Compressible Turbulence Research Articles

: A high-order discontinuous Galerkin solver for flow simulations and multi-physics applications

We present the latest developments of our High-Order Spectral Element Solver (▪), an open source high-order discontinuous Galerkin framework, capable of solving a variety of flow applications, including compressible flows (with or without shocks), incompressible flows, various RANS and LES turbulence models, particle dynamics, multiphase flows, and aeroacoustics. We provide an overview of the high-order spatial discretisation (including energy/entropy stable schemes) and anisotropic p-adaptation capabilities. The solver is parallelised using MPI and OpenMP showing good scalability for up to 1000 processors. Temporal discretisations include explicit, implicit, multigrid, and dual time-stepping schemes with efficient preconditioners. Additionally, we facilitate meshing and simulating complex geometries through a mesh-free immersed boundary technique. We detail the available documentation and the test cases included in the GitHub repository. Program summaryProgram Title:▪CPC Library link to program files:https://doi.org/10.17632/738py2shk4.1Developer's repository link:https://github.com/loganoz/horses3d.Licensing provisions: MITProgramming language: Fortran 2008External routines/libraries: METIS, MPI, HDF5, MKL, PETSc (all are optional).Nature of problem:▪ is a high-order discontinuous Galerkin framework, capable of solving a variety of flow applications, including compressible flows (with or without shocks), incompressible flows, various RANS and LES turbulence models, particle dynamics, multiphase flows, and aeroacoustics.Solution method: high-order discontinuous Galerkin Spectral Element (DGSEM) and explicit/implicit time-steppers.Additional comments including restrictions and unusual features:▪ is a multiphysics environment where the compressible Navier-Stokes equations, the incompressible Navier–Stokes equations, the Cahn–Hilliard equation and entropy–stable variants are solved. Arbitrary high–order, p–anisotropic discretisations are used, including static and dynamic p–adaptation methods (feature-based and truncation error-based). Explicit and implicit time-steppers for steady and time-marching solutions are available, including efficient multigrid and preconditioners. Numerical and analytical Jacobian computations with a colouring algorithm have been implemented. Multiphase flows are solved using a diffuse interface model: Navier–Stokes/Cahn–Hilliard. Turbulent models implemented include RANS: Spalart-Allmaras and LES: Smagorinsky, Wale, Vreman; including wall models. Immersed boundary methods can be used, to avoid creating body fitted meshes. Acoustic propagation can be computed using Ffowcs-Williams and Hawkings models. ▪ supports curvilinear, hexahedral, conforming meshes in GMSH, HDF5 and SpecMesh/HOHQMesh format. A hybrid CPU-based parallelisation strategy (shared and distributed memory) with OpenMP and MPI is followed.

Lagrangian statistics of a shock-driven turbulent dynamo in decaying turbulence

ABSTRACT Small-scale fluctuating magnetic fields of order nG are observed in supernova shocks and galaxy clusters, where its amplification is likely caused by the Biermann battery mechanism. However, these fields cannot be amplified further without the turbulent dynamo, which generates magnetic energy through the stretch-twist-fold (STF) mechanism. Thus, we present here novel 3D magnetohydrodynamic (MHD) simulations of a laser-driven shock propagating into a stratified, multiphase medium, to investigate the post-shock turbulent magnetic field amplification via the turbulent dynamo. The configuration used here is currently being tested in the shock tunnel at the National Ignition Facility (NIF). In order to probe the statistical properties of the post-shock turbulent region, we use 384 × 512 × 384 tracers to track its evolution through the Lagrangian framework, thus providing a high-fidelity analysis of the shocked medium. Our simulations indicate that the growth of the magnetic field, which accompanies the near-Saffman kinetic energy decay (Ekin ∝ t−1.15) without turbulence driving, exhibits slightly different characteristics as compared to periodic box simulations. Seemingly no distinct phases exist in its evolution because the shock passage and time to observe the magnetic field amplification during the turbulence decay are very short (∼0.3 of a turbulent turnover time). Yet, the growth rate is still consistent with those expected for compressive (curl-free) turbulence driving in subsonic, compressible turbulence. Phenomenological understanding of the dynamics of the magnetic and velocity fields are also elucidated via Lagrangian frequency spectra, which are consistent with the expected inertial range scalings in the Eulerian–Lagrangian bridge.

Compressibility effects on turbulence production

Turbulence in compressible flows plays a major role in a variety of applications such as air/fuel mixing strategies for scramjet combustors. Therefore, the ability of controlling its production is of particular interest. However, compressible turbulence is more challenging than its incompressible counterpart due to the fact that thermodynamic quantities also fluctuate. In particular, the compressible turbulent kinetic energy production is a function of both velocities and density fluctuations. The so-called Morkovin's hypothesis has been often used in the literature to express the density fluctuations as a function of the velocity ones and the local Mach number. In this work, we discuss the validity of this hypothesis, and we use its expression to reformulate the turbulence production as a function of velocity only. The resulting expression shows that the planar component of turbulence production is substantially unaffected by compressibility effects. This result validates a previous work aimed at the sustainment of turbulence production using streamwise vortices. On the other hand, the turbulence production terms aligned with the convective velocity are affected by compressibility, even at relatively low Mach numbers.

Vapor mixing in turbulent vaporizing flows

Scalar mixing and evaporation processes are analyzed in a compressible two-phase homogeneous and isotropic turbulence configuration. To this end, the fully compressible Navier–Stokes equations are solved using a pressure-based method and a mass-conservative interface capturing method (CLSVOF). Temperature and vapor mass fraction transport equations are coupled with the momentum equation via the evaporation rate: i.e. heat and mass transfer has an effect on the flow dynamic through the generation of a Stefan flow at the interface. In this formalism, a pressure equation is developed to include the acoustic, thermal dilatation and compressibility effects. Moreover, the method can consider several gas structures in the same domain, each with independent temperature, density, and thermodynamic pressure. The latter is important to simulate atomization, where interaction among the liquid structures (such as breakup or coalescence) can generate multiple gas inclusions. This work is one of the first to describe with high fidelity the vaporization and turbulent mixing occurring in dense two-phase flows.A statistical analysis of the vapor mass fraction field is performed. The obtained results reveal the influence of the non-homogeneous scalar source at the interface, which depend directly on the local interface temperature, on the PDF shape. Under these conditions, the vapor mass fraction PDF deviates from the Gaussian and beta PDF shapes, frequently used for turbulent combustion modeling. Furthermore, access to the local surface averaged vapor mass fraction and evaporation rate at the interface allows a statistical analysis of these variables. Results show a large dispersion of both quantities, especially at the early times of the simulations, which contradict the usual assumption of a constant vapor mass fraction (or vaporization rate) at the interface used in the literature in standard vaporization models. Finally, the influence of the mean interface curvature on the evaporation rate is quantified and discussed. Large evaporation rate are present when the interface is convex (positive mean curvature). On the contrary, local saturation zones are present near concave interface (negative mean curvature), reducing the evaporation rate magnitude.

Multiple-GPU accelerated high-order gas-kinetic scheme for direct numerical simulation of compressible turbulence

High-order gas-kinetic scheme (HGKS) has become a workable tool for the direct numerical simulation (DNS) of turbulence. In this paper, to accelerate the computation, HGKS is implemented with the graphical processing unit (GPU) using the compute unified device architecture (CUDA). Due to the limited available memory size, the computational scale is constrained by single GPU. For large-scale DNS of turbulence, we develop a multi-GPU HGKS simulation using message passing interface (MPI) and CUDA. The benchmark cases for compressible turbulence, including Taylor-Green vortex and turbulent channel flows, are presented to assess the numerical performance of HGKS with Nvidia TITAN RTX and Tesla V100 GPUs. For single-GPU computation, compared with the parallel central processing unit (CPU) code running on the Intel Core i7-9700 with open multi-processing (OpenMP) directives, 7x speedup is achieved by TITAN RTX and 16x speedup is achieved by Tesla V100. For multiple-GPU computation, multiple-GPU accelerated HGKS code scales properly with the increasing number of GPU. The computational time of parallel CPU code running on 1024 Intel Xeon E5-2692 cores with MPI is approximately 3 times longer than that of GPU code using 8 Tesla V100 GPUs with MPI and CUDA. Numerical results confirm the excellent performance of multiple-GPU accelerated HGKS for large-scale DNS of turbulence. Besides reducing memory access pressure, we also exploit single precision floating point arithmetic to accelerate HGKS on GPUs. Reasonably, compared to the computation with FP64 precision, the efficiency is improved and the memory cost is reduced with FP32 precision. Meanwhile, the differences in accuracy for statistical turbulent quantities appear. For turbulent channel flows, difference in long-time statistical turbulent quantities is acceptable between FP32 and FP64 precision solutions. While the obvious discrepancy in instantaneous turbulent quantities can be observed, which shows that FP32 precision is not safe for DNS in compressible turbulence. The choice of precision should be depended on the requirement of accuracy and the available computational resources.

Probing 3D magnetic fields – I. Polarized dust emission

ABSTRACT Polarized dust emission is widely used to trace the plane-of-the-sky (POS) component of interstellar magnetic fields in two dimensions. Its potential to access 3D magnetic fields, including the inclination angle of the magnetic fields relative to the line of sight (LOS), is crucial for a variety of astrophysical problems. Based on the statistical features of observed polarization fraction and POS Alfvén Mach number $\overline{M_{\rm A}}_{,\bot }$ distribution, we present a new method for estimating the inclination angle. The magnetic field fluctuations raised by anisotropic magnetohydrodynamic (MHD) turbulence are taken into account in our method. By using synthetic dust emission generated from 3D compressible MHD turbulence simulations, we show that the fluctuations are preferentially perpendicular to the mean magnetic field. We find the inclination angle is the major agent for depolarization, while fluctuations of magnetic field strength and density have an insignificant contribution. We propose and demonstrate that the mean inclination angle over a region of interest can be calculated from the polarization fraction in a strongly magnetized reference position, where $\overline{M_{\rm A}}_{,\bot }^2\ll 1$. We test and show that the new method can trace the 3D magnetic fields in sub-Alfvénic, trans-Alfvénic, and moderately superAlfvénic conditions (0.4 ≲ MA ≲ 1.2). We numerically quantify that the difference of the estimated inclination angle and actual inclination angle ranges from 0° to 20° with a median value of ≤10°.

A Modal-Decay-Based Shock-Capturing Approach for High-Order Flux Reconstruction Method

The increasing demand for high-fidelity simulations of compressible turbulence on complex geometries poses a number of challenges for numerical schemes, and plenty of high-order methods have been developed. The high-order methods may encounter spurious oscillations or even blow up for strongly compressible flows, and a number of approaches have been developed, such as slope limiters and artificial viscosity models. In the family of artificial viscosity, which measures smoothness using the modal coefficients, the averaged modal decay (MDA) model employs all of the modes instead of only the highest mode as in the highest modal decay (MDH) model, which tends to underestimate the smoothness. However, the MDA approach requires high-order accuracy (usually P≥4) to deliver a reliable estimation of smoothness. In this work, an approach used to extend the MDA model to lower orders, such as P2 and P3, referred to as MDAEX, was proposed, where neighboring elements were incorporated to involve more information in the estimation process. A further controlling of the value of artificial viscosity was also introduced. The proposed model was applied to several typical benchmark cases and compared with other typical models. The results show that the MDAEX model recovers the expected accuracy better than the MDA model for P2 and P3 and captures flow structures well for shock-dominated flows.

Transmittance and energy transfer of Gaussian beam propagation in anisotropic compressible turbulence

Turbulence affects the transmittance of optical wave propagation. Reduced transmittance causes increased power loss in wireless communication systems. This phenomenon is even more pronounced in compressible turbulence, which generally occurs near supersonic or hypersonic aircraft. Compressible turbulence alters the level of power attenuation on optical wave propagation, reducing the performance of aircraft communication. In this paper, the wave structure function (WSF) and optical intensity of a Gaussian beam propagating in anisotropic compressible turbulence are deduced. The effect of anisotropic compressible turbulence on a Gaussian beam is investigated. The results show that the essential effect of turbulence on Gaussian beams is the dispersion of energy instead of attenuation. Anisotropic compressible turbulence improves the power efficiency of wireless communication systems. In addition, compressible turbulence effects on the transmittance of Gaussian beams are represented versus wavelengths and waist widths of the beams.

Large eddy simulation of highly compressible film cooling in transonic crossflow

Large eddy simulation is performed to study the thermal energy transport and mixing process of compressible film cooling in the fully-turbulent high-Mach-number crossflow. Three Mach numbers, 0.8, 1.2, and 1.4, based on the bulk crossflow velocity, are adopted. And the influence of both the compressibility and shock waves on the transverse jet from cylindrical orifices is discussed in detail. The results reveal that the effects of compressibility should be distinguished from shocks in supersonic flows. The compressibility effect strengthens the jet penetration and lateral spreading by increasing the energy contained in the large-scale coherent structures. The mixing of the jet is enhanced by the strong compressibility in the near field whether shocks exist or not. When the crossflow transits from the subsonic to the supersonic state, the effect of shock waves becomes more significant than that of the compressibility. Various interactions between shocks, coherent structures, and thermal energy transport are analyzed in this study. The results show that the appearance of the separation shock and bow shock reduces the jet penetration and strengthens its interaction with the bottom wall. The generation of this type of shock system suppresses the flow separation on the leeward side of the jet, which results in a higher cooling effectiveness in the jet near field. The incident oblique shock wave also induces lifting of the jet trajectory in the far-field region as a result of the intensified separation trend. In the highly compressible film cooling process with great temperature difference, the advection transport associated with turbulent motion, rather than the one associated with mean motion, turns out to dominate the thermal energy transfer in general. Moreover, the counter gradient behavior of this thermal energy transport in compressible turbulence is also shown.

Cascade of circulicity in compressible turbulence

The purpose of this work is to investigate whether a cascading process can be associated with the rotational motions of compressible three-dimensional turbulence. This question is examined through the lens of circulicity, a concept related to the angular momentum carried by large turbulent scales. Point-splitting and coarse-graining analyses are performed in order to uncover some properties of the circulicity nonlinear transfer flux. These properties are established independently from the expression of the equation of state.

A study of initial conditions' effects on thermal properties of compressible homogeneous sheared non-isentropic turbulence using rapid distortion theory (RDT)

This paper investigates the effect of initial conditions characterized by compressibility of turbulence on the changes in scalar such as density, temperature, and pressure within the framework of rapid distortion theory (RDT) in the case of non-isentropic turbulence. This study is a follow-up of the basic work carried out by A. Simone, G.N. Coleman and C. Cambon [J. Fluid Mech. 330, 307 (1997)] in the case of quasi-isentropic turbulence and the previous work of M. Riahi and T. Lili [Fluid Dyn. Res. 52, 025501 (2020)] in the case of non-isentropic turbulence. RDT was used to examine the behavior of the root mean square (rms) fluctuations of density, temperature, and pressure. The coupling between these rms quantities, the partition factor, and the polytropic coefficient was also studied. RDT equations were solved numerically using a code that solves directly evolution equations of two-point spectral correlations for compressible homogeneous sheared non-isentropic turbulence. The RDT analysis was carried out for various initial turbulent Mach numbers Mt 0 ranging from 0.1 to 0.4, and the initial compressible turbulence is to be one of the three states concerning the fraction of kinetic energy χ0: solenoidal ( χ0 = 0), mixed ( χ0 = 0.6), and dilatational ( χ0 = 1) ( χ0 is the ratio of the initial dilatational kinetic energy to the initial total kinetic energy). It is shown from this study that the changes in scalars are strongly dependent on the initial conditions. Magnitudes and asymptotic values of rms thermodynamics fluctuations and correlations between these thermodynamics fluctuations depend of Mt 0. For large times, the isentropic state of the flow is well observed whatever Mt 0 and χ0.

Effect of heat source on kinetic energy transfer in compressible homogeneous shear turbulence

The effects of heat sources on kinetic energy transfer in compressible homogeneous shear turbulence are studied using numerical simulations at turbulent Mach numbers 0.1 and 0.4 for two levels of heat source. It is found that the strong heat source can significantly enhance both positive and negative components of subgrid-scale (SGS) kinetic energy flux and pressure–dilatation. After adding a strong heat source, compression motions enhance the positive SGS flux, and expansion motions enhance the negative SGS flux at a low turbulent Mach number. According to the Helmholtz decomposition, we found that the solenoidal and dilatational components of pressure–dilatation and SGS kinetic energy flux are increased greatly by a strong heat source at a low turbulent Mach number. The solenoidal mode plays a dominant role in the kinetic energy transfer process, but the contribution of the dilatational mode is not negligible. The dilatational component of the production term is increased by a strong heat source at a low turbulent Mach number, providing the main source of kinetic energy to the dilatational mode. The strong heat source also enhances the kinetic energy exchange between solenoidal mode and dilatational mode through nonlinear advection at a low turbulent Mach number. Moreover, the strong heat source enhances pressure anisotropy, redistribution of the kinetic energy of two transverse components, and energy transfer from internal energy to the kinetic energy through pressure–dilatation term. At a high turbulent Mach number, the strong heat source has little impact on the solenoidal and dilatational components of kinetic energy transfer terms.

Direct numerical simulation of compressible turbulence accelerated by graphics processing unit: An open-source high accuracy accelerated computational fluid dynamic software

This paper introduces open-source computational fluid dynamics software named open computational fluid dynamic code for scientific computation with graphics processing unit (GPU) system (OpenCFD-SCU), developed by the authors for direct numerical simulation of compressible wall-bounded turbulence. This software is based on the finite difference method and is accelerated by the use of a GPU, which provides an acceleration by a factor of more than 200 compared with central processing unit (CPU) software based on the same algorithm and a number of Message Passing Interface processes, and the running speed of OpenCFD-SCU with just 512 GPUs exceeds that of CPU software with 130 000 CPUs. GPU-Stream technology is used to implement overlap of computing and communication, achieving 98.7% parallel weak scalability with 24 576 GPUs. The software includes a variety of high-precision finite difference schemes and supports a hybrid finite difference scheme, enabling it to provide both robustness and high precision when simulating complex supersonic and hypersonic flows. When used with the wide range of supercomputers currently available, the software should be able to improve the performance of large-scale simulations by up to two orders on the computational scale. Then, OpenCFD-SCU is applied to a validation and verification case of a Mach 2.9 compression ramp with mesh numbers up to 31.2 × 109.

Dynamic iterative approximate deconvolution model for large-eddy simulation of dense gas compressible turbulence

We study large-eddy simulation of compressible decaying isotropic turbulence of dense gas at initial turbulent Mach numbers of 0.4 and 0.8. The unclosed subgrid-scale (SGS) terms are approximated by the dynamic iterative approximate deconvolution (DIAD) model proposed by Yuan et al. [“Dynamic iterative approximate deconvolution models for large-eddy simulation of turbulence,” Phys. Fluids 33, 085125 (2021)], and compared with the dynamic Smagorinsky (DSM) model. In an a priori test, the correlation coefficients of the DIAD model for most SGS terms are larger than 0.98, and the relative errors are smaller than 0.2, except for the SGS internal energy flux. In an a posteriori test, the DIAD model can well predict the probability density functions (PDFs) of SGS terms involving thermodynamic variables. Moreover, the DIAD model shows greater advantages than the DSM model in predicting various statistics and structures of compressible turbulence of dense gas, including spectra of velocity and thermodynamic variables, PDFs of SGS kinetic energy flux, deviatoric SGS stress and normalized strain-rate tensor, and the instantaneous spatial structures of vorticity.

Modeling and simulation in supersonic three-temperature carbon dioxide turbulent channel flow

This paper pioneers the direct numerical simulation (DNS) and physical analysis in supersonic three-temperature carbon dioxide (CO2) turbulent channel flow. CO2 is a linear and symmetric triatomic molecular, with the thermal non-equilibrium three-temperature effects arising from the interactions among translational, rotational, and vibrational modes at room temperature. Thus, the rotational and vibrational modes of CO2 are addressed. The thermal non-equilibrium effect of CO2 has been modeled in an extended three-temperature kinetic model, with the calibrated translational, rotational, and vibrational relaxation time. To solve the extended kinetic equation accurately and robustly, non-equilibrium high-accuracy gas-kinetic scheme is proposed within the well-established two-stage fourth-order framework. Compared with the one-temperature supersonic turbulent channel flow, supersonic three-temperature CO2 turbulence enlarges the ensemble heat transfer of the wall by approximate 20% and slightly decreases the ensemble frictional force. The ensemble density and temperature fields are greatly affected, and there is little change in Van Driest transformation of streamwise velocity. The thermal non-equilibrium three-temperature effects of CO2 also suppress the peak of normalized root mean square of density and temperature, normalized turbulent intensities and Reynolds stress. The vibrational modes of CO2 behave quite differently with rotational and translational modes. Compared with the vibrational temperature fields, the rotational temperature fields have the higher similarity with translational temperature fields, especially in temperature amplitude. Current thermal non-equilibrium models, high-accuracy DNS and physical analysis in supersonic CO2 turbulent flow can act as the benchmark for the long-term applicability of compressible CO2 turbulence.

Turbulent Reacceleration of Streaming Cosmic Rays

Subsonic, compressive turbulence transfers energy to cosmic rays (CRs), a process known as nonresonant reacceleration. It is often invoked to explain the observed ratios of primary to secondary CRs at ∼GeV energies, assuming wholly diffusive CR transport. However, such estimates ignore the impact of CR self-confinement and streaming. We study these issues in stirring box magnetohydrodynamic (MHD) simulations using Athena++, with field-aligned diffusive and streaming CR transport. For diffusion only, we find CR reacceleration rates in good agreement with analytic predictions. When streaming is included, reacceleration rates depend on plasma β. Due to streaming-modified phase shifts between CR and gas variables, they are slower than canonical reacceleration rates in low-β environments like the interstellar medium but remain unchanged in high-β environments like the intracluster medium. We also quantify the streaming energy-loss rate in our simulations. For sub-Alfvénic turbulence, it is resolution dependent (hence unconverged in large-scale simulations) and heavily suppressed compared to the isotropic loss rate v A · ∇P CR/P CR ∼ v A/L 0, due to misalignment between the mean field and isotropic CR gradients. Unlike acceleration efficiencies, CR losses are almost independent of magnetic field strength over β ∼ 1–100 and are, therefore, not the primary factor behind lower acceleration rates when streaming is included. While this paper is primarily concerned with how turbulence affects CRs, in a follow-up paper we consider how CRs affect turbulence by diverting energy from the MHD cascade, altering the pathway to gas heating and steepening the turbulent spectrum.

Direct numerical simulation of compressible turbulence accelerated by graphics processing unit: An open-access database of high-resolution direct numerical simulation

In the author’s previous work, we introduced an open-source accelerated computational fluid dynamics code for scientific computations using a graphics processing unit system (OpenCFD-SCU). This code offers significantly improved computation speed and can be applied to challenging direct numerical simulation (DNS) problems. This paper presents several high-resolution cases using OpenCFD-SCU: (1) a 24° compression ramp at Mach 2.9, where the length of the ramp is 200 mm and the mesh number is 7.68 × 109; (2) a 34° compression ramp at Mach 6 with a mesh number of 9.3 × 109; (3) a cold-wall flat plate at Mach 10 with a friction Reynolds number of 1550 and mesh number of 4.5 × 109; (4) a blunt cone with a 1 mm head radius and 0° attack angle at Mach 10, where the mesh number is 24 × 109; and (5) a lifting-body model at Mach 6 with a mesh number of 11.1 × 109. Compared with DNS studies of compressible wall-bound turbulent flow under similar conditions, these cases have larger computational domains, finer resolutions, or higher Reynolds numbers, demonstrating the simulation capability of OpenCFD-SCU and broadening the scope of DNS applications. We have conducted preliminary analyses of these cases and have established an open-access database to store these data. The source code of OpenCFD-SCU can be accessed at http://developer.hpccube.com/codes/danggl/opencfd-scu.git; this website also contains detailed database descriptions and data acquisition methods.

Suitability of an Artificial Viscosity Model for Compressible Under-Resolved Turbulence Using a Flux Reconstruction Method

In the simulation of compressible turbulent flows via a high-order flux reconstruction framework, the artificial viscosity model plays an important role to ensure robustness in the strongly compressible region. However, the impact of the artificial viscosity model in under-resolved regions on dissipation features or resolving ability remains unclear. In this work, the performance of a dilation-based (DB) artificial viscosity model to simulate under-resolved turbulent flows in a high-order flux reconstruction (FR) framework is investigated. Comparison is conducted with results via several typical explicit subgrid scale (SGS) models as well as implicit large eddy simulation (iLES) and their impact on important diagnostic quantities including turbulent kinetic energy, total dissipation rate of kinetic energy, and energy spectra are discussed. The dissipation rate of kinetic energy is decomposed into several components including those resulting from explicit SGS models or Laplacian artificial viscosity model; thus, an explicit evaluation of the dissipation rate led by those modeling terms is presented. The test cases consist of the Taylor-Green vortex (TGV) problem at Re=1600, the freely decaying homogeneous isotropic turbulence (HIT) at Mat0=0.5 (the initial turbulent Mach number ), the compressible TGV at Mach number 1.25 and the compressible channel flow at Reb= 15,334 (the bulk Reynolds number based on bulk density, bulk velocity and half-height of the channel), Mach number 1.5. The first two cases show that the DB model behaves similarly to the SGS models in terms of dissipation and has the potential to improve the insufficient dissipation of iLES with the fourth-order-accurate FR method. The last two cases further demonstrate the ability of the DB method on compresssible under-resolved turbulence and/or wall-bounded turbulence. The results of this work suggest the general suitability of the DB model to simulate under-resolved compressible turbulence in the high order flux reconstruction framework and also suggest some future work on controlling the potential excessive dissipation caused by the dilation term.

Mean Velocity Scaling of High-Speed Turbulent Flows Under Nonadiabatic Wall Conditions

The problem of scaling the near-wall mean velocity profiles of turbulent flows and collapsing them with the law of the wall has been traditionally studied using the conservation of momentum, by employing various levels of assumptions. In the van Driest transformation (“Turbulent Boundary Layer in Compressible Fluids,” Journal of the Aeronautical Sciences, Vol. 18, No. 3, 1951, pp. 145–216), the viscous stress was neglected, whereas in the Trettel and Larsson transformation (“Mean Velocity Scaling for Compressible Wall Turbulence with Heat Transfer,” Physics of Fluids, Vol. 28, No. 2, 2016, Paper 026102), the Reynolds stress was assumed to cancel out. Recent work by Griffin, Fu, and Moin (“Velocity Transformation for Compressible Wall-Bounded Turbulent Flows with and Without Heat Transfer,” Proceedings of the National Academy of Sciences of the United States of America, Vol. 118, No. 34, 2021, Paper e2111144118) used a quasi-equilibrium assumption between turbulence production and dissipation in the log layer and demonstrated success for a wide variety of canonical flows. However, the extent of quasi-equilibrium is not verified, particularly for noncanonical flows. In this work, an alternate transformation is developed using the semilocal gradient of the van Driest transformed velocity, which is principally tied to the dynamics of vorticity transport in the boundary layer. In addition, a modified stress balance is utilized to directly account for and scale the buffer region. The transformation was benchmarked using a similar dataset as in Griffin et al., and comparable performance was obtained. Moreover, at supercritical pressures, the present transformation is found to produce significantly better collapse than existing works.

The role of the turbulence driving mode for the initial mass function

ABSTRACT Turbulence is a critical ingredient for star formation, yet its role for the initial mass function (IMF) is not fully understood. Here we perform magnetohydrodynamical (MHD) simulations of star cluster formation including gravity, turbulence, magnetic fields, stellar heating, and outflow feedback to study the influence of the mode of turbulence driving on IMF. We find that simulations that employ purely compressive turbulence driving (COMP) produce a higher fraction of low-mass stars as compared to simulations that use purely solenoidal driving (SOL). The characteristic (median) mass of the sink particle (protostellar) distribution for COMP is shifted to lower masses by a factor of ∼1.5 compared to SOL. Our simulation IMFs capture the important features of the observed IMF form. We find that turbulence-regulated theories of the IMF match our simulation IMFs reasonably well in the high-mass and low-mass range, but underestimate the number of very low-mass stars, which form towards the later stages of our simulations and stop accreting due to dynamical interactions. Our simulations show that for both COMP and SOL, the multiplicity fraction is an increasing function of the primary mass, although the multiplicity fraction in COMP is higher than that of SOL for any primary mass range. We find that binary mass ratio distribution is independent of the turbulence driving mode. The average specific angular momentum of the sink particles in SOL is a factor of 2 higher than that for COMP. Overall, we conclude that the turbulence driving mode plays a significant role in shaping the IMF.