Exponential time integration using Krylov subspaces

The application of exponential integrators based on Krylov techniques to large‐scale simulations of complex fluid flows with multiple time‐scales demonstrates the efficiency of these schemes in reducing the associated time‐step restrictions due to numerical stiffness. Savings of approximately 50% can be achieved for simulations of the three‐dimensional compressible Navier–Stokes equations while still maintaining a truncation error typical of explicit time‐stepping schemes. Exponential time integration techniques of this type are particularly advantageous for fluid flows with a wide range of temporal scales such as low‐Mach number, reactive or acoustically dominated flows. Copyright © 2008 John Wiley & Sons, Ltd.     

Galerkin finite element simulation of convection driven by rotation and gravitation

The performance of the Galerkin finite element method when applied to time-dependent convection involving rotation, self-gravitation and the normal gravity field in a horizontal cylinder is discussed in this paper. The governing equations, the parameters of the problem and our implementation of the numerical schemes are presented. The accuracy, spatial scale of resolution, flexibility and robustness of the resulting code show the element method as a valuable tool for research in this area or in related problems in astrophysical fluid dynamics. The numerical difficulties in large-amplitude flows are associated with an error-control scheme for time integration and the ‘short-time’ wiggles in transient Dirichlet problems. Coarse grids give the correct qualitative picture in most simulations, but the type of solution at short time (and hence grid refinement) presumably resolves the degeneracy in the azimuthal orientation of convection cells in flows driven by self-gravitation and (perhaps) centrifugal buoyancy. The final state in transient flows is a motionless isothermal fluid. However, residual motions can be nullified only in the limit of zero grid size in flows driven by centrifugal buoyancy (self-gravitation), while a fairly coarse grid is sufficient for this purpose in normal gravity-driven flows.     

A diffuse-interface approach to two-phase isothermal flow of a Van der Waals fluid near the critical point

A novel numerical method for simulations of isothermal, compressible two-phase flows of one fluid component near the critical point is presented on the basis of a diffuse-interface model and a Van der Waals equation of state. Because of the non-convexity of the latter, the nature of the set of governing equations is mixed hyperbolic–elliptic. This prevents the application of standard numerical methods for compressible flow. Moreover, the Korteweg capillary stress tensor, characteristic for the diffuse-interface approach, introduces third-order spatial derivatives of mass density in the Navier–Stokes equation, resulting in a dispersive behavior of the solution. Our computational method relies on a transformation of the conserved variables, which controls dispersion, stabilizes the numerical simulation and enables the use of coarser grids. A one-dimensional simulation shows that this method provides better stability and accuracy than without transformation of variables. Two- and three-dimensional simulations for isothermal liquid–vapor flows, in particular the retraction of a liquid non-spherical drop in vapor and the binary droplet collision in vapor, show the applicability of the method. The surface tension calculated from the numerical results is in good agreement with its theoretical value if the computational grid is sufficiently fine.     

Surface breakup of a non-turbulent liquid jet injected into a high pressure gaseous crossflow

We employ detailed numerical simulations to understand the physical mechanism underlying the surface breakup of a non-turbulent liquid jet injected transversely into a high pressure gaseous crossflow under isothermal conditions. The numerical observations reveal the existence of shear instability on the jet periphery as the primary destabilization mechanism. The temporal growth of such azimuthal instabilities leads to the formation of interface corrugations, which are eventually sheared off of the jet surface as sheet-like structures. The sheets next undergo disintegration into ligaments and drops during the surface breakup process. The proposed instability mechanism is inherently an inviscid mechanism, contrary to the previously suggested mechanism of surface breakup (known as “boundary layer stripping”), which is relied on a viscous interpretation. The numerically obtained length and time scales of the shear instabilities on the jet laterals are compared with the results of Behzad et al. (2015) on temporal linear stability analyses of a jet in crossflow at near the nozzle. The stability characteristics of the most amplified modes (i.e., the wavenumber and the corresponding growth rate) obtained from the numerical simulations and the stability analyses are in good agreement.     

Vortices for computing: the engines of turbulence simulation

Vortices have been described as the “sinews of turbulence”. They are also, increasingly, the computational engines driving numerical simulations of turbulence. In this paper, I review some recent advances in vortex-based numerical methods for simulating high Reynolds number turbulent flows. I focus on coherent vortex simulation, where nonlinear wavelet filtering is used to identify and track the few high energy multiscale vortices that dominate the flow dynamics. This filtering drastically reduces the computational complexity for high Reynolds number simulations, e.g. by a factor of 1000 for fluid–structure interaction calculations (Kevlahan and Vasilyevvon in SIAM J Sci Comput 26(6):1894–1915, 2005). It also has the advantage of decomposing the flow into two physically important components: coherent vortices and background noise. In addition to its computational efficiency, this decomposition provides a way of directly estimating how space and space–time intermittency scales with Reynolds number, Re ^α . Comparing α to its non-intermittent values gives a realistic Reynolds number upper bound for adaptive direct numerical simulation of turbulent flows. This direct measure of intermittency also guides the development of new mathematical theories for the structure of high Reynolds number turbulence.     

Multi-scale magnetic resonance measurements and validation of Discrete Element Model simulations

This short review describes the capabilities of magnetic resonance (MR) to image opaque single- and two-phase granular systems, such as rotating cylinders and gas-fluidized beds operated in different fluidization regimes. The unique capability of MR to not only image the solids’ distribution (voidage) but also the velocity of the particulate phase is clearly shown. It is demonstrated that MR can provide measurements over different length and time scales. With the MR equipment used for the studies summarized here, temporal and spatial scales range from sub-millisecond to hours and from a few hundred micrometres to a few centimetres, respectively. Besides providing crucial data required for an improved understanding of the underlying physics of granular flows, multi-scale MR measurements were also used to validate numerical simulations of granular systems. It is shown that predictions of time-averaged properties, such as voidage and velocity of the particulate phase, made using the Discrete Element Model agree very well with MR measurements.     

Modeling of Internal Reacting Flows and External Static Stall Flows Using RANS and PRNS

The reacting flow in a research lean direct injection (LDI) hydrogen combustor and the static stall of NACA0012 airfoil were simulated using both Reynolds averaged Navier–Stokes (RANS) and partially resolved numerical simulation (PRNS) approaches. The concept and the main features of the PRNS approach are briefly described. The PRNS basic equations are grid independent or grid invariant; the subscale models are a dynamic equation system. We consider PRNS as an engineering tool for the very large eddy simulation of complex turbulent flows. Two CFD codes, NCC and Wind-US, with two different subscale models (i.e. two- and one-transport equation models, respectively) are used in the presented PRNS simulations. Based on the comparisons with available experimental data, the numerical results indicate that the PRNS subscale models seem to be able to capture important large scale turbulent structures and to improve the quality of numerical simulations while keeping a relatively low cost comparable to the unsteady RANS simulations.     

Validation of averaged equations for thermal vibrational convection in near-critical fluidsValidation d'équations moyennées pour l'étude de la convection vibrationnelle dans les fluides supercritiques.

Within an averaging approach, the governing equations and effective boundary conditions describing both the average and pulsation motion of a near-critical fluid subjected to high-frequency vibrations are obtained. Vibrations induce the non-homogeneities in average temperature. Owing to these non-homogeneities, the average flows can be generated even in isothermal cavity under weightlessness. These flows are examined for 1D and 2D configurations. The direct numerical simulations fulfilled earlier confirm the averaged model, we obtain the same flow structures by essentially smaller requirements for computational time. To cite this article: A.Vorobev et al., C. R. Mecanique 332 (2004).     

Comparison of several models for multi-size bubbly flows on an adiabatic experiment

This paper deals with the modelling and numerical simulation of isothermal bubbly flows with multi-size bubbles. The study of isothermal bubbly flows without phase change is a first step towards the more general study of boiling bubbly flows. Here, we are interested in taking into account the features of such isothermal flow associated to the multiple sizes of the different bubbles simultaneously present inside the flow. With this aim, several approaches have been developed. In this paper, two of these approaches are described and their results are compared to experimental data, as well as to those of an older approach assuming a single average size of bubbles. These two approaches are (i) the moment density approach for which two different expressions for the bubble diameter distribution function are proposed and (ii) the multi-field approach. All the models are implemented into the NEPTUNE_CFD code and are compared to a test performed on the MTLOOP facility. These comparisons show their respective merits and shortcomings in their available state of development.     

A third-order compact nonlinear scheme for compressible flow simulations

Reynolds-averaged Navier-Stokes simulations based on second-order numerical methods are widely used by commercial codes and work as dominating tools for most industrial applications. They, however, suffer from limitations in accurate and reliable predictions of skin-friction drag and aerodynamic heating, as well as in simulations of complex flows such as large-scale separation and transition. A remedy for this is the development of high-order schemes, by which numerically induced dissipation and dispersion errors of low-order schemes can be effectively reduced. Weighted compact nonlinear schemes (WCNSs) are a family of high-resolution nonlinear shock-capturing methods. A stencil-selection procedure is introduced in the proposed work with an aim to improve the nonlinear weight of the third-order WCNS. By using the approximate dispersion relation analysis, it is demonstrated that the new scheme has reduced dissipation and dispersion errors, compared with WCNSs using two typical nonlinear weights. Improvements are also achieved by the new scheme in numerical tests such as the double Mach reflection problem and the Rayleigh-Taylor instability simulation, which are characterized by strong shock discontinuities and rich small scales, respectively. The new scheme is therefore highly favored in the simulation of flow problems involving strong discontinuities and multiscales phenomena.     

Short-and resonant-range interactions between scales in turbulence and their applications

Interactions between different scales in turbulence were studied starting from the incompressible Navier-Stokes equations. The integral and differential formulae of the shortrange viscous stresses, which express the short-range interactions between contiguous scales in turbulence, were given. A concept of the resonant-range interactions between extreme contiguous scales was introduced and the differential formula of the resonant-range viscous stresses was obtained. The short- and resonant-range viscous stresses were applied to deduce the large-eddy simulation ( LES ) equations as well as the multiscale equations, which are approximately closed and do not contain any empirical constants or relations. The properties and advantages of using the multiscale equations to compute turbulent flows were discussed. The short-range character of the interactions between the scales in turbulence means that the multiscale simulation is a very valuable technique for the calculation of turbulent flows. A few numerical examples were also given.     

Noise radiated by a non-isothermal,temporal mixing layer. Part I: Direct computation and prediction using compressible DNS

Direct numerical simulations (DNSs) are performed in order to study acoustic emissions generated during the transition of isothermal and non-isothermal mixing layers. The sound from temporally evolving mixing layers is computed directly using DNS for a computational domain, which includes both aerodynamic and acoustic fields. Good precision of the computed acoustic field is ensured by using a numerical code based on high-order finite difference schemes of quasi-spectral accuracy. Two- and three-dimensional simulations of mixing layers are performed for various Mach numbers and temperature ratios. For each case, the acoustic radiation of the mixing layer transition is investigated. Comparisons illustrate the importance of the combined effects of temperature and Mach number on the acoustic intensity. Qualitative agreement with existing experimental observations for hot jet flows is observed. It is also found that the appearance of three-dimensional motion leads to a substantial reduction of sound emissions. In the second part of this study, DNS data are used to perform acoustic analogy predictions. Excellent agreement between direct computations and predictions is obtained in all cases. Analysis of the source terms yields a new interpretation of temperature and Mach number effects, based on the predominance of one term over the other.     

三角翼上分离及涡流的数值模拟

综述了三角翼(包括双三角翼,边条-三角翼,近距耦合鸭翼)上分离及涡流问题的数值模拟进展,介绍了用Euler方程、N-S方程的数值方法模拟不同三角翼,在不同攻角、不同来流M数等多种条件下的复杂涡流形态和流动结构,研究了控制方程、网格、湍流模型和计算方法等对计算结果的影响。      

On predicting particle-laden turbulent flows

The paper provides an overview of the challenges and progress associated with the task of numerically predicting particle-laden turbulent flows. The review covers the mathematical methods based on turbulence closure models as well as direct numerical simulation (DNS). In addition, the statistical (pdf) approach in deriving the dispersed-phase transport equations is discussed. The review is restricted to incompressible, isothermal flows without phase change or particle-particle collision. Suggestions are made for improving closure modelling of some important correlations.Lecture presented at a workshop on turbulence in particulate multiphase flow, Fluid Dynamics Laboratory, Battelle Pacific Northwest Laboratory, Richland, WA, March 22–23, 1993.     

Analysis of low-pass filters for approximate deconvolution closure modelling in one-dimensional decaying Burgers turbulence

The idea of spatial filtering is central in approximate deconvolution large-eddy simulation (AD-LES) of turbulent flows. The need for low-pass filters naturally arises in the approximate deconvolution approach which is based solely on mathematical approximations by employing repeated filtering operators. Two families of low-pass spatial filters are studied in this paper: the Butterworth filters and the Padé filters. With a selection of various filtering parameters, variants of the AD-LES are systematically applied to the decaying Burgers turbulence problem, which is a standard prototype for more complex turbulent flows. Comparing with the direct numerical simulations, it is shown that all forms of the AD-LES approaches predict significantly better results than the under-resolved simulations at the same grid resolution. However, the results highly depend on the selection of the filtering procedure and the filter design. It is concluded that a complete attenuation for the smallest scales is crucial to prevent energy accumulation at the grid cut-off.     

基于非结构/混合网格的高阶精度格式研究进展

尽管以二阶精度格式为基础的计算流体力学(CFD) 方法和软件已经在航空航天飞行器设计中发挥了重要的作用, 但是由于二阶精度格式的耗散和色散较大, 对于湍流、分离等多尺度流动现象的模拟, 现有成熟的CFD 软件仍难以给出满意的结果, 为此CFD 工作者发展了众多的高阶精度计算格式. 如果以适应的计算网格来分类, 一般可以分为基于结构网格的有限差分格式、基于非结构/混合网格的有限体积法和有限元方法,以及各种类型的混合方法. 由于非结构/混合网格具有良好的几何适应性, 基于非结构/混合网格的高阶精度格式近年来备受关注. 本文综述了近年来基于非结构/混合网格的高阶精度格式研究进展, 重点介绍了空间离散方法, 主要包括k-Exact 和ENO/WENO 等有限体积方法, 间断伽辽金(DG) 有限元方法, 有限谱体积(SV) 和有限谱差分(SD) 方法, 以及近来发展的各种DG/FV 混合算法和将各种方法统一在一个框架内的CPR (correctionprocedure via reconstruction) 方法等. 随后简要介绍了高阶精度格式应用于复杂外形流动数值模拟的一些需要关注的问题, 包括曲边界的处理方法、间断侦测和限制器、各种加速收敛技术等. 在综述过程中, 介绍了各种方法的优势与不足, 其间介绍了作者发展的基于"静动态混合重构" 的DG/FV 混合算法. 最后展望了基于非结构/混合网格的高阶精度格式的未来发展趋势及应用前景.     

离散型湍流多相流动的研究进展和需求

离散型多相流动,指气体-颗粒(气-固)、液体-颗粒(液-固)、液体-气泡、气体-液雾以及气泡-液体-颗粒等两相或三相流动.这种类型的多相流动广泛存在于能源, 航天和航空, 化工和冶金,交通运输, 水利, 核能等领域.本文阐述了离散型多相流动的国内外基础研究,包括颗粒/液滴/气泡在流场中受流体动力作用力的研究, 颗粒-颗粒,液滴-液滴,气泡-气泡之间以及颗粒/液滴和壁面之间碰撞和聚集规律的研究,颗粒-气体和气泡-液体湍流相互作用的研究, 和数值模拟的研究,包括多相流动的雷诺平均模拟、大涡模拟和直接数值模拟的研究进展.最后, 归纳了目前尚待研究的需求.      

Possible Effects of Small-Scale Intermittency in Turbulent Reacting Flows

It is now well established that quantities such as energy dissipation, scalar dissipation and enstrophy possess huge fluctuations in turbulent flows, and that the fluctuations become increasingly stronger with increasing Reynolds number of the flow. The effects of this small-scale “intermittenc” on various aspects of reacting flows have not been addressed fully. This paper draws brief attention to a few possible effects on reaction rates, flame extinction, flamelet approximation, conditional moment closure methods, and so forth, besides commenting on possible effects on the resolution requirements of direct numerical simulations of turbulence. We also discuss the likelihood that large-amplitude events in a given class of shear flows are characteristic of that class, and that, plausible estimates of such quantities cannot be made, in general, on the hypothesis that large and small scales are independent. Finally, we briefly describe some ideas from multifractals as a potentially useful tool for an economical handling of a few of the problems touched upon here.     

Adaptive resolution refinement for pseudospectral simulations of isotropic homogeneous turbulence

Pseudospectral simulations of homogeneous turbulence provide an important class of benchmark flow problems used for fundamental studies of turbulence and for numerical validation purposes. Depending on the numerical resolution, fully resolved computations of homogeneous turbulence can consume large amounts of central processing unit (CPU) time. Here, we present an approach analogous to adaptive mesh refinement for computations performed in physical space to adaptively refine the spectral resolution for pseudospectral computations of isotropic homogeneous turbulent flows. The method is applied to simulations of two-dimensional and three-dimensional isotropic homogeneous turbulence, and the results are compared with direct numerical simulations (DNS) performed using a fixed fine mesh. Significant savings in computational time are found in each case, with little to no compromise in the accuracy of the solutions.