浸入边界法及其应用

浸入边界法主要用于模拟存在复杂外形结构的流场的运动情况和处理各种动边界问题,目前已广泛应用于计算流体力学领域.浸入边界法既是数学建模方法又是数值离散方法,它将物体边界与流体的相互作用通过在流体运动方程中加体积力项来体现,并在数值计算中采用简单的笛卡尔网格,避免了按照物体边界形状生成贴体网格时所遇到的各种问题.浸入边界法分为连续力法和离散力法:连续力法主要用于处理弹性边界问题,它的力源项满足特定的力学关系式;离散力法主要用于处理固体界面问题,它的力源项由边界条件推导得到.着重阐述了浸入边界法的基本原理和数学构造,对目前已有的几种不同的浸入边界法做了简单地介绍,并给出了一些应用实例,最后提出了浸入边界法未来的发展方向.     

不可压粘性流体浸入边界直接力法及软件实现

浸入边界法通过在N-S方程中施加体积力模拟不可滑移固壁边界及动边界,避免生成复杂贴体网格及动网格,极大地节省了网格建模时间及动网格计算消耗。本文提出一种新型附加体积力简化计算方法,将简化附加体积力以源项形式嵌入动量方程迭代中,通过用户自定义函数对CFD软件FLUENT二次开发,实现了浸入边界法和通用流体力学求解器的耦合计算。通过静止圆柱和动圆柱绕流数值模拟进行了验证,并探讨了插值函数对计算精度的影响。研究表明,通过引入浸入边界模型,能够提高计算效率,并实现结构网格背景下复杂边界和动边界的高效建模。     

不可压粘性流体浸入边界直接力法及软件实现

浸入边界法通过在N-S方程中施加体积力模拟不可滑移固壁边界及动边界,避免生成复杂贴体网格及动网格,极大地节省了网格建模时间及动网格计算消耗。本文提出一种新型附加体积力简化计算方法,将简化附加体积力以源项形式嵌入动量方程迭代中,通过用户自定义函数对CFD软件FLUENT二次开发,实现了浸入边界法和通用流体力学求解器的耦合计算。通过静止圆柱和动圆柱绕流数值模拟进行了验证,并探讨了插值函数对计算精度的影响。研究表明,通过引入浸入边界模型,能够提高计算效率,并实现结构网格背景下复杂边界和动边界的高效建模。     

复杂边界附近气泡的动态特性研究

本文假设气泡周围流场为无粘、无旋、不可压缩的理想流体,基于势流理论,运用边界元法模拟近边界水下爆炸气泡的动力学特征,建立气泡、壁面以及自由面三者之间复杂耦合动力学模型,在气泡运动模拟过程中引入数值光顺技术及弹性网格技术(EMT),避免因网格扭曲而导致的数值发散,开发相应的三维计算程序,并与自由表面附近气泡运动的实验数据进行对比分析,计算结果表明本文的计算方法及程序具有较高的精度.在此基础上,用本文开发的三维程序模拟了单个及多个气泡与自由表面及圆筒等复杂边界的相互作用,其中包括水面漂浮结构和水下结构,气泡在自由表面及结构的联合作用下呈现出强非线性.本主文旨在为相关复杂边界附近气泡动力学特性研究提供参考.     

非结构重叠网格方法研究及应用

航空、航天和兵器技术等领域的研究中存在大量包含运动边界的流场。非结构重叠网格方法是一种高效的处理动边界问题的新方法。围绕相对运动的每个物体单独生成非结构网格,在网格重叠区域通过搜索和插值完成网格系之间的信息传递,提出了动态八叉树搜索算法,发展了绝对坐标系和相对坐标系相结合的流场求解方式,采用二阶精度Van Leer/Hanel格式和四阶Runge-Kutta法分别进行空间和时间离散,形成了一种新的非结构重叠网格算法。对三维Riemann问题的求解结果与精确解能很好吻合,证明了本文的重叠网格算法具有较好的时空离散精度和插值精度。对7.62mm步枪射击过程进行了数值模拟,描述了弹丸离开膛口后膛口流场的发展过程,与实验结果体现的发展过程较为吻合,验证了本文提出的非结构网格算法体系具有较好的计算性能,是研究含动边界复杂流场的一种有效手段。     

当地DFD方法在扑翼流动数值模拟中的应用

应用当地DFD（Domain-Free Discretization）方法对包含复杂运动边界的扑翼流场进行了数值模拟。该方法通过壁面法线方向的外插确定外部相关点上的流动变量值,同时强加相应的边界条件。应用这种方法,动边界流动的模拟可以在固定网格上实现,无需为了跟随物体的运动而在每个时间步上对网格进行实时更新。对三种拍动模式的双翅流场进行了数值模拟,升、阻力系数时间历程的计算结果与参考文献的实验数据吻合很好,验证了当地DFD方法处理复杂动边界问题的可靠性。最后,数值模拟了完整昆虫模型的扑翼流场,并详细分析了涡系结构和飞行机理。     

近边界三维水下爆炸气泡动态特性研究

模拟了近壁、近自由面的水下爆炸气泡的非线性动态特性,假定水下爆炸气泡脉动阶段的流场是无旋、不可压缩的,采用高阶曲面三角形单元离散三维气泡表面,用边界积分法求解气泡的运动,在计算奇异积分时通过重新构造双层位势的主值积分消除双层奇异积分的奇异性,得到更精确的结果,并通过合理的加权方法精确的求解边界面上各节点的真实速度,结合弹性网格技术（elastic mesh technique, EMT）得到优化速度,在整个模拟过程中不需要采用数值光顺。将本文的三维模型与轴对称模型进行的对比分析表明,两种模型计算结果吻合很好,并用三维模型模拟了气泡与自由表面及圆筒的相互作用,水下爆炸气泡在自由表面及圆筒的联合作用下呈现出强非线性。     

界面不稳定性的自适应欧拉数值计算

采用欧拉网格自适应算法数值模拟Richtmyer Meshkov和Rayleigh Taylor不稳定多介质流界面,获得了高精度界面特征。对不同流体引入不同位标函数跟踪界面运动,将位标函数方程与流体动力学方程耦合求解,在笛卡儿坐标系中运用二阶精度有限体积算法,保持流场守恒条件下,通过采用多层网格级对笛卡儿网格嵌套细化,从而实现多介质流体界面的高精度自适应跟踪。给出的方法逻辑简单,可以大大节省CPU时间。     

用于ALE有限元模拟的网格更新方法

任意拉格朗日欧拉法(ALE)可以通过定义参考网格的运动,实现自由液面跟踪,完成液体晃动的数值计算. 综合用于更新网格节点的3种基本计算方法,将多方向更新网格速度的技术应用于任意拉格朗日欧拉网格节点的速度计算. 给出了水平圆柱形贮箱和椭圆形贮箱内液体晃动算例,实现了多方向更新网格运动与晃动流场计算的耦合,使ALE方法能胜任复杂几何边界下的自由液面流动的数值模拟.      

膛口反应流并行数值模拟

采用轴对称多组分N-S方程对含有高速运动弹丸的膛口反应流进行了数值模拟.控制方程采用时间分裂方法并在大型计算机上采用MPI方法进行多核并行求解,其中对流项采用二阶AUSM+格式和MUSCL插值方法进行处理,燃气采用氢气-空气混合气,反应机理为9组分19步基元反应.对于弹丸引起的网格运动,采用嵌套网格法处理.并行验证算例与串行计算结果一致,采用20个CPU计算时效率为64％.根据数值结果详细讨论了发射过程中的气体动力学和化学动力学过程,并且通过对两种条件下的计算结果比较分析了化学反应对膛口流场发展的影响.结果表明,上述算法能够较为正确地模拟弹丸和化学反应对膛口流场的影响,并大大提高了计算速度.     

HYDRODYNAMIC RESISTANCE EFFECT OF FLUID LAYER BETWEEN TWO IMMERSED APPROACHING PARTICLES

1. Introduction The mechanisms of impact and rebound of solid parti- cles in particulate flow systems are of interest over a wide range of application areas such as fluidized beds, pneu- matic transport, filtration processes, erosion and pollution control of suspended particles. In many cases, the colli- sions of particles against themselves and against walls may affect the properties of the mixture. Efforts have been made to describe the fundamental mechanics of particle collisions. The conta…     

A hybrid immersed boundary and material point method for simulating 3D fluid–structure interaction problems

A numerical method is developed for solving the 3D, unsteady, incompressible Navier–Stokes equations in curvilinear coordinates containing immersed boundaries (IBs) of arbitrary geometrical complexity moving and deforming under forces acting on the body. Since simulations of flow in complex geometries with deformable surfaces require special treatment, the present approach combines a hybrid immersed boundary method (HIBM) for handling complex moving boundaries and a material point method (MPM) for resolving structural stresses and movement. This combined HIBM & MPM approach is presented as an effective approach for solving fluid–structure interaction (FSI) problems. In the HIBM, a curvilinear grid is defined and the variable values at grid points adjacent to a boundary are forced or interpolated to satisfy the boundary conditions. The MPM is used for solving the equations of solid structure and communicates with the fluid through appropriate interface‐boundary conditions. The governing flow equations are discretized on a non‐staggered grid layout using second‐order accurate finite‐difference formulas. The discrete equations are integrated in time via a second‐order accurate dual time stepping, artificial compressibility scheme. Unstructured, triangular meshes are employed to discretize the complex surface of the IBs. The nodes of the surface mesh constitute a set of Lagrangian control points used for tracking the motion of the flexible body. The equations of the solid body are integrated in time via the MPM. At every instant in time, the influence of the body on the flow is accounted for by applying boundary conditions at stationary curvilinear grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface. The influence of the fluid on the body is defined through pressure and shear stresses acting on the surface of the body. The HIBM & MPM approach is validated for FSI problems by solving for a falling rigid and flexible sphere in a fluid‐filled channel. The behavior of a capsule in a shear flow was also examined. Agreement with the published results is excellent. Copyright © 2007 John Wiley & Sons, Ltd.     

A new modification of the immersed‐boundary method for simulating flows with complex moving boundaries

In this paper, a new immersed‐boundary method for simulating flows over complex immersed, moving boundaries is presented. The flow is computed on a fixed Cartesian mesh and the solid boundaries are allowed to move freely through the mesh. The present method is based on a finite‐difference approach on a staggered mesh together with a fractional‐step method. It must be noted that the immersed boundary is generally not coincident with the position of the solution variables on the grid, therefore, an appropriate strategy is needed to construct a relationship between the curved boundary and the grid points nearby. Furthermore, a momentum forcing is added on the body boundaries and also inside the body to satisfy the no‐slip boundary condition. The immersed boundary is represented by a series of interfacial markers, and the markers are also used as Lagrangian forcing points. A linear interpolation is then used to scale the Lagrangian forcing from the interfacial markers to the corresponding grid points nearby. This treatment of the immersed‐boundary is used to simulate several problems, which have been validated with previous experimental results in the open literature, verifying the accuracy of the present method. Copyright © 2006 John Wiley & Sons, Ltd.     

Instability of the flow around an impacting sphere

Results from an experimental and numerical study of the flow generated by a sphere immersed in fluid, impacting normally without rebound on a solid wall, are presented. The parameters are the running distance before impact and the sphere Reynolds number. For running lengths less than 7.5 diameters, the sphere wake before impact is axisymmetric in the form of an attached vortex ring. After impact, this ring overtakes the sphere and spreads out along the wall. For Reynolds numbers below 1000, the flow remains axisymmetric at all times. For higher values, perturbations of azimuthal wavenumbers 20–25 are observed on the vortex ring, leading to a breakdown of the flow. We analyse different hypotheses concerning the origin of this instability, with the conclusion that a centrifugal instability mechanism is likely to be acting in this flow. Comparisons are made with the flow involving an isolated vortex ring approaching a wall. Numerical simulations of this case have revealed that two distinct instability mechanisms are operating, one of which appears to be similar to the centrifugal instability observed for the sphere impact.     

Simulation of three‐dimensional flows over moving objects by an improved immersed boundary–lattice Boltzmann method

An improved immersed boundary–lattice Boltzmann method (IB–LBM) developed recently [28] was applied in this work to simulate three‐dimensional (3D) flows over moving objects. By enforcing the non‐slip boundary condition, the method could avoid any flow penetration to the wall. In the developed IB–LBM solver, the flow field is obtained on the non‐uniform mesh by the efficient LBM that is based on the second‐order one‐dimensional interpolation. As a consequence, its coefficients could be computed simply. By simulating flows over a stationary sphere and torus [28] accurately and efficiently, the proposed IB–LBM showed its ability to handle 3D flow problems with curved boundaries. In this paper, we further applied this method to simulate 3D flows around moving boundaries. As a first example, the flow over a rotating sphere was simulated. The obtained results agreed very well with the previous data in the literature. Then, simulation of flow over a rotating torus was conducted. The capability of the improved IB–LBM for solving 3D flows over moving objects with complex geometries was demonstrated via the simulations of fish swimming and dragonfly flight. The numerical results displayed quantitative and qualitative agreement with the date in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

On the immersed boundary‐lattice Boltzmann simulations of incompressible flows with freely moving objects

For simulating freely moving problems, conventional immersed boundary‐lattice Boltzmann methods encounter two major difficulties of an extremely large flow domain and the incompressible limit. To remove these two difficulties, this work proposes an immersed boundary‐lattice Boltzmann flux solver (IB‐LBFS) in the arbitrary Lagragian–Eulerian (ALE) coordinates and establishes a dynamic similarity theory. In the ALE‐based IB‐LBFS, the flow filed is obtained by using the LBFS on a moving Cartesian mesh, and the no‐slip boundary condition is implemented by using the boundary condition‐enforced immersed boundary method. The velocity of the Cartesian mesh is set the same as the translational velocity of the freely moving object so that there is no relative motion between the plate center and the mesh. This enables the ALE‐based IB‐LBFS to study flows with a freely moving object in a large open flow domain. By normalizing the governing equations for the flow domain and the motion of rigid body, six non‐dimensional parameters are derived and maintained to be the same in both physical systems and the lattice Boltzmann framework. This similarity algorithm enables the lattice Boltzmann equation‐based solver to study a general freely moving problem within the incompressible limit. The proposed solver and dynamic similarity theory have been successfully validated by simulating the flow around an in‐line oscillating cylinder, single particle sedimentation, and flows with a freely falling plate. The obtained results agree well with both numerical and experimental data. Copyright © 2016 John Wiley & Sons, Ltd.     

一种模拟动边界绕流的锐利界面浸入边界法

When the structural wall moves over a fixed grid, the structure coverage will change, resulting in many dead and emerging elements. To avoid the influence of malformation and reconstruction of body-fitted grids on the calculation efficiency and accuracy of the fluid-structure interaction problems with coupled boundary movement on the fixed grid, an improved numerical method for describing the interaction between an immersed rigid body and fluid based on a sharp-interface is proposed. In this method, both the fluid and solid are regarded as pure fluid domains in the whole computational domain, and the solid boundary is divided into several Lagrangian grid points. The flow parameter or velocity is reconstructed by interpolation at the interface element, which is then directly used as the boundary condition of the flow field, thus reflecting the influence of the wall boundary conditions. The method constructs the calculation structure of “virtual point, force point and vertical foot point”, and the velocity of the virtual point is obtained by bilinear interpolation. Then, the velocity of the force point is calculated by forcing the solid boundary to meet the no-slip condition, and the equations of the coupling system based on the immersion boundary method are finally solved to realize the numerical simulation of the flow with a complex moving boundary. The numerical program for this immersed boundary method is established using C++, then the accuracy and reliability of the proposed method are validated by comparison with the literature and experimental results of the basic numerical example of flow around a cylinder. Furthermore, the effects of the structural shape and the angle of attack on the trailing vortex structure, the vortex shedding frequency, and the lift/ coefficient characteristics of the flow around the elliptical cylinder have been analyzed. The anti-symmetric S-type, “P+S” Ⅰ-type and “P+S” Ⅱ-type trailing vortex shedding modes, as well as the variation laws of the vortex structure size, vortex shedding frequency and lift-drag coefficients ratio with axis ratio and angle of attack, are captured. The critical angle of attack (25°) corresponding to the maximum lift-drag ratio is determined as 25°.     

Mesh Node Distribution in Terms of Wall Distance for Large-eddy Simulation of Wall-bounded Flows

In this note, basic turbulent statistics in a pipe flow are computed accurately by large-eddy simulation using a mesh resolution coarser than the viscous sublayer. These results are obtained when a regular Cartesian mesh is used for the spatial discretization of the circular pipe thanks to an immersed boundary method combined with high-order schemes. In this particular computational configuration, the near-wall features of mean velocity and Reynolds stress profiles are found to be correctly captured at a scale significantly smaller than the mesh size. Comparisons between channel and pipe flow configurations suggest that an irregular mesh distribution in terms of wall distance may be a favourable condition to explicitly compute by large-eddy simulation reliable wall turbulence without any extra-modelling in the near-wall region.     

Extension of the local domain-free discretization method to large eddy simulation of turbulent flows

In this work, an immersed boundary method, called the local domain-free discretization (DFD) method, is extended to large eddy simulation (LES) of turbulent flows. The discrete form of partial differential equations at an interior node may involve some nodes outside the solution domain. The flow variables at these exterior dependent nodes are evaluated via linear extrapolation along the direction normal to the wall. To alleviate the requirement of mesh resolution in the near-wall region, a wall model based on the turbulence boundary layer equations is introduced. The wall shear stress yielded by the wall model and the no-penetration condition are enforced at the immersed boundary to evaluate the velocity components at an exterior dependent node. For turbulence closure, a dynamic subgrid scale (SGS) model is adopted and the Lagrangian averaging procedure is used to compute the model coefficient. The SGS eddy viscosity at an exterior dependent node is set to be equal to that at the outer layer. To maintain the mass conservation near the immersed boundary, a mass source/sink term is added into the continuity equation. Numerical experiments on relatively coarse meshes with stationary or moving solid boundaries have been conducted to verify the ability of the present LES-DFD method. The predicted results agree well with the published experimental or numerical data.     

An adaptive moving finite element method for steady low Mach number compressible combustion problems

This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the computation of such a problem is often extremely time-consuming. Importantly, to capture the significant characteristics of the flame structure when using detailed chemistry, a much more stringent requirement on the spatial resolution of the interior layers of some intermediate species is necessary. Here, we propose a moving mesh method in which the mesh is obtained from the solution of so-called moving mesh partial differential equations. Such equations result from the variational formulation of a minimization problem for a given target functional that characterizes the inherent difficulty in the numerical approximation of the underlying physical equations. Adaptive mesh movement has emerged as an area of intense research in mesh adaptation in the last decade. With this approach, points are only allowed to be shifted in space leaving the topology of the grid unchanged. In contrast to methods with local refinement, data structure hence is unchanged and load balancing is not an issue as grid points remain on the processor where they are. We will demonstrate the high potential of moving mesh methods for effectively optimizing the distribution of grid points to reach the required resolution for chemically reacting flows with extremely thin boundary layers.