重叠网格方法的研究进展

从网格装配和插值计算两个主要方面对现有的重叠网格方法进行了综述。首先,从挖洞方法和建立嵌入网格关系环节的寻点技术出发归纳和介绍了网格装配方法;其次,介绍了数值迭代过程中的插值计算方法,并特别讨论了插值守恒性以及插值计算精度等问题;另外,对重叠网格方法的并行计算和应用成果也作了介绍;最后,通过总结认为重叠网格方法在改进网格装配方法、改善插值和并行计算效率等方面仍需进一步研究。     

基于ALE方程的动网格膛口流场数值研究

基于ALE(Arbitrary Lagrangian-Eulerian Equation)方程的有限体积法,采用高精度Roe方法及结构化动网格,利用嵌入网格技术及动边界条件,对弹丸由膛内高压气体推动射出到完全飞高初始流场的整个过程进行了数值模拟.根据数值结果绘制了膛口流场密度和压力分布的时序图,形象地再现了膛口流场中初始激波、弓形激波及膛口冲击波,以及接触闻断、漩涡和剪切层等的动力学发展过程.结果基本反映了膛口流场的典型变化特征,为进一步研究真实膛口流场(如带化学反应、湍流等)奠定了基础.     

非结构网格变形方法研究进展

动网格技术中的非结构网格变形是计算流体力学和计算固体力学的关键技术之一.本文在总结现有非结构网格变形方法的基础上, 提出了一种网格变形方法的详细分类, 将现有方法归类为虚拟结构法、偏微分方程法和代数法. 本文综述了各类方法的最新研究进展, 分析并比较了各类方法的特性, 评述了当前网格变形研究的几个主要方向:复杂结构外形在不规则变形下的动网格生成、三维动网格生成、并行动网格生成和动节点技术. 最后简要地探讨了该领域的发展趋势.      

含化学反应膛口流场的无网格数值模拟

基于无网格方法,对包含大位移运动边界和非平衡化学反应的膛口流场进行了数值模拟。所发展算法是基于线性基函数最小二乘显式无网格方法,忽略黏性及湍流的影响,对流场采用ALE(arbitrary Lagrangian-Eulerian)形式的Euler方程描述,对流通量和化学反应源项采用多组分HLLC(Harten-Lax-van Leer-Contact)格式和有限速率反应模型计算,对于运动边界造成的点云畸形采用局部点云重构方法处理,重构过程中采用虚拟边阵面推进。对圆柱绕流和激波诱导燃烧流场进行了数值模拟,验证了重构方法和化学反应计算的有效性。最后对12.7 mm口径机枪膛口流场进行了模拟,结果同实验照片、非结构网格方法结果吻合较好,数值结果清晰地再现了膛口初始冲击波、膛口冲击波、欠膨胀射流波系结构的动力学发展过程,以及膛口焰的时间、空间分布特征。

     

一种快速稳健的并行多块结构动网格方法

为解决传统网格处理方法不能满足复杂外形在大设计空间内进行优化时对网格质量的要求的问题,提出了一种并行多块动网格方法,该方法基于初始外形的多块结构网格,根据优化过程中个体外形与初始外形拓扑结构相近的特性,利用体样条插值方法来拟合多块结构网格各块顶点的位移,得到几何外形变化后的拓扑结构,再利用无限插值方法并行地移动初始外形多块结构网格的边、面和块内的网格点,进行光顺处理后得到变形后几何外形的空间网格;该方法在保证网格质量的同时,可以极大地提高网格生成效率,本文以某翼身组合体为例结果表明,该方法在大设计空间的复杂外形设计问题中具有很强的实用性。     

非结构动网格在可动边界问题中的应用研究

本文对用于非结构动网格生成的弹簧近似方法进行了研究.通过采用顶点弹簧方法,分析研究了弹簧倔强系数的取值,同时通过引入挤压倔强系数和边界修正,对标准弹簧近似方法进行了改进.改进后的方法可以大大提高网格变形能力和网格质量.应用本文发展的非结构动网格生成方法并通过耦合求解基于(Arbitrary Lagrangian-Eulerian ALE)描述的Euler方程,模拟了谐和振动NACA0012翼型及M6机翼的跨音速绕流,计算结果与参考文献提供的结果及实验结果吻合良好.     

三维非结构网格DSMC方法的实现及其应用

研究了三维非结构网格DSMC方法实现的过程.将Bird位置元方案中的子网格思想引入到非结构网格上来,只存储子网格的总体标识号,利用较少的计算网格提高了分子的分辨率与计算精度.提出了将体积元坐标搜索算法与交替数字二叉树搜索算法(ADT)相结合的方法来跟踪模拟分子在网格之间的迁移,使用ADT方法判别分子与物面是否作用,避免了分子表面反射的非确定论判据.利用Fortran 90的动态分配内存技术编制了通用计算程序.最后对高超声速过渡流域航天飞机头部外形绕流进行了数值模拟,数值结果初步验证了算法的可行性.     

非结构动网格在三维可动边界问题中的应用

研究用于非结构动网格的弹簧近似方法,采用顶点弹簧描述, 导出并讨论了弹簧倔强系数的取值. 通过引入边界修正和扭转效应修正,对标准弹簧近似方法进行了改进. 转动翼型算例的结果表明,改进后的方法大大提高了网格变形能力和网格质量. 应用该动网格方法耦合求解基于(Arbitrary Lagrangian-Eulerian, ALE)描述的三维Euler方程,模拟了作俯仰振动的矩形机翼绕流,计算结果与实验数据及文献计算结果十分一致. 作为多个自由刚体与流体耦合运动问题的简单例证,耦合刚体动力学方程,模拟了激波与双立方体的相互作用,得到了非定常流场结构. 研究表明,基于弹簧近似的非结构动网格与有限体积格式流场解算器相结合,是模拟包含运动边界的非定常流动问题的有效方法.     

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。     

基于重叠网格与结构网格的圆柱绕流数值模拟

为研究重叠网格与结构网格在圆柱绕流数值模拟中的区别,以二维圆柱为例,利用有限元分析软件ANSYS 19.2中的DM与Mesh建立模型并划分重叠网格,利用ANSYS 19.2中的ICEM建立模型并划分结构网格。采用FLUENT 19.2中laminar模型模拟分析系统中的平均升力系数、平均阻力系数、斯特劳哈尔数St等流体动力特性。通过改变流体流速得到两种不同网格下各6组雷诺数Re,这6组雷诺数在60~160之间。结果表明:结构网格与重叠网格的St都随着Re的增加而增加,但相同雷诺数下重叠网格对应的St数值更大,St的增长速度更快;重叠网格与结构网格的平均升力系数与平均阻力系数随着Re的增加趋于稳定的速度都加快,但结构网格的平均升力系数与平均阻力系数趋于稳定的速度更快,且两种网格的平均升力系数与平均阻力系数趋于稳定速度的差距逐渐缩小,当Re=160时,两种网格的平均升力系数与平均阻力系数趋于稳定的速度几乎相同;当雷诺数在60~160之间时,采用重叠网格计算出来的斯特劳哈尔数比结构网格更加接近理论值;从升力功率谱密度分布曲线中可以看出,随着雷诺数的增加,两种网格下的频率逐渐变大,并且相同雷诺数下重叠网格的频率比结构网格大。     

Integral vorticity transport method on an overset grid

We present an overset grid method for solution of the integro‐differential vorticity–velocity formulation of the Navier–Stokes equations for two‐dimensional, incompressible flow. The method uses a body‐fitted inner grid, on which vorticity is evolved semi‐implicitly, and a Cartesian outer grid with explicit vorticity evolution. The Biot–Savart integral is solved using an adaptive, optimized multipole acceleration method. The Biot–Savart integration is performed over all inner grid cells, over all ‘active cells’ of the outer grid that lie entirely outside of the inner grid, and over sub‐elements of a set of ‘overhanging’ cells of the outer grid that overlap part of the inner grid. A novel method is developed using a level‐set distance function to rapidly and easily partition the overhanging grid cells, which is essential for the Biot–Savart integration in order to avoid double‐counting vorticity in the overhanging region. A similar decomposition into outer, inner and overhanging cells is used in solving for pressure using a boundary‐element formulation, which requires evaluation of an integral over the vorticity field using a method similar to that used for the Biot–Savart integral. The new overset grid method is applied to flow past stationary and moving bodies in two dimensions and found to agree well with prior experimental and numerical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Flows around moving bodies using a dynamic unstructured overset-grid method

In this article, a computational fluid dynamics algorithm is presented for simulations of complex unsteady flows around rigid moving bodies using an unstructured overset-grid method. For this purpose, a highly automated, three-dimensional, tetrahedral, unstructured overset-grid method is developed with one-cell-width overlapping zone in order to model the arbitrary geometries for steady and unsteady flow simulations. A method has been described to obtain the inter-grid boundaries of the one-cell-wide overlapping zone shared by a background grid and a minor grid. In the overset-grid methodology, vector intersection algorithm and bounding box techniques have been utilised. The mesh refinement and overset-scheme conservation studies proved the accuracy and efficiency of the method developed here. The applications of the developed algorithms were also performed through simulations that included complex internal flows around a flow-control butterfly valve as well as flows in an internal combustion engine with a moving piston. Lastly, validations with experimental data were conducted for both steady and unsteady flows around rigid bodies with relative motions.     

A geometry‐based level set method for curvilinear overset grids with application to ship hydrodynamics

In a previous work (Int. J. Numer. Meth. Fluids 2007; 55 :867–897), we presented a two‐phase level set method to simulate air/water turbulent flows using curvilinear body‐fitted grids for ship hydrodynamics problems. This two‐phase level set method explicitly enforces jump conditions across the interface, thus resulting in a fully coupled representation of the air/water flow. Though the method works well with multiblock curvilinear grids, severe robustness problems were found when attempting to use it with overset grids. The problem was tracked to small unphysical level set discontinuities across the overset grids with large differences in curvature. Though negligible for single‐phase approaches, the problem magnifies with large density differences between the phases, causing computation failures. In this paper, we present a geometry‐based level set method for curvilinear overset grids that overcomes these difficulties. The level set transport and reinitialization equations are not discretized along grid coordinates, but along the upwind streamline and level set gradient directions, respectively. The method is essentially an unstructured approach that is transparent to the differences between overset grids, but still the discretization is under the framework of a finite differences approach. As a result, significant improvements in robustness and to a less extent in accuracy are achieved for the level set function interpolation between overset grids, especially with big differences in grid curvature. Example tests are shown for the case of bow breaking waves around the surface combatant model David Taylor Model Basin (DTMB) 5415 and for the steady‐state ONR Tumblehome DTMB 5613 with superstructure. In the first case, the results are compared against experimental data available and in the second against results of a semi‐coupled method. Copyright © 2011 John Wiley & Sons, Ltd.     

CFD computations of NAL experimental airplane with rocket booster using overset unstructured grids

Flows around the NAL jet‐powered experimental airplane with a small rocket booster under the fuselage are computed by solving the Euler equations using the overset unstructured grid method. The main objective of the present study is to evaluate the effect of a small rocket booster, which accelerates the airplane to supersonic speed, on the aerodynamic performance of the airplane during the ascent flight and the booster separation. Two unstructured meshes, one for the airplane and one for the booster, overlap. For the accurate separation simulation, the two bodies are in contact at first, and then the booster mesh is contact mesh is moved relative to the airplane mesh to evaluate flow interactions between two bodies. Copyright © 2005 John Wiley & Sons, Ltd.     

A Mach‐uniform unstructured staggered grid method

A novel Mach‐uniform method to compute flows using unstructured staggered grids is discussed. The Mach‐uniform method is a generalization of the pressure‐correction approach for incompressible flows, and is valid for Mach numbers ranging from 0 (incompressible) to > 1 (supersonic). The primary variables (ρ u ,p and ρ) are updated sequentially. The grid consists of triangles. A staggered positioning of the variables is employed: the scalar variables are located at the centroids of the triangles, whereas the normal momentum components are positioned at the midpoints of the faces of the triangles. Discretization of the two‐dimensional flow equations on unstructured staggered grids is discussed. For the cell face fluxes there is a choice between first‐order upwind and central approximation. Flows around the NACA 0012 airfoil with freestream Mach numbers ranging from 0 to 1.2 are computed to demonstrate the Mach‐uniform accuracy and efficiency of the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

非结构动网格在多介质流体数值模拟中的应用

采用非结构动网格方法对含多介质的流场进行数值模拟.采用改进的弹簧方法来处理由于边界运动而产生的网格变形.采用基于格心的有限体积方法求解守恒型的ALE(Arbitrary Lagrangiall-Eulerian)方程,控制面通量的计算采用HLLC(Hartem,Lax,van Leer,Contact)方法,采用几何构造的方法使空间达到二阶精度,时间离散采用四阶Runge-Kutta方法.物质界面的处理采用虚拟流体方法.本文对含动边界的激波管、水下爆炸等流场进行数值模拟,取得较好的结果,不同时刻界面的位置和整个扩张过程被准确模拟.     

A nodal Godunov method for Lagrangian shock hydrodynamics on unstructured tetrahedral grids

We present a nodal Godunov method for Lagrangian shock hydrodynamics. The method is designed to operate on three‐dimensional unstructured grids composed of tetrahedral cells. A node‐centered finite element formulation avoids mesh stiffness, and an approximate Riemann solver in the fluid reference frame ensures a stable, upwind formulation. This choice leads to a non‐zero mass flux between control volumes, even though the mesh moves at the fluid velocity, but eliminates volume errors that arise due to the difference between the fluid velocity and the contact wave speed. A monotone piecewise linear reconstruction of primitive variables is used to compute interface unknowns and recover second‐order accuracy. The scheme has been tested on a variety of standard test problems and exhibits first‐order accuracy on shock problems and second‐order accuracy on smooth flows using meshes of up to O(10⁶) tetrahedra. Copyright © 2014 John Wiley & Sons, Ltd.     

用鲁棒Riemann求解器和运动重叠网格计算旋翼粘性绕流

发展了一种基于鲁棒Riemann求解器和运动重叠网格技术计算直升机悬停旋翼流场的方法。基于惯性坐标系,悬停旋翼流场是非定常流场,控制方程为可压缩Reynolds平均Navier-Stoke方程,其对流项采用Roe近似Reimann求解器离散,使用改进的五阶加权基本无振荡格式进行高阶重构,非定常时间推进采用含牛顿型LUSGS子迭代的全隐式双时间步方法。为实施旋转运动和便于捕捉尾迹,计算采用运动重叠网格技术。计算得到的桨叶表面压力分布及桨尖涡涡核位置都与实验结果吻合较好。数值结果表明:所发展方法对桨尖涡具有较高的分辨率,对激波具有较好的捕捉能力,该方法可进一步推广到前飞旋翼粘性绕流的计算。     

基于非结构化同位网格的SIMPLE算法

通过基于非结构化网格的有限体积法对二维稳态Navier—Stokes方程进行了数值求解。其中对流项采用延迟修正的二阶格式进行离散;扩散项的离散采用二阶中心差分格式;对于压力-速度耦合利用SIMPLE算法进行处理;计算节点的布置采用同位网格技术,界面流速通过动量插值确定。本文对方腔驱动流、倾斜腔驱动流和圆柱外部绕流问题进行了计算,讨论了非结构化同位网格有限体积法在实现SIMPLE算法时,迭代次数与欠松弛系数的关系、不同网格情况的收敛性、同结构化网格的对比以及流场尾迹结构。通过和以往结果比较可知,本文的方法是准确和可信的。     

Semi‐coupled air/water immersed boundary approach for curvilinear dynamic overset grids with application to ship hydrodynamics

For many problems in ship hydrodynamics, the effects of air flow on the water flow are negligible (the frequently called free surface conditions), but the air flow around the ship is still of interest. A method is presented where the water flow is decoupled from the air solution, but the air flow uses the unsteady water flow as a boundary condition. The authors call this a semi‐coupled air/water flow approach. The method can be divided into two steps. At each time step the free surface water flow is computed first with a single‐phase method assuming constant pressure and zero stress on the interface. The second step is to compute the air flow assuming the free surface as a moving immersed boundary (IB). The IB method developed for Cartesian grids (Annu. Rev. Fluid Mech. 2005; 37 :239–261) is extended to curvilinear grids, where no‐slip and continuity conditions are used to enforce velocity and pressure boundary conditions for the air flow. The forcing points close to the IB can be computed and corrected under a sharp interface condition, which makes the computation very stable. The overset implementation is similar to that of the single‐phase solver (Comput. Fluids 2007; 36 :1415–1433), with the difference that points in water are set as IB points even if they are fringe points. Pressure–velocity coupling through pressure implicit with splitting of operators or projection methods is used for water computations, and a projection method is used for the air. The method on each fluid is a single‐phase method, thus avoiding ill‐conditioned numerical systems caused by large differences of fluid properties between air and water. The computation is only slightly slower than the single‐phase version, with complete absence of spurious velocity oscillations near the free surface, frequently present in fully coupled approaches. Validations are performed for laminar Couette flow over a wavy boundary by comparing with the analytical solution, and for the surface combatant model David Taylor Model Basin (DTMB) 5512 by comparing with Experimental Fluid Dynamics (EFD) and the results of two‐phase level set computations. Complex flow computations are demonstrated for the ONR Tumblehome DTMB 5613 with superstructure subject to waves and wind, including 6DOF motions and broaching in SS7 irregular waves and wind. Copyright © 2008 John Wiley & Sons, Ltd.