用物理黏性构建高阶不振荡对流扩散差分格式

利用数值摄动算法, 通过扩散格式数值摄动重构把对流扩散方程的2阶中心差分格式(2-CDS)重构为高精度高分辨率格式, 解析分析和模型方程计算证实了新格式的高精度不振荡性质. 新格式是把物理黏性使流动光滑化的扩散运动规律引入2-CDS 中的结果. 该法显然与构建高级离散格式的常见方法不同. 证实: 数值摄动重构中引入扩散运动规律的结果格式与引入对流运动规律(下游不影响上游的规律)的结果格式一致, 说明对离散方程的数值摄动运算, 在维持原格式结构形式不动的条件下, 不仅能提高格式精度和稳健性, 且可揭示对流离散运动规律与扩散离散运动规律之间的内在关联;同时证实, 文中提出和使用的上、下游分裂方法是构建高精度不振荡离散格式的一个有效方法.     

加权型紧致格式与加权本质无波动格式的比较

线性紧致格式和加权本质无波动格式是两种典型的高阶精度数值格式,它们各有优缺点.线性紧致格式在具有高阶精度的同时,格式的分辨率也比较高,耗散低,是计算多尺度流场结构的较好格式,但是不能计算具有强激波的流场.加权本质无波动格式是一种高阶精度捕捉激波格式,鲁棒性好,但耗散比较高,分辨率也不理想.近年来,在莱勒的线性紧致格式基础上,采用加权本质无波动格式捕捉激波思想,发展了一系列加权型紧致格式.本文较全面地比较了加权型紧致格式和加权本质无波动格式,包括构造方法、鲁棒性、分辨率、耗散特性、收敛特性以及并行计算效率.结果表明,现有的加权型紧致格式基本保持了加权本质无波动格式的性质,对于气动力等宏观量的计算,比加权本质无波动格式没有明显的优势.      

双同守恒律方程的加权本质无振荡格式新进展

近几年,在计算流体力学中,高精度、高分辨率的加权本质无振荡(weighted essentially non-oscillatory , WENO)格式得到很大的发展.WENO格式的主要思想是通过低阶的数值流通量的凸组合重构得到高阶的逼近,并且在间断附近具有本质无振荡的性质.本文综合介绍了双曲守恒律方程的有限差分和有限体积迎风型WENO,中心WENO,紧致中心WENO以及优化的WENO格式等,讨论了负权的处理和多维问题的解决方法.最后,通过一些算例证明WENO格式的高精度,本质无振荡的性质.图6参40      

一个基于非均匀网格上的二阶基本振荡差分格式

在基本无振荡格式的构造中，将通常的对流通量f的逼近方式推广到对通量导数的逼近，这一构造方法可以有效地应用到非均匀或非结构网格。直接基于非均匀网格上，构造了一个二阶的基本无振荡（ENO）差分格式，该格式具有形式简单，对网格的划分灵活，对传统格式相比不增加计算量等优点，几个数值算例证明了格式的有效性。     

高精度加权紧致非线性格式的研究进展

综述了高精度加权紧致非线性格式WCNS在理论分析以及复杂流动应用方面的研究进展. 首先回顾了国内外高精度格式研究的概况, 然后介绍了WCNS的研究与发展历程. 在对WCNS进行了Fourier分析和渐近稳定性分析后, 给出了WCNS求解多维复杂流动的算例.      

求解多维双曲守恒律方程组的四阶半离散格式

提出了求解多维双曲守恒律方程组的四阶半离散格式。该方法以中心加权基本无振荡(CWENO)重构为基础,同时考虑到在R iemann扇内波传播的局部速度,从而回避了计算过程中的网格交错,建立了数值耗散较小的介于迎风格式和中心格式之间的半离散格式。本文的四阶半离散格式是Kurganov等人的三阶半离散格式的高阶推广。大量的数值算例充分说明了本文方法的高分辨率和稳定性。     

数值摄动算法及其CFD格式

作者提出的数值摄动算法把流体动力学效应耦合进NS方程组和对流扩散（CD）方程离散的数学基本格式（MBS）,特别是耦合进最简单的MBS即一阶迎风和二阶中心格式之中,由此构建成一系列新格式,称呼方便和强调耦合流体动力学起见,称它们为流体力学基本格式（FMBS）。构建FMBS的主要步骤是把MBS中的通量摄动重构为步长的幂级数,利用空间分裂和导出的高阶流体动力学关系式,把结点变量展开成Taylor级数,通过消除重构格式修正微分方程的截断误差诸项求出幂级数的待定系数,由此获得非线性FMBS。FMBS的公式是MBS与 （及 ）之简单多项式的乘积, 和 分别是网格Reynolds数和网格CFL数。FMBS和MBS使用相同结点,简单性彼此相当,但FMBS精度高稳定范围大,例如FMBS包含了许多绝对稳定和绝对正型、高阶迎风和中心有限差分（FD）格式和有限体积（FV）格式,这些格式对网格Reynolds数的任意值均为不振荡格式。可见对不振荡CFD格式的构建,数值摄动算法提供了不同于调节数值耗散等常见的人为构建方法,而利用流体力学自身关系以及把迎风机制通过上、下游摄动重构引入中心MBS的解析构建方法,FMBS除了直接应用于流体计算外;对于通过调节数值耗散、色散和数值群速度特性重构高分辨率格式的研究,最简单FMBS提供了比最简单MBS更精确、但同样简单的基础和起步格式。FMBS用于计算不可压缩流,可压缩流,液滴萃取传质,微通道两相流等,均获得良好数值结果或与已有Benchmark解一致的数值结果。已有文献称数值摄动算法为新型高精度格式和高的算法和高的格式;本文FMBS比数值摄动格式的称呼可更好反映FMBS的物理内容。文中也讨论了值得进一步研究的一些课题,该法亦可用于其它一些数学物理方程（例如,简化Boltzmann方程、磁流体方程、KdV-Burgers方程等）MBS耦合物理动力学效应的重构。      

应用于计算气动声学的优化有限紧致格式

对于含间断的计算气动声学问题,数值计算的格式不仅要求低耗散低色散的设计,对短波具有较高的分辨率,还要求能捕捉激波.中心紧致格式具有高精度,具有无耗散和低色散特征,但不能捕捉间断和激波;WENO格式处理间断较为成功,而耗散和色散误差相对较大.有限紧致格式可以将紧致格式与WENO格式相结合构造成混合格式,利用光滑因子之间的关系对激波区域进行自动判断,将传统的全域求解的紧致格式划分为有限的局部紧致求解,间断点上的激波捕捉铜梁自动作为局部紧致求解的边界通量,在在光滑区域具有紧致格式的高精度低耗散性质,在激波附近不产生非物理振荡.本文利用有限紧致格式思想,构造了新的适合于气动声学问题的优化有限紧致格式,将其应用于计算气动声学一维标准测试问题,对相关格式的模拟性能进行了评估,显示该格式在宽频声波传播和含有间断的声波传播模拟方面具有优势.     

无粘可压缩流动的改进高精度方法

为更准确捕捉复杂流场的流动细节,通过对WENO格式的光滑因子进行改进,发展了一种新的五阶WENO格式。对三阶ENO格式进行加权可以得到五阶WENO格式,但是不同的加权处理,WENO格式在极值处保持加权基本无振荡的效果不同,本文构造了二阶精度的局部光滑因子,及不含一阶二阶导数的高阶全局光滑因子,从而实现WENO格式在极值处有五阶精度。基于改进五阶WENO格式,对一维对流方程、一维和二维可压缩无粘问题进行算例验证,并与传统WENO-JS格式和WENO-Z格式进行比较。计算结果表明,改进五阶WENO格式有较高的精度和收敛速度,有较低的数值耗散,能有效捕捉间断、激波和涡等复杂流动。     

关于无振荡、无自由参数有限元格式的研究

利用双曲守恒律方程的Ｔａｙｌｏｒ弱解表达式，建立了有限元法修正方程，选择合适的展开式系数能得到一系列数值格式．通过稳定性分析研究了格式的稳定性、色散误差与有限元修正方程导数项系数之间的关系，该关系与差分法的ＮＮＤ格式一致．在选定格式下，通过ＣＦＬ数可控制有限元离散解的振荡而使格式不含自由参数．最后，用数值算例验证了这一关系，并在二、三维欧拉方程作了推广应用．     

非定常俯抑振荡下的横向喷流数值模拟

采用高精度格式数值求解RANS方程,研究了定常状态下横向喷流流场,压力分布计算结果与实验结果基本吻合,并捕捉到喷流干扰流场中多种流动结构.在非定常计算过程中,飞行器的振动引起了法向力和俯仰力矩系数的相位滞后,推力放大因子随俯仰角周期变化.飞行器振动过程中,喷流流场的动态气动特性与稳态喷流有明显的区别,因此在利用横向喷流对飞行器进行姿态控制时,应该考虑由于飞行器姿态的变化对横向喷流所产生的非定常影响问题.     

在工程流体力学教学中引入CFD工程案例的探讨

在长期的工程流体力学教学过程中,发现学生对这门课普遍存在畏难情绪,对复杂的理论知识掌握困难.考虑到工程流体力学的研究方法分为理论分析方法,实验方法和数值方法,而其中数值方法在传统教学中应用的较少,所以试图通过适当增加数值方法的应用来改善教学效果.随着本科生对计算机应用能力的增强以及知识面的逐渐扩展,本文提出增加结合专业背景,理论知识及软件应用的综合案例以满足当前课程及学生发展的需求.     

Incompact3d: A powerful tool to tackle turbulence problems with up to O(105) computational cores

Understanding the nature of complex turbulent flows remains one of the most challenging problems in classical physics. Significant progress has been made recently using high performance computing, and computational fluid dynamics is now a credible alternative to experiments and theories in order to understand the rich physics of turbulence. In this paper, we present an efficient numerical tool called Incompact3d that can be coupled with massive parallel platforms in order to simulate turbulence problems with as much complexity as possible, using up to O(10⁵) computational cores by means of direct numerical simulation (DNS). DNS is the simplest approach conceptually to investigate turbulence, featuring the highest temporal and spatial accuracy and it requires extraordinary powerful resources. This paper is an extension of Laizet et al.(Comput. Fluids 2010; 39 (3):471–484) where the authors proposed a strategy to run DNS with up to 1024 computational cores. Copyright © 2010 John Wiley & Sons, Ltd.     

Development of optimized weighted‐ENO schemes for multiscale compressible flows

The present paper deals with the development of optimized weighted–ENO schemes to improve the resolution of a class of compressible flows characterized by a wide disparity of scales, typical of compressible turbulence and/or aeroacoustic phenomena, and shock waves. The approach relies on a least square minimization of both the dispersion and dissipation error components together with the use of symmetric stencil support. Extensive numerical simulations of sound propagation, shock–sound interaction and isotropic compressible turbulence have been carried out, and the results confirm that the optimized schemes yield a resolution in wave number space greater than the non‐optimized ones. Copyright © 2003 John Wiley & Sons, Ltd.     

On the Accuracy of Upwind and Symmetric TVD Schemes in Simulating Low Mach Number Flow

The accuracy of MUSCL upwind and Yee-Roe-Davis symmetric TVD schemes for simulating low Mach number flow is studied through a numerical experiment of the 2-D lid driven cavity problem. The steady slate solution is reached by using a marching approach based on the pseudocompressibilty method in conjunction with implicit approximate factorization. A finite volume discretization of the conservation equations is used with a four level multigrid method to accelerate the convergence. The tests performed which were in the range of 100 ≤ Re ≤ 5000, show that the Yee-Roe-Davis symmetric scheme generates results in very good agreement with the benchmark results over this range of Re. The MUSCL upwind scheme accuracy deteriorates with the increasing Re.     

A study of the effect of step excrescences and free‐stream disturbances on boundary layer stability

In this work, a study of the mechanism by which free‐stream acoustic and vorticity disturbances interact with a boundary layer flow developing over a flat plate featuring a step excrescence located at a certain distance from a blunt leading edge is included. The numerical tool is a high‐fidelity implicit numerical algorithm solving for the unsteady, compressible form of the Navier–Stokes equations in a body‐fitted curvilinear coordinates and employing high‐accurate compact differencing schemes with Pade‐type filters. Acoustic and vorticity waves are generated using a source term in the momentum and energy equations, as opposed to using inflow boundary conditions, to avoid spurious waves that may propagate from boundaries. The results show that the receptivity to surface step excrescences is largely the result of an overall adverse pressure gradient posed by the step, and that the free‐stream disturbances accelerate the generation of instabilities in the downstream. As expected, it is found that the acoustic disturbance interacting with the surface imperfection is more efficient in exciting the Tollmien–Schlichting waves than the vorticity disturbance. The latter generates Tollmien–Schlichting waves that are grouped in wave packets consistent with the wavelength of the free‐stream disturbance. Copyright © 2015 John Wiley & Sons, Ltd.     

High‐order numerical simulations of flow‐induced noise

In this paper, the flow/acoustics splitting method for predicting flow‐generated noise is further developed by introducing high‐order finite difference schemes. The splitting method consists of dividing the acoustic problem into a viscous incompressible flow part and an inviscid acoustic part. The incompressible flow equations are solved by a second‐order finite volume code EllipSys2D/3D. The acoustic field is obtained by solving a set of acoustic perturbation equations forced by flow quantities. The incompressible pressure and velocity form the input to the acoustic equations. The present work is an extension of our acoustics solver, with the introduction of high‐order schemes for spatial discretization and a Runge–Kutta scheme for time integration. To achieve low dissipation and dispersion errors, either Dispersion‐Relation‐Preserving (DRP) schemes or optimized compact finite difference schemes are used for the spatial discretizations. Applications and validations of the new acoustics solver are presented for benchmark aeroacoustic problems and for flow over an NACA 0012 airfoil. Copyright © 2010 John Wiley & Sons, Ltd.     

On spurious behavior of CFD simulations1

Spurious behavior in underresolved grids and/or semi‐implicit temporal discretizations for four computational fluid dynamics (CFD) simulations are studied. The numerical simulations consist of (a) a 1‐D chemically relaxed non‐equilibrium flow model, (b) the direct numerical simulation (DNS) of 2D incompressible flow over a backward facing step, (c) a loosely coupled approach for a 2D fluid–structure interaction, and (d) a 3D unsteady compressible flow simulation of vortex breakdown on delta wings. These examples were chosen based on their non‐apparent spurious behaviors that were difficult to detect without extensive grid and/or temporal refinement studies and without some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations, underresolved grids, semi‐implicit procedures, loosely coupled implicit procedures, and insufficiently long‐time integration in DNS are most often unavoidable. Consequently, care must be taken in both computation and in interpretation of the numerical data. The results presented confirm the important role that dynamical systems theory can play in the understanding of the non‐linear behavior of numerical algorithms and in aiding the identification of the sources of numerical uncertainties in CFD. Copyright © 1999 John Wiley & Sons, Ltd.     

Weighted essential non‐oscillatory schemes for tidal bore on unstructured meshes

In this paper, the third‐order weighted essential non‐oscillatory (WENO) schemes are used to simulate the two‐dimensional shallow water equations with the source terms on unstructured meshes. The balance of the flux and the source terms makes the shallow water equations fit to non‐flat bottom questions. The simulation of a tidal bore on an estuary with trumpet shape and Qiantang river is performed; the results show that the schemes can be used to simulate the current flow accurately and catch the stronger discontinuous in water wave, such as dam break and tidal bore effectively. Copyright © 2008 John Wiley & Sons, Ltd.     

High‐order accurate numerical solutions of incompressible flows with the artificial compressibility method

A high‐order accurate, finite‐difference method for the numerical solution of incompressible flows is presented. This method is based on the artificial compressibility formulation of the incompressible Navier–Stokes equations. Fourth‐ or sixth‐order accurate discretizations of the metric terms and the convective fluxes are obtained using compact, centred schemes. The viscous terms are also discretized using fourth‐order accurate, centred finite differences. Implicit time marching is performed for both steady‐state and time‐accurate numerical solutions. High‐order, spectral‐type, low‐pass, compact filters are used to regularize the numerical solution and remove spurious modes arising from unresolved scales, non‐linearities, and inaccuracies in the application of boundary conditions. The accuracy and efficiency of the proposed method is demonstrated for test problems. Copyright © 2004 John Wiley & Sons, Ltd.