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NASA Turbulence 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 Common Research Model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.     

非结构网格二阶有限体积法中黏性通量离散格式精度分析与改进

非结构网格二阶有限体积离散方法广泛应用于计算流体力学工程实践中,研究非结构网格二阶精度有限体积离散方法的计算精度具有现实意义. 计算精度主要受到网格和计算方法的影响,本文从单元梯度重构方法、黏性通量中的界面梯度计算方法两个方面考察黏性流动模拟精度的影响因素. 首先从理论上分析了黏性通量离散中的“奇偶失联”问题,并通过基于标量扩散方程的制造解方法验证了“奇偶失联”导致的精度下降现象,进一步通过引入差分修正项消除了“奇偶失联”并提高了扩散方程计算精度;其次,在不同类型、不同质量的网格上进行基于扩散方程的制造解精度测试,考察单元梯度重构方法、界面梯度计算方法对扩散方程计算精度的影响,结果显示,单元梯度重构精度和界面梯度计算方法均对扩散方程计算精度起重要作用;最后对三个黏性流动算例(二维层流平板、二维湍流平板和二维翼型近尾迹流动)进行网格收敛性研究,初步验证了本文的结论,得到了计算精度和网格收敛性均较好的黏性通量计算格式.      

基于制造解的非结构二阶有限体积离散格式的精度测试与验证

随着计算机技术的飞速进步,计算流体力学得到迅猛发展,数值计算虽能够快速得到离散结果,但是数值结果的正确性与精度则需要通过严谨的方法来进行验证和确认.制造解方法和网格收敛性研究作为验证与确认的重要手段已经广泛应用于计算流体力学代码验证、精度分析、边界条件验证等方面.本文在实现标量制造解和分量制造解方法的基础上,通过将制造解方法精度测试结果与经典精确解(二维无黏等熵涡)精度测试结果进行对比,进一步证实了制造解精度测试方法的有效性,并将两种制造解方法应用于非结构网格二阶精度有限体积离散格式的精度测试与验证,对各种常用的梯度重构方法、对流通量格式、扩散通量格式进行了网格收敛性精度测试.结果显示,基于Green-Gauss公式的梯度重构方法在不规则网格上会出现精度降阶的情况,导致流动模拟精度严重下降,而基于最小二乘(least squares)的梯度重构方法对网格是否规则并不敏感.对流通量格式的精度测试显示,所测试的各种对流通量格式均能达到二阶精度,且各方法精度几乎相同;而扩散通量离散中界面梯度求解方法的选择对流动模拟精度有显著影响.     

非结构网格二阶有限体积法中黏性通量离散格式精度分析与改进

非结构网格二阶有限体积离散方法广泛应用于计算流体力学工程实践中,研究非结构网格二阶精度有限体积离散方法的计算精度具有现实意义.计算精度主要受到网格和计算方法的影响,本文从单元梯度重构方法、黏性通量中的界面梯度计算方法两个方面考察黏性流动模拟精度的影响因素.首先从理论上分析了黏性通量离散中的"奇偶失联"问题,并通过基于标量扩散方程的制造解方法验证了"奇偶失联"导致的精度下降现象,进一步通过引入差分修正项消除了"奇偶失联"并提高了扩散方程计算精度;其次,在不同类型、不同质量的网格上进行基于扩散方程的制造解精度测试,考察单元梯度重构方法、界面梯度计算方法对扩散方程计算精度的影响,结果显示,单元梯度重构精度和界面梯度计算方法均对扩散方程计算精度起重要作用;最后对三个黏性流动算例(二维层流平板、二维湍流平板和二维翼型近尾迹流动)进行网格收敛性研究,初步验证了本文的结论,得到了计算精度和网格收敛性均较好的黏性通量计算格式.     

谱体积方法单元分割与问题单元标记方法的改进研究

谱体积方法是一种本质上解决网格依赖性的高精度CFD计算方法,本文研究了二维Euler方程的谱体积方法,提出一种基于切比雪夫多项式的单元分割方法,建立了基于WENO的变量限制器方法,并发展了结合谱体积和控制体的问题单元标记方法.采用15°超声速压缩拐角和NACA0012跨声速流动两个典型算例进行验证,结果表明,该分区方法具有更好的计算精度,标记方法可有效识别不连续区域,在较少的网格下即可获得与密网格传统有限体积法相当的计算精度.     

非结构混合网格高超声速绕流与磁场干扰数值模拟

对均匀磁场干扰下的二维钝头体无粘高超声速流场进行了基于非结构混合网格的数值模拟.受磁流体力学方程组高度非线性的影响及考虑到数值模拟格式的精度,目前在此类流场的数值模拟中大多使用结构网格及有限差分方法,因而在三维复杂外形及复杂流场方面的研究受到限制.本文主要探索使用非结构网格(含混合网格)技术时的数值模拟方法.控制方程为耦合了Maxwell方程及无粘流体力学方程的磁流体力学方程组,数值离散格式采用Jameson有限体积格心格式,5步Runge-Kutta显式时间推进.计算模型为二维钝头体,初始磁场均匀分布.对不同磁感应强度影响下的高超声速流场进行了数值模拟,并与有限的资料进行了对比,得到了较符合的结果.     

计算流体力学中的验证与确认

计算流体力学(CFD)在航空航天等诸多领域的应用越来越广泛.特别是近年来, CFD在实际飞行器的设计中扮演着越来越重要的角色, 许多设计参数直接来源于CFD的计算结果.由此, 飞行器设计师对CFD提供结果的可信度提出了更高的要求.验证(verification)与确认(validation)是评价数值解精度和可信度的主要手段.本文综述了国内外开展CFD验证与确认研究的进展.在引言中论述了开展CFD验证与确认的重要性和必要性, 简述了国内外CFD验证与确认研究的历史和发展现状.第2节中讨论了CFD验证与确认的一些基本概念,以及这些概念定义的形成过程, 并指出了进行CFD验证与确认的基本步骤.第3节和第4节分别讨论了CFD验证与确认的方法, 如CFD验证中的精确解比较方法, 制造解比较方法, 网格收敛性研究;CFD确认中的层次结构, 流动分类法, 确认实验指南.在第5节中我们列举了几个CFD验证与确认的应用实例.最后, 对我国开展CFD验证与确认研究工作提出了若干建议, 包括:(1)开展流动分类法研究,(2)推行软件质量工程方法,(3)开展规范精细的实验, 建立国内的网络数据库.      

基于混合网格多维梯度重构的热流预测方法研究

高超声速气动热环境的数值计算对算法和网格的敏感度极高. 随着高超声速飞行器外形日益复杂, 生成高质量的结构网格时间成本呈指数增加, 难以满足工程应用的需求. 非结构/混合网格因具有很强的复杂外形适应能力, 为了缩短任务周期, 有必要在非结构/混合网格上开展高精度的气动热环境数值计算方法研究. 梯度重构方法是影响非结构/混合网格热流计算精度的重要因素之一. 本文通过引入多维梯度重构方法, 发展了基于常规的非结构/混合网格的高精度热流计算方法, 对典型的高超声速Benchmark算例(二维圆柱)进行了模拟, 并与气动力计算广泛采用的Green-Gauss类方法和最小二乘类方法进行了对比. 计算结果表明, 多维梯度重构方法能有效提高非结构/混合网格热流预测精度, 其鲁棒性和收敛性更好. 最后将多维梯度重构方法应用于常规混合网格的三维圆柱和三维双椭球绕流问题, 得到了与实验值吻合较好的热流计算结果, 展现了良好的应用前景.      

基于混合网格多维梯度重构的热流预测方法研究

高超声速气动热环境的数值计算对算法和网格的敏感度极高.随着高超声速飞行器外形日益复杂,生成高质量的结构网格时间成本呈指数增加,难以满足工程应用的需求.非结构/混合网格因具有很强的复杂外形适应能力,为了缩短任务周期,有必要在非结构/混合网格上开展高精度的气动热环境数值计算方法研究.梯度重构方法是影响非结构/混合网格热流计算精度的重要因素之一.本文通过引入多维梯度重构方法,发展了基于常规的非结构/混合网格的高精度热流计算方法,对典型的高超声速Benchmark算例(二维圆柱)进行了模拟,并与气动力计算广泛采用的Green-Gauss类方法和最小二乘类方法进行了对比.计算结果表明,多维梯度重构方法能有效提高非结构/混合网格热流预测精度,其鲁棒性和收敛性更好.最后将多维梯度重构方法应用于常规混合网格的三维圆柱和三维双椭球绕流问题,得到了与实验值吻合较好的热流计算结果,展现了良好的应用前景.     

高超声速再入体表面热流计算

运用非结构网格计算外部无粘流场,并结合边界层内粘性主导区域的工程算法,计算高超声速飞行器的气动加热。通过求解三维Euler方程确定复杂外形飞行器的边界层外缘参数,在理论与经验公式的基础上,利用局部相似性解的方法计算了钝锥和钝双锥外形有攻角再入的表面热流,并与国内外文献的NS方程数值计算结果和风洞试验结果进行了对比,三者的结果吻合较好。     

An immersed boundary solver for inviscid compressible flows

In this paper, a simple and efficient immersed boundary (IB) method is developed for the numerical simulation of inviscid compressible Euler equations. We propose a method based on coordinate transformation to calculate the unknowns of ghost points. In the present study, the body‐grid intercept points are used to build a complete bilinear (2‐D)/trilinear (3‐D) interpolation. A third‐order weighted essentially nonoscillation scheme with a new reference smoothness indicator is proposed to improve the accuracy at the extrema and discontinuity region. The dynamic blocked structured adaptive mesh is used to enhance the computational efficiency. The parallel computation with loading balance is applied to save the computational cost for 3‐D problems. Numerical tests show that the present method has second‐order overall spatial accuracy. The double Mach reflection test indicates that the present IB method gives almost identical solution as that of the boundary‐fitted method. The accuracy of the solver is further validated by subsonic and transonic flow past NACA2012 airfoil. Finally, the present IB method with adaptive mesh is validated by simulation of transonic flow past 3‐D ONERA M6 Wing. Global agreement with experimental and other numerical results are obtained.     

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.     

A second-order upwind finite-volume method for the Euler solution on unstructured triangular meshes

A scheme for the numerical solution of the two-dimensional (2D) Euler equations on unstructured triangular meshes has been developed. The basic first-order scheme is a cell-centred upwind finite-volume scheme utilizing Roe's approximate Riemann solver. To obtain second-order accuracy, a new gradient based on the weighted average of Barth and Jespersen's three-point support gradient model is used to reconstruct the cell interface values. Characteristic variables in the direction of local pressure gradient are used in the limiter to minimize the numerical oscillation around solution discontinuities. An Approximate LU (ALU) factorization scheme originally developed for structured grid methods is adopted for implicit time integration and shows good convergence characterisitics in the test. To eliminate the data dependency which prohibits vectorization in the inversion process, a black-gray-white colouring and numbering technique on unstructured triangular meshes is developed for the ALU factorization scheme. This results in a high degree of vectorization of the final code. Numerical experiments on transonic Ringleb flow, transonic channel flow with circular bump, supersonic shock reflection flow and subsonic flow over multielement aerofoils are calculated to validate the methodology.     

基于自适应直角网格的二维全速势方程有限体积解法A finite volume method for 2D Full-Potential equation on adaptive Cartesian grids

为满足亚声速和跨声速飞机概念设计中快速气动计算的需求,研究和发展一种基于自适应直角网格的非线性全速势方程有限体积解法。要点如下。（1）在几何自适应直角网格的基础上,使用结合单元融合的网格切割算法处理物面边界,提出一种修正非贴体切割网格的方法。（2）采用隐式格式结合GM RES算法求解该非线性位流方程,针对流场的自适应来捕捉激波。（3）采用镜像法处理物面边界处的无穿透条件,并提出解析的方法来修正镜像单元的值。（4）针对直角网格的特点,提出在库塔线上插入库塔单元的方法施加库塔条件。NACA0012翼型绕流的算例结果表明,该方法用于亚声速和跨声速气动计算能得到令人满意的结果,且自动化程度高、收敛速度快。     

A gas‐kinetic scheme for the simulation of turbulent flows on unstructured meshes

This paper presents a numerical method for simulating turbulent flows via coupling the Boltzmann BGK equation with Spalart–Allmaras one equation turbulence model. Both the Boltzmann BGK equation and the turbulence model equation are carried out using the finite volume method on unstructured meshes, which is different from previous works on structured grid. The application of the gas‐kinetic scheme is extended to the simulation of turbulent flows with arbitrary geometries. The adaptive mesh refinement technique is also adopted to reduce the computational cost and improve the efficiency of meshes. To organize the unstructured mesh data structure efficiently, a non‐manifold hybrid mesh data structure is extended for polygonal cells. Numerical experiments are performed on incompressible flow over a smooth flat plate and compressible turbulent flows around a NACA 0012 airfoil using unstructured hybrid meshes. These numerical results are found to be in good agreement with experimental data and/or other numerical solutions, demonstrating the applicability of the proposed method to simulate both subsonic and transonic turbulent flows. Copyright © 2016 John Wiley & Sons, Ltd.     

Validation of CFD‐CSD coupling interface methodology using commercial codes

Coupling interface between computational fluid dynamics (CFD) and computational structural dynamics (CSD) is required to provide exchange of information for the simulation of fluid–structure interaction (FSI) phenomena. Accuracy and consistency of information exchanged through coupling interface between the independent CFD and CSD solvers plays a central role in the simulation and prediction of FSI phenomenon, like flutter. In this paper validation of an implemented coupling interface methodology is presented for subsonic, transonic and near supersonic mach regime. The test case chosen for this purpose is the flutter of AGARD445.6 standard I‐wing weakened model configuration for subsonic to near transonic flow regime. Gambit^® and Fluent^® are used for CFD grid generation and solution of fluid dynamic equations, respectively. CSD modeling and simulation are provided by numerical time integration of modal dynamic equations derived through the finite element modeling in ANSYS^® environment. Copyright © 2009 John Wiley & Sons, Ltd.     

A three‐dimensional hydrodynamic model for shallow waters using unstructured Cartesian grids

This paper presents a three‐dimensional unstructured Cartesian grid model for simulating shallow water hydrodynamics in lakes, rivers, estuaries, and coastal waters. It is a flux‐based finite difference model that uses a cut‐cell approach to fit the bottom topography and shorelines and, at the same time, has the flexibility of discretizing complex geometries with Cartesian grids that can be arbitrarily downsized in the two horizontal directions simultaneously. Because of the use of Cartesian grids, the grid generation is very simple and does not suffer the grid generation headache often seen in many other unstructured models, as the unstructured Cartesian grid model does not have any requirements on the orthogonality of the grids. The newly developed unstructured Cartesian grid model was validated against analytical solutions for a three‐dimensional seiching case in a rectangular basin, before it was compared with another three‐dimensional model named LESS3D for circulations and salinity transport processes in an idealized embayment that is driven by tides and freshwater inflows. Model tests show that the numerical procedure used in the unstructured Cartesian grid model is robust. Similar to other unstructured models, a variable grid size has resulted in a smaller number of grids required for a reasonable model simulation, which in turn reduces the CPU time used in the model run. Copyright © 2010 John Wiley & Sons, Ltd.     

非结构网格质量对梯度重构及无粘流动模拟精度的影响

综合利用理论分析和数值测试手段,研究了非结构格心型有限体积离散中梯度重构算法的计算精度,分别给出了非结构算法中常用的基于Green-Gauss公式(GG方法)和基于Least squares方法(LSQ方法)的梯度重构方法达到至少一阶精度的条件。其中,GG方法在面积分低阶项不能互相抵消的情况下,要求面心插值精度达到至少二阶;而LSQ方法对于任意网格均能实现梯度重构一阶精度。在各向同性网格上的梯度重构精度数值测试验证了数学推导结论;进一步通过制造解方法量化无粘流动数值离散误差,结合网格收敛性测试研究了网格质量(网格点随机扰动、网格弯曲度和网格倾斜度等因素)以及网格类型(三角形和四边形)对无粘流动模拟精度的影响,验证了理论分析结论。     

An exact non‐linear Navier–Stokes compressible‐flow solution for CFD code verification

An exact similarity solution of the compressible‐flow Navier–Stokes equations is presented, which embeds supersonic, transonic, and subsonic regions. Describing the viscous and heat‐conducting high‐gradient flow in a shock wave, the solution accommodates non‐linear temperature‐dependent viscosity as well as heat‐conduction coefficients and provides the variation of all the flow variables and their derivatives. Also presented are methods to obtain time‐dependent and/or multi‐dimensional solutions as well as verification benchmarks of increasing severity. Comparisons between the developed analytical solution and CFD solutions of the Navier–Stokes equations, with determination of convergence rates and orders of accuracy of these solutions, illustrate the utility of the developed exact solution for verification purposes. Copyright © 2012 John Wiley & Sons, Ltd.