Turbulence Resolution Scale Dependence in Large-Eddy Simulations of a Jet Flame

The explicit dependence of LES fields on the turbulence resolution scale Δ implies that LES statistics usually vary with Δ and exhibit different convergence behaviors for different types of statistics, flow variables and subgrid LES models. The present work compares the performance of two popular subgrid models—the dynamic Smagorinsky model and the Vreman model—based on the convergence of their LES statistics with respect to Δ for a piloted methane-air (Sandia D) flame. The Δ-dependence of the LES statistics is studied based on five grids with progressively increased resolution ranging from 3 × 10⁵ to about 10.4 × 10⁶ cells. The simulation results show that the resolved velocity statistics converge for the finest grids with some weak Δ-dependence observed in the variance fields. The mixture fraction statistics are found to be more sensitive to the turbulence resolution scale upstream in the flame signifying the importance of the estimation of the Δ-invariant LES statistics at the DNS limit. For the considered flame the Vreman subgrid model exhibits good performance with the statistics being very close to those given by the dynamic Smagorinsky model, and being rather insensitive to a choice of the model constant.     

Demonstration of ultra hi-fi (UHF) methods

Computational aero-acoustics (CAA) requires efficient, high-resolution simulation tools. Most current techniques utilize finite-difference approaches because high order accuracy is considered too difficult or expensive to achieve with finite volume or finite element methods. However, a novel finite volume approach i.e. ultra hi-fi (UHF) which utilizes Hermite fluxes is presented which can achieve both arbitrary accuracy and fidelity in space and time. The technique can be applied to unstructured grids with some loss of fidelity or with multi-block structured grids for maximum efficiency and resolution. In either paradigm, it is possible to resolve ultra-short waves (defined as waves having wavelengths that are shorter than a grid cell). This is demonstrated here by solving the 4th CAA workshop Category 1 Problem 1.     

HyperFLOW软件非结构网格亚跨声速湍流模拟的验证与确认

计算流体力学(computational fluid dynamics,CFD)数值模拟在航空航天等领域发挥越来越重要的作用,然而CFD数值模拟结果的可信度仍然需要通过不断地验证与确认来提高.本文给出了从制造解精度测试、简单到复杂外形湍流模拟网格收敛性研究等三个方面开展CFD软件验证与确认的方法,并对自主研发的CFD软件平台HyperFLOW在非结构网格上模拟亚跨声速湍流问题的能力进行了验证与确认.首先通过基于Euler方程和标量扩散方程的制造解精度测试,分别验证了HyperFLOW在非结构网格上对Euler方程和黏性项的求解精度,结果表明其能够在任意非结构网格上达到设计的二阶精度. 其次,通过NASATurbulence Modeling Resource中的湍流平板、二维翼型近尾迹流动、二维Bump等几个典型的亚声速湍流算例的网格收敛性研究,量化考察了数值结果的观测精度阶和网格收敛性指数,并与国外知名CFD解算器CFL3D,FUN3D的计算结果进行了对比,验证了HyperFLOW对简单湍流问题的模拟能力,且具有良好的网格收敛性和计算精度(阶). 最后,通过NASA CommonResearchModel标模定升力系数的网格收敛性研究和升阻极曲线预测,验证了软件在复杂外形亚跨声速湍流流动数值模拟中也具有良好的可信度.      

Impact of the fourth‐order compact difference scheme on computational properties of 3D grids in a nonhydrostatic model

To investigate the potential of the fourth‐order compact difference scheme within the specific context of numerical atmospheric models, a linear baroclinic adjustment system is discretized, using a variety of candidates for practically meaningful staggered 3D grids. A unified method is introduced to derive the dispersion relationship of the baroclinic geostrophic adjustment process. Eight popular 3D grids are obtained by combining contemporary horizontal staggered grids, such as the Arakawa C and Eliassen grids, with optimal vertical grids, such as the Lorenz and Charney‐Phillip (CP) grids, and their time‐staggered versions. The errors produced on the 3D grids in describing the baroclinic geostrophic adjustment process relative to the differential case are compared in terms of frequency and group velocity components with the elimination of implementation error. The results show that by utilizing the fourth‐order compact difference scheme with high precision, instead of the conventional second‐order centered difference scheme, the errors in describing baroclinic geostrophic adjustment process decrease but only when using the combinations of the horizontally staggered Arakawa C grid and the vertically staggered CP or the C/CP grid, the time‐horizontally staggered Eliassen (EL) grid and vertically staggered CP or the EL/CP grid, the C grid and the vertically time‐staggered versions of Lorenz (LTS) grid or C/LTS grid, EL grid and LTS grid or EL/LTS grid. The errors were found to increase for specific waves on the rest grids. It can be concluded that errors produced on the chosen 3D grids do not universally decrease when using the fourth‐order compact difference scheme; hence, care should be taken when implementing the fourth‐order compact difference scheme, otherwise, the expected benefits may be offset by increased errors. Copyright © 2008 John Wiley & Sons, Ltd.     

Reliability Issues of LES-Related Approaches in an Industrial Context

Large-Eddy Simulation (LES), Detached-Eddy Simulation (DES) and Scale-Adaptive Simulation (SAS) are increasingly being used as engineering tools to predict the behaviour of complex industrial flows. Often the flows studied have not been examined previously and the required grid resolution is unknown. Industrial users studying these flows tend to be using commercial CFD codes and do not usually have access to high-performance computing facilities. Due to the significant computing times required, it is difficult to undertake systematic grid-dependence studies. There is therefore a risk that LES, DES and SAS will be performed using overly coarse grids which may lead to unreliable predictions. The present work surveys a number of practical techniques that provide a means of assessing the quality of the grid resolution in large-eddy simulations and related approaches. To examine the usefulness of these techniques, a gas release in a ventilated room is examined using DES and SAS. The grid resolution measures indicate that overall the grids used are relatively coarse. Both DES and SAS model predictions are found to be in poor agreement with experimental data compared to steady and unsteady Reynolds-averaged Navier–Stokes (RANS) results using the SST model. The SAS model also shows the greatest grid sensitivity of the four models tested. The work highlights the need for grid-dependence studies and the potential problems of using coarse grids.     

动网格生成技术及非定常计算方法进展综述

对应用于飞行器非定常运动的数值计算方法(包括动态网格技术和相应的数值离散格式)进行了综述.根据网格拓扑结构的不同,重点论述了基于结构网格的非定常计算方法和基于非结构/混合网格的非定常计算方法,比较了各种方法的优缺点.在基于结构网格的非定常计算方法中,重点介绍了刚性运动网格技术、超限插值动态网格技术、重叠动网格技术、滑移动网格技术等动态结构网格生成方法,同时介绍了惯性系和非惯性系下的控制方程,讨论了非定常时间离散方法、动网格计算的几何守恒律等问题.在基于非结构/混合网格的非定常计算方法中,重点介绍了重叠非结构动网格技术、重构非结构动网格技术、变形非结构动网格技术以及变形/重构耦合动态混合网格技术等方法,以及相应的计算格式,包括非定常时间离散、几何守恒律计算方法、可压缩和不可压缩非定常流动的计算方法、各种加速收敛技术等.在介绍国内外进展的同时,介绍了作者在动态混合网格生成技术和相应的非定常方法方面的研究与应用工作.     

Simulation of viscous water column collapse using adapting hierarchical grids

An adaptive hierarchical grid‐based method for predicting complex free surface flows is used to simulate collapse of a water column. Adapting quadtree grids are combined with a high‐resolution interface‐capturing approach and pressure‐based coupling of the Navier–Stokes equations. The Navier–Stokes flow solution scheme is verified for simulation of flow in a lid‐driven cavity at Re=1000. Two approaches to the coupling of the Navier–Stokes equations are investigated as are alternative face velocity and hanging node interpolations. Collapse of a water column as well as collapse of a water column and its subsequent interaction with an obstacle are simulated. The calculations are made on uniform and adapting quadtree grids, and the accuracy of the quadtree calculations is shown to be the same as those made on the equivalent uniform grids. Results are in excellent agreement with experimental and other numerical data. A sharp interface is maintained at the free surface. The new adapting quadtree‐based method achieves a considerable saving in the size of the computational grid and CPU time in comparison with calculations made on equivalent uniform grids. Copyright © 2005 John Wiley & Sons, Ltd.     

Improving the accuracy of discontinuous Galerkin schemes at boundary layers

The resolution of boundary layers typically requires fine grids in the wall normal direction, which leads to anisotropic elements being refined towards the wall. Best practice guidelines for the mesh generation of stretched boundary layer grids exist for the finite volume or finite difference discretizations. A similar resolution of boundary layers with DG schemes can be achieved with a coarser grid because of the subgrid resolution of the DG scheme. High order schemes incorporate the possibility of high order element mappings, resulting in different resolution properties inside the element. In this paper, we show that the use of an internal element mapping in combination with a stretched grid can be used to reduce the error of the boundary layer approximation by an order of magnitude in comparison with the classical linear internal element mapping. The boundary layer is modeled by a one‐dimensional singular perturbation problem. In addition, we discuss the construction of the element mappings by interpolation and investigate the limits of the stretching function such that the resulting element Jacobian remains positive. A parameter study shows the influence of the element mapping for different polynomial degrees on the solution. Copyright © 2014 John Wiley & Sons, Ltd.     

A structured but non‐uniform Cartesian grid‐based model for the shallow water equations

In large‐scale shallow flow simulations, local high‐resolution predictions are often required in order to reduce the computational cost without losing the accuracy of the solution. This is normally achieved by solving the governing equations on grids refined only to those areas of interest. Grids with varying resolution can be generated by different approaches, e.g. nesting methods, patching algorithms and adaptive unstructured or quadtree gridding techniques. This work presents a new structured but non‐uniform Cartesian grid system as an alternative to the existing approaches to provide local high‐resolution mesh. On generating a structured but non‐uniform Cartesian grid, the whole computational domain is first discretized using a coarse background grid. Local refinement is then achieved by directly allocating a specific subdivision level to each background grid cell. The neighbour information is specified by simple mathematical relationships and no explicit storage is needed. Hence, the structured property of the uniform grid is maintained. After employing some simple interpolation formulae, the governing shallow water equations are solved using a second‐order finite volume Godunov‐type scheme in a similar way as that on a uniform grid. Copyright © 2010 John Wiley & Sons, Ltd.     

Large eddy simulation of flow around a rectangular cylinder

A large eddy simulation (LES) of turbulent flow around a stationary rectangular cylinder at high Reynolds number of 2.2×10⁴ is conducted as the first step to prove the applicability of LES to practical engineering problems. Time-averaged and phase-averaged velocities and turbulent stresses are obtained and they are compared with the experimental data. To investigate mesh dependence on computational results of the LES, two kinds of grid resolution are used. In addition, the effect of a second-order upwind scheme QUICK for convection terms is also investigated due to its dependence on grid resolution. The drag coefficients, the base pressure coefficients and Strouhal numbers are in fairly good agreement with the experimental results, while the computational results show that the artificial dissipative and dispersive effect of QUICK is large in the vicinity of the cylinder in our computation. Thus, it is necessary to use higher-order upwind schemes to reduce the numerical errors, since it is effective in applying LES to practical engineering problems with complicated geometry.     

Chimera technique for transporting disturbances

The Chimera technique for moving grids is used to take into account nonhomogeneous unsteady inflow conditions in the simulation of aerodynamic flows. The method is applied to simulate the transport of a large‐scale vortex by a mean velocity field over a large distance, where it finally interacts with an airfoil. The Chimera approach allows one to resolve the vortex on a fine grid, whereas the unstructured background grid covering most of the computational domain can be much coarser. This method shows the same low numerical dissipation as a simulation on a globally fine grid. Several precursor tests are performed with a finite modified analytical Lamb–Oseen type vortex to study the influence of spatial and temporal resolution and the employed numerical scheme. Then, the interaction of an analytical vortex with a NACA0012 airfoil and with an ONERA‐A airfoil near stall is studied. Finally, a realistic vortex is generated by a ramping airfoil and is transported on a moving Chimera block and then interacts with a two‐element airfoil, which allows one to simulate a typical setup for a gust generator in aerodynamic facilities. Copyright © 2012 John Wiley & Sons, Ltd.     

On the influence of numerical schemes and subgrid–stress models on large eddy simulation of turbulent flow past a square cylinder

Influence of finite difference schemes and subgrid‐stress models on the large eddy simulation calculation of turbulent flow around a bluff body of square cylinder at a laboratory Reynolds number, has been examined. It is found that the type and the order of accuracy of finite‐difference schemes and the subgrid‐stress model for satisfactory results are dependent on each other, and the grid resolution and the Reynolds number. Using computational grids manageable by workstation‐level computers, with which the near‐wall region of the separating boundary layer cannot be resolved, central‐difference schemes of realistic orders of accuracy, either fully conservative or non‐conservative, suffer stability problems. The upwind‐biased schemes of third order and the Smagorinsky eddy‐viscosity subgrid model can give reasonable results resolving much of the energy‐containing turbulent eddies in the boundary layers and in the wake and representing the subgrid stresses in most parts of the flow. Noticeable improvements can be obtained by either using higher order difference schemes, increasing the grid resolution and/or by implementing a dynamic subgrid stress model, but each at a cost of increased computational time. For further improvements, the very small‐scale eddies near the upstream corners and in the laminar sublayers need to be resolved but would require a substantially larger number of grid points that are out of the range of easily accessible computers. Copyright © 2002 John Wiley & Sons, Ltd.     

多维迎风方法在非结构/混合网格热流计算中的应用研究

非结构/混合网格具有极强的几何灵活性,在复杂外形飞行器的气动力特性数值模拟中已得到广泛应用,但目前还难以准确地预测气动热环境。本文从非结构/混合网格热流计算的三个需求出发,选取了多维迎风方法,并与其他方法进行了对比研究。以二维圆柱高超声速绕流这一Benchmark典型问题为例,对比研究了多维迎风方法和几种广泛使用的无粘通量格式(Roe格式、Van Leer格式和AUSMDV格式)对混合网格热流计算精度的影响。结果表明,多维迎风方法在热流计算精度、鲁棒性以及收敛性方面表现良好。最后,将多维迎风方法应用于常规混合网格上的圆柱和钝双锥绕流问题,均得到了较好的热流计算结果,为非结构/混合网格热流计算在复杂高超飞行器中的应用奠定了基础。     

Selection of a staggered grid for inertia‐gravity waves in shallow water

The problem of accuracy in propagating inertia‐gravity waves on Arakawa grids is investigated. It is shown that the sole analysis of spatial discretization and the recommendation of the B‐grid for coarse resolution models and C‐grid for high resolution models must be re‐analysed when time discretization is taken into account as well. For a chosen time discretization, a coarse C‐grid is shown for example, to increase precision when using larger time‐steps (up to the stability limit) whereas the precision of the B‐grid decreases. Here, an analysis of error for different grids in function of the space–time resolutions and computational costs is presented and some recommendations on the choice of the particular staggered grid for a given application are outlined. Copyright © 2002 John Wiley & Sons, Ltd.     

含泥质夹层油藏蒸汽注采过程的自适应网格算法研究

根据泥质夹层的低渗特性及空间分布，本文提出了一种含泥质夹层油藏网格渗透率的粗化计算方法，并在此基础上，将自适应网格算法应用于含泥质夹层油藏的数值模拟，提升其计算效率．在计算过程中，网格的动态划分仅依据流体物理量的变化，泥质夹层区域不全部采用细网格，仅针对流动锋面处的泥质夹层采用细网格，其余泥质夹层处采用不同程度的粗网格．相较于传统算法，网格数大幅下降．数值算例表明，自适应网格算法的计算结果精度与全精细网格一致，能够准确模拟出泥质夹层对于流体的阻碍作用，同时计算效率得到大幅提升，约为全精细网格算法的3~7 倍．     

时刻追踪多介质界面运动的动网格方法

在对可压缩多介质流动的数值模拟中,定义介质界面为一种内部边界,由网格的边组成,界面边两侧对应两种不同介质中的网格。通过求解Riemann问题追踪介质界面上网格节点的运动,同时采用局部重构的动网格技术处理介质界面的大变形问题,并将介质界面定义为网格变形边界,以防止该边界上网格体积为负。运用HLLC格式求解ALE方程组得到整个多介质流场的数值解。最后从几个多介质流模型的计算结果可以看出,本文的动网格方法是可行的,而且可以时刻追踪介质界面的运动状态。     

Performance of very‐high‐order upwind schemes for DNS of compressible wall‐turbulence

The purpose of the present paper is to evaluate very‐high‐order upwind schemes for the direct numerical simulation (DNS ) of compressible wall‐turbulence. We study upwind‐biased (UW ) and weighted essentially nonoscillatory (WENO ) schemes of increasingly higher order‐of‐accuracy (J. Comp. Phys. 2000; 160 :405–452), extended up to WENO 17 (AIAA Paper 2009‐1612, 2009). Analysis of the advection–diffusion equation, both as Δx→0 (consistency), and for fixed finite cell‐Reynolds‐number Re_Δx (grid‐resolution), indicates that the very‐high‐order upwind schemes have satisfactory resolution in terms of points‐per‐wavelength (PPW ). Computational results for compressible channel flow (Re∈[180, 230]; M?_CL ∈[0.35, 1.5]) are examined to assess the influence of the spatial order of accuracy and the computational grid‐resolution on predicted turbulence statistics, by comparison with existing compressible and incompressible DNS databases. Despite the use of baseline O(Δt²) time‐integration and O(Δx²) discretization of the viscous terms, comparative studies of various orders‐of‐accuracy for the convective terms demonstrate that very‐high‐order upwind schemes can reproduce all the DNS details obtained by pseudospectral schemes, on computational grids of only slightly higher density. Copyright © 2009 John Wiley & Sons, Ltd.     

网格与高精度差分计算问题

研究NS方程差分求解时来流雷诺数、计算格式精度和计算网格之间的关系．给出了判定空间三个方向上的粘性贡献在给定雷诺数、格式精度和网格下是否能够正确计入的估计方法．指出在NS方程的二阶差分方法的数值模拟中,由于物面法向采用了压缩网格技术,物面附近的网格间距很小,该方向上的粘性贡献可被计入．但是如果流向和周向的网格较粗,相应的差分方程中的粘性贡献可能落入截断误差相同的量级,因此在精度上等于仍是求解略去流向和周向粘性项的薄层近似方程．指出,高阶精度的差分计算格式,可以避免对网格要求苛刻的困难．并进一步讨论了建立高阶精度格式的问题,提出了建立高阶精度格式应该满足的原则：耗散控制原则以及色散控制原则．为了避免激波附近可能出现的微小非物理振荡,建议发展混合高阶精度格式,即在激波区,采用网格自适应的NND格式,在激波以外的区域,采用按上述原则发展的高阶格式．     

Consistent discretization for simulations of flows with moving generalized curvilinear coordinates

We develop a consistent discretization of conservative momentum and scalar transport for the numerical simulation of flow using a generalized moving curvilinear coordinate system. The formulation guarantees consistency between the discrete transport equation and the discrete mass conservation equation due to grid motion. This enables simulation of conservative transport using generalized curvilinear grids that move arbitrarily in three dimensions while maintaining the desired properties of the discrete transport equation on a stationary grid, such as constancy, conservation, and monotonicity. In addition to guaranteeing consistency for momentum and scalar transport, the formulation ensures geometric conservation and maintains the desired high‐order time accuracy of the discretization on a moving grid. Through numerical examples we show that, when the computation is carried out on a moving grid, consistency between the discretized scalar advection equation and the discretized equation for flow mass conservation due to grid motion is required in order to obtain stable and accurate results. We also demonstrate that significant errors can result when non‐consistent discretizations are employed. Copyright © 2009 John Wiley & Sons, Ltd.     

On the characterization of grid density in grid refinement studies for discretization error estimation

This paper discusses the estimation of discretization errors on the basis of power series expansions for grid sets that are not geometrically similar, that is, grids not exhibiting a constant grid refinement ratio for the entire computational domain. Simple test cases with structured and unstructured grids are used to demonstrate that reliable error estimates on the basis of power series expansions can be made if the grids are refined systematically. However, if the grid refinement ratio is not constant in the complete domain, the definition of the typical cell size is not obvious, and the observed order of accuracy may not be equal to the expected theoretical order of the discretization. Some alternatives for the definition of the typical cell size are tested. In these tests, the error estimation does not show a significant effect of the definition of the typical cell size even for some cases with data sets clearly outside the ‘asymptotic range’. For non‐geometrically similar grids, the best estimates of the observed order of accuracy are obtained with the typical cell size on the basis of the mode of the cell size (the cell size that occurs more often in a given grid). Copyright © 2012 John Wiley & Sons, Ltd.