction.For the wet flow, vortex properties are computed for each resolution and compared with experimental data. Comparisons show that at least 16 cells per vortex radius is required to predict the tip vortex in the near field region. Employed numerical approach is fully capable of capturing the accelerated axial velocity at the vortex core, and shows good agreement with the experimental observations.The analysis of bubble dynamics shows that tip vortex inception strongly depends on the initial bubble radius, especially where the radius is smaller than 50μm. The predicted azimuthal velocity, the diameter of the cavitating tip vortex, and the velocity flow fields are compared with experimental measurements. The comparisons show that the current numerical approach can provide accurate prediction of tip vortex flows also in cavitating conditions.

Resolved dynamics and subgrid stresses in separating and reattaching flows

Direct numerical simulation data of the separating and reattaching flow around a blunt bluff body are used for the assessment of the combined role played by the numerical resolution and subgrid turbulence closure in large eddy simulation. The ability of the large-scale resolved field to capture the main flow features is first analyzed. The behavior of the intensity of the resolved fluctuations as a function of the filter lengths reveals a higher sensitivity of the resolved flow on a reduction of resolution in the streamwise direction rather than in the spanwise one. On the other hand, the analysis of the subgrid stresses shows the presence of two challenging phenomena, a reversal of flow of energy from the fluctuating to the mean field in the leading-edge shear layer and a backward energy transfer from small to large scale within the main recirculating bubble. These two phenomena challenge for subgrid closures that should be able to reproduce a flow of energy from the space of small unknown subgrid scales to drive the resolved mean and fluctuating motion. In particular, it is found that the formalism of subgrid viscosity models allows us to capture neither the negative turbulence production of the leading-edge shear layer nor the backward energy transfer within the main flow recirculation. On the other hand, the subgrid similarity models are able to capture both these two phenomena but, from a quantitative point of view, the intensity of the reproduced stresses is very weak. In conclusion, the need of subgrid closures based on a mixed modeling approach for the solution of the flow is envisaged.